E 2320 = 0, to 3-decimals, find the average change in
|
|
|
- Phillip Martin
- 6 years ago
- Views:
Transcription
1 Name Date Period Worksheet 2.5 Rates of Change and Particle Motion I Show all work. No calculator unless otherwise stated. Short Answer 1. Let E( x) be the elevation, in feet, of the Mississippi River x miles from its headwaters at Lake Itasca in Park Rapids, Minnesota, for 0 x 2320.? (a) What are the units of E ( x) (b) What is the sign (positive or negative) of E ( x)? Why? (c) (Calculator Permitted) If E ( 0) = 1475 ( ) E 2320 = 0, to 3-decimals, find the average change in elevation, in feet per mile, of the Mississippi River for 0 x Show the work that leads to your answer. Using correct units, explain the meaning of your answer. 2. An economist is interested in how the price of a graphing calculator affects its sales. Suppose that at a price of p dollars, a quantity, q, calculators are sold, then the quantity of calculators sold is a function of the calculator s price, that is, if q = f ( p). (a) In a complete sentence using correct units, explain the meaning of f (150) = 20, 000. (b) In a complete sentence using correct units, explain the meaning of f (150) = 50 (c) Assuming the rate from part (b) holds for 150 p 170, how many calculators are predicted to sell when the price of a calculator is $160? Show the work that leads to your answer. Page 1 of 8
2 3. Suppose M() t is the amount of time, in minutes, it takes to boil a cup of water if the water has an initial temperature of t, degrees Fahrenheit. In a complete sentence, with units, explain the meaning of each of the following: (a) M ( 50) = 19 (b) M 1 ( 19) = 50 (c) M ( 50) = 3 (d) ( 1 ) ( ) M 18 = If g (v) is the fuel efficiency, in miles per gallon, of a car going at v miles per hour, (a) What are the units of g () v? (b) In a complete sentence with units, what is the practical meaning of the statement g ( 55) = 0. 54? 5. Suppose that CT ( ) is the cost of heating your house, in dollars per day, when the temperature outside is T degrees Fahrenheit. (a) Explain in practical terms the meaning of C (23) = (b) If C (23) = 2.94and C (23) = 0.21, approximate the cost to heat your house when the temperature is 20 degrees, C ( 20). Show the work that leads to your answer. Page 2 of 8
3 6. If xt ( ) represents the position of a particle along the x-axis at any time, t, fill in the blanks in the statements below with the best answer so that they become true facts (not opinions). (a) Initially means when = 0. (b) At the origin means = 0. (c) At rest means = 0. (d) If the velocity of the particle is positive, then the particle is moving to the. (e) If the velocity of the particle is, then the particle is moving to the left. (f) To find average velocity over a time interval, divide the change in by the change in time. (g) velocity is the velocity at a single moment (instant) in time. (h) If the acceleration of the particle is positive, then the is increasing. (i) If the acceleration of the particle is, then the velocity is decreasing. (j) In order for a particle to change directions, the must change signs. (k) One way to determine over a time interval, when given the position function or graph, is to find the sum of the absolute values of the differences in position between all resting points. 7. If the position of a particle along a horizontal line is given by ( ) 2 (a) Sketch the graph of the particle s position on the given interval. xt = x + x 6 for 0 t 3 (b) What is the particle s displacement on the given interval? Show the work that leads to your answer. (c) Find the total distance traveled by the particle on the given interval. Show the work that leads to your answer. Page 3 of 8
4 8. The data in the table below gives selected values for the velocity, in meters/minute, of a particle moving along the x-axis. The velocity v is a differentiable function of time t. Time t (min) vt (meters/min) Velocity ( ) (a) At t = 0, is the particle moving to the right or to the left? Justify. (b) Is there a time during the time interval 0 t 12 minutes when the particle is at rest? Explain your answer. (c) Use data from the table to find an approximation for v ( 10) and explain the meaning of ( 10) v in terms of the motion of the particle. Show the computations that lead to your answer, and indicate units of measure. (d) Find the average acceleration of the particle for 8 t 12 min. Explain what this number means in terms of the particle s velocity on that interval. (e) Let a( t ) denote the acceleration of the particle at time t, such that v ( t) a( t) to be a time t = c in the interval 0 t 12 such that ac= ( ) 0 =. Is there guaranteed? Justify your answer. Page 4 of 8
