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wh8-F182.pdf
Written Homework 8, Due November 16
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Question 1 (5 points) A stone was dropped off a cliff and hit the ground with a speed of 120 ft/s. You may assume that the acceleration due to gravity is −32 ft/s2. (a) (2 points) Use antiderivatives to find a formula for the velocity at time t. Hint: Since the stone is dropped, what is the initial velocity?
(b) (2 points) Use antiderivatives to find a formula for the height of the stone at time t. Your formula may contain a constant C.
(c) (1 point) What is the height of the cliff ?
Page 1
Written Homework 8, Due November 16
Question 2 (4 points) A car is braking with a constant decelaration of 16 ft/s2, producing skid marks measuring 200 ft before coming to a stop. (Use antiderivatives to solve this problem!) (a) (3 points) How fast was the car traveling when brakes were first applied?
(b) (1 point) The speed limit was 55mph, was the car speeding?
Page 2
Written Homework 8, Due November 16
Question 3 (4 points)
Let f(x) = 1
x on [1, 5]; n = 4.
(a) Illustrate the left and right Riemann sums for f on the given interval and for the given value of n. Determine which Riemann sum underestimates and which sum overestimates the area under the curve.
(b) Calculate the left and right Riemann sums.
Page 3
Written Homework 8, Due November 16
Question 4 (6 points) The graph of the function y = f(x) is shown below.
1 2 3 4 5 6
−1
1
2
3
4
5
In order to estimate the integral
∫ 6 0
f(x)dx find the following Riemann sums.
(a) The left Riemann sum using 6 intervals.
(b) The right Riemann sum using 6 intervals.
(c) The midpoint Riemann sum using 3 intervals.
Page 4
Written Homework 8, Due November 16
Question 5 (3 points) Using the graph of f(x) from the previous question find the exact value for the
integral
∫ 6 0
f(x)dx.
1 2 3 4 5 6
−1
1
2
3
4
5
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