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Unformatted text preview: Name: Sec. No: Math 10B Midterm 1 August 12, 2010 PID: Sec. Time: Please turn oﬀ and but away all electronic devices, except for calculators. You may use 1 page of handwritten notes, but no other resources during the exam. Show all of your work, no credit will be given for unsupported answers. Please write neatly and make sure the answer is clear. 1. (6 points) The table below shows a car’s velocity, v (t), with respect to time, t. Time is in seconds and velocity is in feet per seconds. t 0 2 4 6 8 10 12 v (t) 70 73 76 80 85 90 100 (a) Find an overestimate for the distance traveled during this 12 second period. Use 3 left or right endpoint rectangles. (b) Find an underestimate for the distance traveled during this 12 second period. Use 3 left or right endpoint rectangles. No. 1 2 3 4 Total Points Score 6 5 6 8 25 2. (5 points) Find the area under the function f (x) = b = e2 . 5 and above the x-axis, between a = 1 and x 3. (6 points) Compute the following integrals. (a) (3x + 4)2 dx 1 (b)
−1 (x4 − 3x2 + 1) dx (c) (−5ex + cos(x)) dx 4. (8 points) Below is a graph of the derivative of f (x). Assume that f (0) = 0. Answer the following questions. Assume that the area of region A is 0.4, the area of region B is 0.3, and the area of region C is 3.
3 2 f (x) 1 0 −1 −2 C
1 2 3 5 B (a) Esimate the location(s) of inﬂection point(s) for f (x). (b) Find the location of the absolute minimum of f (x) on [0, 5]. Find the value of the f (x) at this location. (c) Find the location of the absolute maximum of f (x) on [0, 5]. Find the value of f (x) at this location. ...
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