5 9. The graph above represents the velocity v, in feet per second, of a particle moving along the x-axis over the time interval for 0 t 9seconds. (a) At t = 4 seconds, is the particle moving to the right or left? Justify. (b) At what time(s) is the particle at rest? Justify. (c) At what time(s) does the particle change direction? Justify. (d) On what open intervals 0< t < 9 is the particle moving left? Justify. (e) What is the acceleration of the particle at t = 4 seconds? Show the work that leads to your answer. (f) On what open intervals 0< t < 9 is the acceleration of the particle positive? Justify. (g) What is the average acceleration of the particle over the interval t [ 3, 6] seconds? Show the computations that lead to your answer, and indicate units of measure. (h) On what open intervals 0< t < 9 is the speed of the particle decreasing? Justify. (i) Without knowing the initial position of the particle, is it still possible to determine the time at which the particle is farthest right for 0 t 9? If not, explain. If so, find this value of t, and explain. Page 5 of 8
6 10. A particle moves along the x-axis so that at time t 0 hours, its position is given by xt = t 3t 9t+ 2 miles. ( ) 3 2 (a) At t = 0, is the particle moving to the right or to the left? Justify. (b) At what time(s) does the particle change directions. Justify. (c) At t = 1/2, is the velocity of the particle increasing or decreasing? Explain your answer. (d) At t = 1/2, is the speed of the particle increasing or decreasing? Explain your answer. (e) Find all values of t for which the particle is moving to the left. (f) What is the particle s acceleration at terms of the particle s velocity. 1 t =? Explain, with units, the meaning of your answer in Fill in the blanks so that each statement below is true. (a) If velocity is negative and acceleration is positive, then speed is. (b) If velocity is positive and speed is decreasing, then acceleration is. (c) If velocity is positive and decreasing, then speed is. (d) If speed is increasing and acceleration is negative, then velocity is. (e) If velocity is negative and increasing, then speed is. (f) If the particle is moving to the left and speed is decreasing, then acceleration is. Page 6 of 8
7 12. The graph above shows the velocity, vt, ( ) in miles per hour of a particle moving along the x-axis for 0 t 11 hours. It consists of a semi circle and two line segments. Use the graph and your knowledge of motion to answer the following questions. (a) At what time, 0 t 11 hours, is the speed of the particle the greatest? (b) At which of the times, t = 2, t = 6, or t = 9 hours, is the acceleration of the particle greatest? Justify. (c) Over what open time interval(s) 0 < t < 11 hours is the particle moving to the left? Justify. (d) Over what open time interval(s) 0 < t < 11 hours is the velocity of the particle increasing? Justify. (e) Over what open time interval(s) 0 < t < 11 hours is the speed of the particle increasing? Justify. (f) At what times on 0 < t < 11is the acceleration of the particle undefined? (g) Find the area of the semicircle on the interval 0 t 4 bounded by the curve and the x-axis, then find the area of the triangle on the interval 4 t 10 bounded by the curve and the x-axis, and finally, find the area of the triangle on the interval 10 t 11 bounded by the curve and the x-axis. If all of these areas were positive and added together, propose what quantity this might be in terms of the particle s movement on 0 t 11hours. Page 7 of 8
8 Multiple Choice 13. A violent storm system is in the Central Texas area is moving in a straight line through New Braunfels. The Weather Service Office forecasts that t hours after mid-day, the storm will be a 2 distance of st ( ) = 12 + t t miles from New Braunfels. How fast will the storm be moving at 2:00 pm, and in what direction, in relation to NB, will it be moving, respectively? (A) 10 mph, towards NB (B) 5 mph, towards NB (C) 10 mph, away from NB (D) 3 mph, towards NB (E) 3 mph, away from NB 14. (Calculator Permitted) It took Mr. Wenzel from noon until 7 pm to drive from NB to his in-laws house North of Dallas 385 miles away. After t hours of driving, his distance from NB was given in miles by st () = t t (i) What was his average speed for the trip to his in-laws? (A) 53 mph (B) 54 mph (C) 55 mph (D) 56 mph (E) 57 mph (F) 58 mph (ii) (Calculator Permitted) Mr. Wenzel s instantaneous speed twice coincided with his average speed. At what time did it first happen? (A) 1:33 pm (B) 1:28 pm (C) 5:41 pm (D) 5:31 pm (E) 1:38 pm 15. (Calculator Permitted) If a rock is thrown vertically upwards from the surface of the planet 1 2 Newton with an initial velocity of 11 ft/sec, its height after t seconds is given by h= 11t t. 2 Find the velocity of the rock after it has risen 56 feet. (A) 1ft/sec (B) 2 ft/sec (C) 0 ft/sec (D) 1ft/sec (E) 3 ft/sec 16. (Calculator Permitted) A particle moves along a straight line with velocity given by = t2 at time t 0. What is the acceleration of the particle at time t = 4? ( ) ( ) vt (A) (B) (C) (D) (E) Page 8 of 8
Worksheet 1. What You Need to Know About Motion Along the x-axis (Part 1)
Curriculum Module: Calculus: Motion Worksheet 1. What You Need to Know About Motion Along the x-axis (Part 1) In discussing motion, there are three closely related concepts that you need to keep straight.
