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Unformatted text preview: Name: Sec. No: Math 10B Midterm 2 August 26, 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) Consider the function h(x) = 25 − 2x2 on [0, 3] (a) Compute TRAP(3). (b) Compute MID(3) 3 (c) State whether MID(3) or TRAP(3) overestimates
0 h(x) dx . Explain your answer. No. 1 2 3 4 5 Total Points Score 6 5 5 12 6 34 2. (5 points) Consider the function f (x) = tan2 (x) (a) Use the second fundamental theorem of calculus to compute the antiderivative, F (x), of f (x) with the property that F (1) = 3. (b) Compute F (π ). 3. (5 points) Determine the value of the following improper integral or justify why it diverges. Hint: You may assume that limx→∞ xe−x = 0.
∞ xe−x dx
3 4. (12 points) Compute the following integrals. (a) √ 2x dx 9 + x2 2 (b)
1 (z + 1)e3z dz (c) √ 1 dx 16 − x2 5. (6 points) A calculus book is dropped from the top of a 50 f t building with an initial downward velocity of 0 f t/sec. Assume that air resistance is negligible and that acceleration due to gravity is 32 f t/sec2 , downward. (a) Determine how long it takes for the book to hit the ground. (b) Determine the velocity at which the book impacts the ground. ...
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 Summer '10
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 Math, Fundamental Theorem Of Calculus, initial downward velocity, Math 10B Midterm

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