Question Details Warmup Tangent [ ]

Size: px

Start display at page:

Download "Question Details Warmup Tangent [ ]"

Amy Beatrice Sanders
5 years ago
Views:

1 Tangents ( ) Due: Fri Sep :31 AM MDT Question Instructions Read today's Notes and Learning Goals 1. Question Details Warmup Tangent [ ] NOTE: Don't read too much into this problem. It's meant to be very straightforward. It provides an outline for the general process of computing an exact derivative using the limit of a secant slope formula. The height of a falling object is given by h(t) 30 5t 2 with h in meters and t in seconds. Follow the steps below to compute the velocity at the instant t 2 seconds. Step 1. Create an interval with 2 at one end and a variable at the other end. Usually you will choose your own variable, but in this problem use the interval [2, u]. Step 2. Write a formula for average velocity on your interval. At this stage you don't have to simplify if you don't want to. Δh Step 3. Shrink your interval down to a point. What value of u would cause your interval to shrink to a point? (No units required.) u Step 4. Simplify your formula to a point where you could successfully plug in u 2. Simplified Δh Step 5. Finish by plugging in u 2. Your final answer needs units. dh t2 1/5

2 2. Question Details Tangent from Limit 2 [ ] An object is thrown straight up. Its height is given by with y in feet and t in seconds. Write a formula for the average velocity on the interval [1.7, x]. Simplify your formula to a point where you could successfully plug in x 1.7. (Hint: This is easiest if you factor by grouping.) y(t) 100t 16t 2 What value of x would shrink the interval to a single point? (Units not required.) x Compute instantaneous velocity at t 1.7. Enter an exact decimal value with units. No guessing. t Question Details Tangent from Limit 1 [ ] An object is thrown straight up. Its height is given by y(t) 100t 16t 2 with y in feet and t in seconds. Write a formula for the average velocity on the interval [3, 3 + h]. Simplify your formula to a point where you could successfully plug in h 0. What value of h would shrink the interval to a single point? (Units not required.) h Compute instantaneous velocity at t 3. Enter an exact value with units. No guessing. t3 2/5

3 4. Question Details Tangent from Limit 3 [ ] The pressure in a cylinder is dropping according to with t in seconds and p in atmospheres (WebAssign abbreviation: atm). Write a formula for the average rate of change of p on the interval [3, u]. Simplify your formula to a point where you could successfully plug in u 3. (Hint: A common denominator is going to be a good idea.) p(t) 1 + Δp 1 t+1 Compute the instantaneous rate of change when t 3 seconds. Enter an exact decimal value with units. dp t3 5. Question Details Tangent from Limit 4 [ ] Water is draining out of a tank. The volume of water remaining in the tank is a function of time: V(t) 10 3 t with V in gallons t in minutes. Write a formula for the average rate of change of V on the interval [4, 4 + h]. Simplify your formula to a point where you could successfully plug in h 0. Hint: Multiply by h+4 h+4 ΔV Compute the instantaneous flow rate when t 4 minutes. Enter an exact decimal value with units. dv t4 3/5

4 6. Question Details Tangent from Limit 5 [ ] The height of a falling object is given by y(t) t 2 with y in meters and t in seconds. Assume that a is a fixed, but unknown, instant in time. Write a formula for the average velocity on the interval [a, a + h]. Simplify your formula to a point where you could successfully plug in h 0. It should involve both a and h. Compute the velocity at the instant when t a. Your answer will be a formula that contains a. You do not need units. ta What value of a gives a velocity of 25 m/s? Give an answer with correct units and 3 decimal places of accuracy. 7. Question Details Tangent from Limit 6 [ ] The pressure in a cylinder is dropping according to p(t) t+1 with t in seconds and p in atmospheres (WebAssign abbreviation: atm). Think of the letter t as the fixed location in a tangent slope problem. Write a formula for secant slope on [t, u]. Simplify your formula to a point where you could successfully plug in t everywhere you see u. It will involve t and u. Δp Compute the instantaneous rate of change at the location t. Your answer will be a formula that includes t. p'(t) When is the pressure changing at 0.1 atm/sec? Give an answer with correct units and 3 decimal places of accuracy. Assignment Details Name (AID): Tangents ( ) Submissions Allowed: 100 Category: Homework Code: Locked: Yes Author: Velasquez, Elena ( elenavelasquez@boisestate.edu ) Last Saved: Aug 28, :43 AM MDT Group: BSU Calculus Randomization: Person Which graded: Last Feedback Settings Before due date Question Score Assignment Score Publish Essay Scores Question Part Score Mark Help/Hints Response Save Work After due date Question Score 4/5

5 Assignment Score Publish Essay Scores Key Question Part Score Solution Mark Add Practice Button Help/Hints Response 5/5

Question Details Secant Formula 1 [ ]

Derivatives (10862385) Due: Mon Aug 28 2017 07:31 AM MDT Question 1 2 3 4 5 6 7 8 9 10 11 12 13 14 Instructions Read today's Notes and Learning Goals 1. Question Details Secant Formula 1 [2852835] An object