PARTICLE MOTION: DAY 2
PARTICLE MOTION: DAY 2 Section 3.6A Calculus AP/Dual, Revised 2018 viet.dang@humbleisd.net 7/30/2018 1:24 AM 3.6A: Particle Motion Day 2 1 WHEN YOU SEE THINK When you see Think Initially t = 0 At rest
(A) 47 ft/sec (B) 52 ft/sec (C) 120 ft/sec (D) 125 ft/sec (E) 141 ft/sec
Name Date Period Worksheet 6.1 Integral as Net Change Show all work. Calculator Permitted, but show all integral set ups. Multiple Choice 1. The graph at right shows the rate at which water is pumped from
AP Calculus BC Summer Assignment (June)
AP Calculus BC Summer Assignment (June) Solve each problem on a separate sheet of paper as if they are open ended AP problems. This means you must include all justifications necessary as on the AP AB exam.
PARTICLE MOTION. Section 3.7A Calculus BC AP/Dual, Revised /30/2018 1:20 AM 3.7A: Particle Motion 1
PARTICLE MOTION Section 3.7A Calculus BC AP/Dual, Revised 2017 viet.dang@humbleisd.net 7/30/2018 1:20 AM 3.7A: Particle Motion 1 WHEN YOU SEE THINK When you see Think Initially t = 0 At rest v t = 0 At
a t of a car from 0 to 15 seconds are given in the table below. If the
Name Date Period Worksheet 8.1 Integral as Net Change Show all work. Calculator Permitted, but show all integral set ups. Multiple Choice 1. The graph at right shows the rate at which water is pumped from
Chapter 7: Practice/review problems The collection of problems listed below contains questions taken from previous MA123 exams.
Word problems Chapter 7: Practice/review problems The collection of problems listed below contains questions taken from previous MA3 exams. Max-min problems []. A field has the shape of a rectangle with
Particle Motion. Typically, if a particle is moving along the x-axis at any time, t, x()
Typically, if a particle is moving along the x-axis at any time, t, x() t represents the position of the particle; along the y-axis, yt () is often used; along another straight line, st () is often used.
x 3x 1 if x 3 On problems 8 9, use the definition of continuity to find the values of k and/or m that will make the function continuous everywhere.
CALCULUS AB WORKSHEET ON CONTINUITY AND INTERMEDIATE VALUE THEOREM Work the following on notebook paper. On problems 1 4, sketch the graph of a function f that satisfies the stated conditions. 1. f has
CALCULUS EXPLORATION OF THE SECOND FUNDAMENTAL THEOREM OF CALCULUS. Second Fundamental Theorem of Calculus (Chain Rule Version): f t dt
CALCULUS EXPLORATION OF THE SECOND FUNDAMENTAL THEOREM OF CALCULUS d d d d t dt 6 cos t dt Second Fundamental Theorem of Calculus: d f tdt d a d d 4 t dt d d a f t dt d d 6 cos t dt Second Fundamental
3.4 Solutions.notebook March 24, Horizontal Tangents
Note Fix From 3.3 Horizontal Tangents Just for fun, sketch y = sin x and then sketch its derivative! What do you notice? More on this later 3.4 Velocity and Other Rates of Change A typical graph of the
Unit 1 Test Review Physics Basics, Movement, and Vectors Chapters 2-3
A.P. Physics B Unit 1 Test Review Physics Basics, Movement, and Vectors Chapters - 3 * In studying for your test, make sure to study this review sheet along with your quizzes and homework assignments.
Particle Motion. Typically, if a particle is moving along the x-axis at any time, t, x()
Typically, if a particle is moving along the x-axis at any time, t, x() t represents the position of the particle; along the y-axis, yt () is often used; along another straight line, st () is often used.
=. Consider the following properties
Name Date Period Worksheet 3.2 Rolle s Theorem and the MVT Show all work. No calculator unless otherwise stated. Multiple Choice 1. Determine if the function f ( x) = x 6 x satisfies the hypothesis of
Motion with Integrals Worksheet 4: What you need to know about Motion along the x-axis (Part 2)
Motion with Integrals Worksheet 4: What you need to know about Motion along the x-axis (Part 2) 1. Speed is the absolute value of. 2. If the velocity and acceleration have the sign (either both positive
t over the interval 0 t
Student Name: Period: Applications of Riemann Sums (AP Style) 1. A plane has just crashed six minutes after takeoff. There may be survivors, but you must locate the plane quickly without an extensive search.
