Due: Fri Nov :31 AM MST. Question Instructions Read today's Notes and Learning Goals

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1 The Fundamental Theorem: Basic ( ) Due: Fri Nov :31 AM MST Question Instructions Read today's Notes and Learning Goals

2 1. Question Details Fa 14 FTC Basic List 1 [ ] a. If = 3x 2 find a possible function f dx f(x) = 1 b. If = find a possible function f dx x f(x) = c. If = sin(t) find a possible function f f(t) = d. If = e t find a possible function f f(t) = 3 e. If = find a possible function f t 2 f(t) =

3 2. Question Details Fa 14 FTC 1 [317866] dh The velocity of a moving object is = 12 32t ft/s, with t in seconds. 3 (12 32t) 1 by following these steps. a. Guess a possible formula for h(t). h(t) = b. Evaluate the integral. Include units. 3. Question Details Fa 14 FTC 3 [317863] dh The velocity of a moving object is = 35cos(t) cm/s, with t in seconds. π/2 35cos(t) by following these steps. a. Guess a possible formula for h(t). h(t) = b. Evaluate the integral. Give an exact answer with units.

4 4. Question Details Fa 14 FTC 4 [ ] dp The rate of change in a rabbit population is = 4.5e t 2t ΔP = 5 (4.5e t 2t) by following these steps. rabbits per year, with t in years. a. Guess a possible formula for P(t). P(t) = b. Evaluate the integral. Round to the nearest rabbit. Do not include units. rabbits

5 5. Question Details Fa 14 FTC 5 [ ] dh The velocity of a moving object is = 35sin(1.4t) cm/s, with t in seconds. Four students plan to use the FTC to compute sin(1.4t) a. They begin by guessing possible formulas for h(t). Alice guesses Bob guesses Chris guesses Dani guesses Take the derivative of each student's guess to check if it is correct or not. Which student's guess was correct? Alice Bob Chris Dani h(t) = 35cos(1.4t). h(t) = 49cos(1.4t). h(t) = 25cos(1.4t). h(t) = 25cos(1.4t). b. Use the correct student's formula to evaluate the integral. Be accurate to one decimal place. Include units.

6 6. Question Details Fa 14 FTC 6 [317994] dt An object heats up at a rate of = 15e.25t kelvin/min, with t in minutes. Four students plan to use the FTC to compute 5 15e.25t a. They begin by guessing formulas for T(t). Alice guesses Bob guesses Chris guesses Dani guesses Take the derivative of each student's guess to check if it is correct or not. Which student's guess was correct? Alice Bob Chris Dani T(t) = 3.75e.25t. T(t) = 15e.25t. T(t) = 6e.25t. T(t) = 6e.25t + 1. b. Use the correct student's formula to evaluate the integral. Be accurate to one decimal place. Include units.

7 7. Question Details Fa 14 FTC Basic List 1.5 [ ] a. If = (3x 5) 3 find a possible function f dx f(x) = 1 b. If = find a possible function f dx 7x + 4 f(x) = c. If = e 3t 5 find a possible function f f(t) = d. If = 2t + 6 find a possible function f f(t) = 8. Question Details Fa 14 def int full 3 DGB mod [317927] The velocity of a falling object is v(t) = e.25t m/s, with t in seconds. Compute the integral below. Give an exact symbolic answer in terms of t. t v(u) du = Compute the change in the height of the object on the time interval t 4 seconds. Be accurate to 2 decimal places and include units.

8 9. Question Details Fa 14 FTC 1b [ ] dh The velocity of a moving object is = t. t ( u) du 1 Give an exact symbolic answer involving t. 1. Question Details Fa 14 FTC 1c [ ] dh The velocity of a moving object is = v gt. 3 (v gt) Give an exact symbolic answer involving v and g.

9 11. Question Details Fa 14 FTC 1d [ ] The pressure in a cylinder changes at a rate of 9 r(t) 1 Give an exact symbolic answer involving k. k r(t) = ; t 1. t 12. Question Details Fa 14 FTC last [ ] Use the FTC to find an exact symbolic answer for the integral (a bt 2 + ct 1 ) 3 1 = Assignment Details Name (AID): The Fundamental Theorem: Basic ( ) Submissions Allowed: 1 Category: Homework Code: Locked: Yes Author: Velasquez, Elena ( elenavelasquez@boisestate.edu ) Last Saved: Aug 15, :11 AM MDT Group: BSU Calculus Randomization: Assignment 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 Assignment Score Publish Essay Scores

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Due: Mon Nov :31 AM MST. Question Instructions

Due: Mon Nov :31 AM MST. Question Instructions Exact Change (108624) Due: Mon Nov 6 2017 07:1 AM MST Question 1 2 4 5 6 7 8 9 10 11 Instructions Read today's Notes and Learning Goals Nearly every problem requires graphing and shading. Expect penalty