Name Date Period. Worksheet 1.5 Continuity on Intervals & IVT. Show all work. No Calculator (unless stated otherwise) Short Answer
Name Date Period Worksheet 1.5 Continuity on Intervals & IVT Show all work. No Calculator (unless stated otherwise) Short Answer 1. A piece of the graph of (a) Sketch a graph of f ( x). x, x 1 f( x) =
Name Date. Answers 1.
Name Date Honors Algebra 2 Summer Work Due at Meet the Teacher Night Show all work. You will be graded on accuracy and completion. Partial credit will be given on problems where work is not shown. 1. Plot
All work must be shown in this course for full credit. Unsupported answers may receive NO credit.
AP Calculus.4 Worksheet All work must be shown in this course for full credit. Unsupported answers may receive NO credit.. What is a difference quotient?. How do you find the slope of a curve (aka slope
A.P. Calculus BC First Semester Exam Calculators Allowed Two Hours Number of Questions 10
A.P. Calculus BC First Semester Exam Calculators Allowed Two Hours Number of Questions 10 Each of the ten questions is worth 10 points. The problem whose solution you write counted again, so that the maximum
APPLICATIONS OF DERIVATIVES UNIT PROBLEM SETS
APPLICATIONS OF DERIVATIVES UNIT PROBLEM SETS PROBLEM SET #1 Related Rates ***Calculators Allowed*** 1. An oil tanker spills oil that spreads in a circular pattern whose radius increases at the rate of
Final Value = Starting Value + Accumulated Change. Final Position = Initial Position + Displacement
Accumulation, Particle Motion Big Ideas Fundamental Theorem of Calculus and Accumulation AP Calculus Course Description Goals page 6 Students should understand the meaning of the definite integral both
Particle Motion Problems
Particle Motion Problems Particle motion problems deal with particles that are moving along the x or y axis. Thus, we are speaking of horizontal or vertical movement. The position, velocity, or acceleration
All work must be shown in this course for full credit. Unsupported answers may receive NO credit.
AP Calculus 5. Worksheet All work must be shown in this course for full credit. Unsupported answers may receive NO credit.. Suppose an oil pump is producing 8 gallons per hour for the first 5 hours of
v t 2 2t 8. Fig. 7 (i) Write down the velocity of the insect when t 0. (ii) Show that the insect is instantaneously at rest when t 2and when t 4.
1 Fig. 7 is a sketch of part of the velocity-time graph for the motion of an insect walking in a straight line. Its velocity, v ms 1, at time t seconds for the time interval 3 t 5 is given by v ms -1 v
( ) 4 and 20, find the value. v c is equal to this average CALCULUS WORKSHEET 1 ON PARTICLE MOTION
CALCULUS WORKSHEET 1 ON PARTICLE MOTION Work these on notebook paper. Use your calculator only on part (f) of problems 1. Do not use your calculator on the other problems. Write your justifications in
A. 1 B. 2 C. 4.5 D. 7 E. 8
Calculus & Advanced Topics Spring 2011 1. The derivative of x 2 cos(x) is 2x sin(x) x 2 sin(x) 2x cos(x) x 2 sin(x) 2x sin(x) 2x cos(x) 2. 1 2 4.5 7 8 3. 0 1 6/5 3/2 undefined 4. Find the derivative of
Unit 3 Review for SchoolNet Test
Unit 3 Review for SchoolNet Test Student Class Date 1. The table below lists pairs of x- and y-coordinates that represent points on the graph of a linear equation. x y 3 10 5 5 7 0?? 11 10 Which coordinates
y=5 y=1+x 2 AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions
AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions. Which of the following integrals correctly corresponds to the area of the shaded region in the figure to the right? (A) (B) (C) (D) (E)
( ) for t 0. Rectilinear motion CW. ( ) = t sin t ( Calculator)
Rectilinear motion CW 1997 ( Calculator) 1) A particle moves along the x-axis so that its velocity at any time t is given by v(t) = 3t 2 2t 1. The position x(t) is 5 for t = 2. a) Write a polynomial expression
AP Calculus Worksheet: Chapter 2 Review Part I
AP Calculus Worksheet: Chapter 2 Review Part I 1. Given y = f(x), what is the average rate of change of f on the interval [a, b]? What is the graphical interpretation of your answer? 2. The derivative
Remember... Average rate of change slope of a secant (between two points)
3.7 Rates of Change in the Natural and Social Sciences Remember... Average rate of change slope of a secant (between two points) Instantaneous rate of change slope of a tangent derivative We will assume
As you already know by now, when you're finding derivatives, you're finding the slope.
As you already know by now, when you're finding derivatives, you're finding the slope. Slope is a "rate of change" There are many other "rates of change" out there in the Real World. For example, a doctor
Full file at
. Find the equation of the tangent line to y 6 at. y 9 y y 9 y Ans: A Difficulty: Moderate Section:.. Find an equation of the tangent line to y = f() at =. f y = 6 + 8 y = y = 6 + 8 y = + Ans: D Difficulty:
3. Go over old quizzes (there are blank copies on my website try timing yourself!)
final exam review General Information The time and location of the final exam are as follows: Date: Tuesday, June 12th Time: 10:15am-12:15pm Location: Straub 254 The exam will be cumulative; that is, it
Position, Velocity, and Acceleration. Mr. Miehl
Position, Velocity, and Acceleration Mr. Miehl www.tesd.net/miehl miehlm@tesd.net Velocity is the rate of change of position with respect to time. Velocity ΔD = Δ T Acceleration is the rate of change of
AP Calculus. Particle Motion. Student Handout
AP Calculus Particle Motion Student Handout 016-017 EDITION Use the following link or scan the QR code to complete the evaluation for the Study Session https://www.surveymonkey.com/r/s_sss Copyright 016
Position, Velocity, Acceleration
191 CHAPTER 7 Position, Velocity, Acceleration When we talk of acceleration we think of how quickly the velocity is changing. For example, when a stone is dropped its acceleration (due to gravity) is approximately
L. Function Analysis. ). If f ( x) switches from decreasing to increasing at c, there is a relative minimum at ( c, f ( c)
L. Function Analysis What you are finding: You have a function f ( x). You want to find intervals where f ( x) is increasing and decreasing, concave up and concave down. You also want to find values of
an expression, in terms of t, for the distance of the particle from O at time [3]
![an expression, in terms of t, for the distance of the particle from O at time [3]](/thumbs/88/114967411.jpg "an expression, in terms of t, for the distance of the particle from O at time [3]")
HORIZON EDUCATION SINGAPORE Additional Mathematics Practice Questions: Kinematics Set 1 1 A particle moves in a straight line so that t seconds after passing through O, its velocity v cm s -1, is given
p105 Section 2.2: Basic Differentiation Rules and Rates of Change
1 2 3 4 p105 Section 2.2: Basic Differentiation Rules and Rates of Change Find the derivative of a function using the Constant Rule Find the derivative of a function using the Power Rule Find the derivative
M1 Exam Workshop 1. Workbook
M1 Exam Workshop 1 Workbook 1. A racing car moves with constant acceleration along a straight horizontal road. It passes the point O with speed 12 m s 1. It passes the point A 4 s later with speed 60 m
What You Will Learn In This Chapter. Displacement Vector Distance Velocity Vectors Acceleration Vectors Motion with constant Acceleration
Chapter 2 What You Will Learn In This Chapter Displacement Vector Distance Velocity Vectors Acceleration Vectors Motion with constant Acceleration 2.1 Introduction to kinematics Kinematics is the study
Final Exam Review / AP Calculus AB
Chapter : Final Eam Review / AP Calculus AB Use the graph to find each limit. 1) lim f(), lim f(), and lim π - π + π f 5 4 1 y - - -1 - - -4-5 ) lim f(), - lim f(), and + lim f 8 6 4 y -4 - - -1-1 4 5-4
Exam 1 Review Sp16 O Brien. Exam 1 Review:
Exam Review:..6 Directions: Try to work the following problems with your book, notes, and homework closed. You may have your graphing calculator and some blank paper. The idea is to practice working problems
DMA 50 Worksheet #1 Introduction to Graphs: Analyzing, Interpreting, and Creating Graphs
DMA 0 Worksheet #1 Introduction to Graphs: Analzing, Interpreting, and Creating Graphs A graph will be given followed b a set of questions to answer. Show our work. The bar graph below shows the number
Students! (1) with calculator. (2) No calculator
Students! (1) with calculator Let R be the region bounded by the graphs of y = sin(π x) and y = x 3 4x, as shown in the figure above. (a) Find the area of R. (b) The horizontal line y = splits the region
CHAPTER 2 Differentiation
CHAPTER Differentiation Section. The Derivative and the Slope of a Graph............. 9 Section. Some Rules for Differentiation.................. 56 Section. Rates of Change: Velocit and Marginals.............
Accl g Motion graph prac
Accl g Motion graph prac 1. An object starts from rest and falls freely. What is the velocity of the object at the end of 3.00 seconds? A) 9.81 m/s B) 19.6 m/s C) 29.4 m/s D) 88.2 m/s 2. An object is dropped
Using Derivatives To Measure Rates of Change
Using Derivatives To Measure Rates of Change A rate of change is associated with a variable f(x) that changes by the same amount when the independent variable x increases by one unit. Here are two examples:
Exam 2 - Part I 28 questions No Calculator Allowed. x n D. e x n E. 0
1. If f x! ( ) = ln e A.!n x " x n # $ Exam - Part I 8 questions No Calculator Allowed, and n is a constant, then f % ( x) = B. x n e C.!1 x n D. e x n E. 0. Let f be the function defined below. Which
Created by T. Madas CALCULUS KINEMATICS. Created by T. Madas
CALCULUS KINEMATICS CALCULUS KINEMATICS IN SCALAR FORM Question (**) A particle P is moving on the x axis and its acceleration a ms, t seconds after a given instant, is given by a = 6t 8, t 0. The particle
Name Date Class Unit 4 Test 1 Review: Linear Functions
Name Date Class Unit 4 Test 1 Review: Linear Functions Select the best answer. 1. Does this graph represent a linear function? Explain your answer in the space provided. 2. A jogger runs 4 mi/h. The function
A.P. Calculus BC Summer Assignment 2018 I am so excited you are taking Calculus BC! For your summer assignment, I would like you to complete the
A.P. Calculus BC Summer Assignment 2018 I am so excited you are taking Calculus BC! For your summer assignment, I would like you to complete the attached packet of problems, and turn it in on Monday, August
MATH 150/GRACEY EXAM 2 PRACTICE/CHAPTER 2. MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.
MATH 0/GRACEY EXAM PRACTICE/CHAPTER Name MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question. Find the indicated derivative. ) Find if = 8 sin. A) = 8
Logarithmic Differentiation (Sec. 3.6)
Logarithmic Differentiation (Sec. 3.6) Logarithmic Differentiation Use logarithmic differentiation if you are taking the derivative of a function whose formula has a lot of MULTIPLICATION, DIVISION, and/or
Name Date Period. AP Calculus AB/BC Practice TEST: Curve Sketch, Optimization, & Related Rates. 1. If f is the function whose graph is given at right
Name Date Period AP Calculus AB/BC Practice TEST: Curve Sketch, Optimization, & Related Rates. If f is the function whose graph is given at right Which of the following properties does f NOT have? (A)
Remember... Average rate of change slope of a secant (between two points)
3.7 Rates of Change in the Natural and Social Sciences Remember... Average rate of change slope of a secant (between two points) Instantaneous rate of change slope of a tangent derivative We will assume
MAC 2233, Survey of Calculus, Exam 3 Review This exam covers lectures 21 29,
MAC 2233, Survey of Calculus, Exam 3 Review This exam covers lectures 21 29, This review includes typical exam problems. It is not designed to be comprehensive, but to be representative of topics covered
Each dot represents an object moving, between constant intervals of time. Describe the motion that you see. equation symbol: units: Velocity
What is displacement, velocity and acceleration? what units do they have? vector vs scalar? One dimensional motion, and graphing Moving man worksheet moving man doc - todo Introduction to simple graphing
Multiple-Choice Questions
Multiple-Choice Questions 1. A rock is thrown straight up from the edge of a cliff. The rock reaches the maximum height of 15 m above the edge and then falls down to the bottom of the cliff 35 m below
Applications of Derivatives
Applications of Derivatives Big Ideas Connecting the graphs of f, f, f Differentiability Continuity Continuity Differentiability Critical values Mean Value Theorem for Derivatives: Hypothesis: If f is
Particle Motion Notes Position When an object moves, its position is a function of time. For its position function, we will denote the variable s(t).
Particle Motion Notes Position When an object moves, its position is a function of time. For its position function, we will denote the variable s(t). Example 1: For s( t) t t 3, show its position on the
Section 2-2: Constant velocity means moving at a steady speed in the same direction
Section 2-2: Constant velocity means moving at a steady speed in the same direction 1. A particle moves from x 1 = 30 cm to x 2 = 40 cm. The displacement of this particle is A. 30 cm B. 40 cm C. 70 cm
Chapter 3: The Derivative in Graphing and Applications
Chapter 3: The Derivative in Graphing and Applications Summary: The main purpose of this chapter is to use the derivative as a tool to assist in the graphing of functions and for solving optimization problems.
What s Your Mileage?
Overview Math Concepts Materials Students use linear equations to model and solve real-world slope TI-30XS problems. Students also see the correlation between the fractions MultiView graph of an equation
5) A stone is thrown straight up. What is its acceleration on the way up? 6) A stone is thrown straight up. What is its acceleration on the way down?
5) A stone is thrown straight up. What is its acceleration on the way up? Answer: 9.8 m/s 2 downward 6) A stone is thrown straight up. What is its acceleration on the way down? Answer: 9.8 m/ s 2 downward
MOTION ALONG A STRAIGHT LINE
MOTION ALONG A STRAIGHT LINE 2 21 IDENTIFY: The average velocity is Let be upward EXECUTE: (a) EVALUATE: For the first 115 s of the flight, When the velocity isn t constant the average velocity depends
Quarter 1 Calculus Test. The attached problems do not comprise a comprehensive test review. Test topics
Quarter 1 Calculus Test The attached problems do not comprise a comprehensive test review. As review, use: this packet your 3 quizzes and first test your 3 quiz review packets and first test review packet
Math 1710 Final Review 1 1
Math 7 Final Review. Use the ɛ δ definition of it to prove 3 (2 2 +)=4. 2. Use the ɛ δ definition of it to prove +7 2 + =3. 3. Use the ɛ-δ definition of it to prove (32 +5 ) = 3. 4. Prove that if f() =
What is a Vector? A vector is a mathematical object which describes magnitude and direction
What is a Vector? A vector is a mathematical object which describes magnitude and direction We frequently use vectors when solving problems in Physics Example: Change in position (displacement) Velocity
Chapter 2 One-Dimensional Kinematics. Copyright 2010 Pearson Education, Inc.
Chapter 2 One-Dimensional Kinematics Units of Chapter 2 Position, Distance, and Displacement Average Speed and Velocity Instantaneous Velocity Acceleration Motion with Constant Acceleration Applications
Limits, Rates of Change, and Tangent Lines
Limits, Rates of Change, and Tangent Lines jensenrj July 2, 2018 Contents 1 What is Calculus? 1 2 Velocity 2 2.1 Average Velocity......................... 3 2.2 Instantaneous Velocity......................
DEFINITION Function A function from a set D to a set R is a rule that assigns a unique element in R to each element in D.
AP Calculus Assignment #2; Functions and Graphs Name: Functions The values of one variable often depend on the values for another:! The temperature at which water boils depends on elevation (the boiling
All work must be shown in this course for full credit. Unsupported answers may receive NO credit.
AP Calculus 6.. Worksheet Estimating with Finite Sums All work must be shown in this course for full credit. Unsupported answers may receive NO credit.. Suppose an oil pump is producing 8 gallons per hour
BC Exam 2 - Part I 28 questions No Calculator Allowed. C. 1 x n D. e x n E. 0
1. If f x ( ) = ln e A. n x x n BC Exam - Part I 8 questions No Calculator Allowed, and n is a constant, then f ( x) = B. x n e C. 1 x n D. e x n E.. Let f be the function defined below. Which of the following
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA
AAAAAAAAAAAAAAAAAAAAAAAAAAAAAAA CALCULUS AB SECTION I, Part A Time 55 minutes Number of questions 8 A CALCULATOR MAY NOT BE USED ON THIS PART OF THE EXAM. Directions: Solve each of the following problems,
1. Joseph runs along a long straight track. The variation of his speed v with time t is shown below.
Kinematics 1. Joseph runs along a long straight track. The variation of his speed v with time t is shown below. After 25 seconds Joseph has run 200 m. Which of the following is correct at 25 seconds? Instantaneous
Motion Along a Straight Line
PHYS 101 Previous Exam Problems CHAPTER Motion Along a Straight Line Position & displacement Average & instantaneous velocity Average & instantaneous acceleration Constant acceleration Free fall Graphical
Average rates of change May be used to estimate the derivative at a point
Derivatives Big Ideas Rule of Four: Numerically, Graphically, Analytically, and Verbally Average rate of Change: Difference Quotient: y x f( a+ h) f( a) f( a) f( a h) f( a+ h) f( a h) h h h Average rates
M112 Short Course In Calculus V. J. Motto Spring 2013 Applications of Derivatives Worksheet
M11 Short Course In Calculus V. J. Motto Spring 01 Applications of Derivatives Worksheet 1. A tomato is thrown from the top of a tomato cart its distance from the ground in feet is modeled by the equation
PDF Created with deskpdf PDF Writer - Trial ::
y 3 5 Graph of f ' x 76. The graph of f ', the derivative f, is shown above for x 5. n what intervals is f increasing? (A) [, ] only (B) [, 3] (C) [3, 5] only (D) [0,.5] and [3, 5] (E) [, ], [, ], and
AP Physics C: Mechanics Ch. 2 Motion. SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.
Name: Period: Date: AP Physics C: Mechanics Ch. Motion SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question. ) Car A is traveling at twice the speed of car
Motion Graphs Refer to the following information for the next four questions.
Motion Graphs Refer to the following information for the next four questions. 1. Match the description provided about the behavior of a cart along a linear track to its best graphical representation. Remember
K. Function Analysis. ). This is commonly called the first derivative test. f ( x) is concave down for values of k such that f " ( k) < 0.
K. Function Analysis What you are finding: You have a function f ( ). You want to find intervals where f ( ) is increasing and decreasing, concave up and concave down. You also want to find values of where
2.5 Rates of Change and Particle Motion I
2.5 Rates of Change and Particle Motion I If f ( x ) represents a quantity, then f ( x) quantity. As we have seen, ( ) or df represents the instantaneous rate of change of that dx f x can represent f x
The Definite Integral. Day 6 Motion Problems Strategies for Finding Total Area
The Definite Integral Day 6 Motion Problems Strategies for Finding Total Area ARRIVAL---HW Questions Working in PODS Additional Practice Packet p. 13 and 14 Make good use of your time! Practice makes perfect!
y=5 y=1+x 2 AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions
AP Calculus Chapter 5 Testbank Part I. Multiple-Choice Questions. Which of the following integrals correctly corresponds to the area of the shaded region in the figure to the right? (A) (B) (C) (D) (E)
IB Math SL Year 2 Name Date Lesson 10-4: Displacement, Velocity, Acceleration Revisited
Name Date Lesson 10-4: Displacement, Velocity, Acceleration Revisited Learning Goals: How do you apply integrals to real-world scenarios? Recall: Linear Motion When an object is moving, a ball in the air
and 3 on a number line.
EXAMPLE 1 Graph real numbers on a number line Graph the real numbers 5 4 and 3 on a number line. 5 Note that = 1.25. Use a calculator to approximate 3 4 to the nearest tenth: 3 1.7. (The symbol means is
Section 1.3 Rates of Change and Behavior of Graphs
Section 1. Rates of Change and Behavior of Graphs 5 Section 1. Rates of Change and Behavior of Graphs Since functions represent how an output quantity varies with an input quantity, it is natural to ask
AP Calculus AB Chapter 4 Packet Implicit Differentiation. 4.5: Implicit Functions
4.5: Implicit Functions We can employ implicit differentiation when an equation that defines a function is so complicated that we cannot use an explicit rule to find the derivative. EXAMPLE 1: Find dy
ANOTHER FIVE QUESTIONS:
No peaking!!!!! See if you can do the following: f 5 tan 6 sin 7 cos 8 sin 9 cos 5 e e ln ln @ @ Epress sin Power Series Epansion: d as a Power Series: Estimate sin Estimate MACLAURIN SERIES ANOTHER FIVE
INTERMEDIATE VALUE THEOREM
THE BIG 7 S INTERMEDIATE VALUE If f is a continuous function on a closed interval [a, b], and if k is any number between f(a) and f(b), where f(a) f(b), then there exists a number c in (a, b) such that
[ 0,6 ], and if it does, find all numbers c satisfying the conclusion of that theorem.
![[ 0,6 ], and if it does, find all numbers c satisfying the conclusion of that theorem.](/thumbs/84/91195235.jpg "[ 0,6 ], and if it does, find all numbers c satisfying the conclusion of that theorem.")
Rolle s Theorem and the MVT 1. Determine if the function f ( x) = x 6 x satisfies the hypothesis of Rolle s Theorem on the interval [ 0,6 ], and if it does, find all numbers c satisfying the conclusion
Problems to practice for FINAL. 1. Below is the graph of a function ( ) At which of the marked values ( and ) is: (a) ( ) greatest = (b) ( ) least
Problems to practice for FINAL. Below is the graph of a function () At which of the marked values ( and ) is: (a) () greatest = (b) () least = (c) () the greatest = (d) () the least = (e) () = = (f) ()
Practice Problem List II
Math 46 Practice Problem List II -------------------------------------------------------------------------------------------------------------------- Section 4.: 3, 3, 5, 9, 3, 9, 34, 39, 43, 53, 6-7 odd
Kinematics Multiple-Choice Questions
Kinematics Multiple-Choice Questions 1. An object moves around a circular path of radius R. The object starts from point A, goes to point B and describes an arc of half of the circle. Which of the following
Chapter 3 The Integral Business Calculus 197
Chapter The Integral Business Calculus 97 Chapter Exercises. Let A(x) represent the area bounded by the graph and the horizontal axis and vertical lines at t=0 and t=x for the graph in Fig.. Evaluate A(x)
g( x) = 3x 4 Lesson 10 - Practice Problems Lesson 10 Rational Functions and Equations Practice Problems
Lesson 10 - Practice Problems Section 10.1: Characteristics of Rational Functions 1. Complete the table below. Function Domain a) f ( x) = 4x 6 2x b) f ( x) = 8x + 2 3x 9 c) s( t ) = 6t + 4 t d) p( t )