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Unformatted text preview: Name: TA: Math 10B. Midterm Exam 1 January 27, 2009 Sec. No: PID: Sec. Time: Turn oﬀ and put away your cell phone. You may use any type of calculator, but no other electronic devices during this exam. You may use one page of notes, but no books or other assistance during this exam. Read each question carefully, and answer each question completely. Show all of your work; no credit will be given for unsupported answers. Write your solutions clearly and legibly; no credit will be given for illegible solutions. If any question is not clear, ask for clariﬁcation. 1. (6 points) Evaluate the following integrals. (a) cos (x) − x2 + 4x dx e2 (b)
1 4 dx x # 1 2 3 4 Σ Points 6 8 6 8 28 Score 2. (8 points) Suppose that f and g are continuous functions such that
5 5 f (x) dx = 5,
0 5 4 5 f (x) dx = 11, g (x) dx = 3, and
0 4 g (x) dx = −3. Find the value of each of the following deﬁnite integrals:
4 (a)
0 f (x) dx 5 (b)
4 [g (x) − f (x)] dx 5 (c)
−5 f (x) dx, given that f is an even function 4 (d)
−4 g (x) dx, given that g is an odd function 3. (6 points) Values of a function f for 0 ≤ x ≤ 16 are tabulated below. x f (x) 0 2 4 6 8 10 80 52 40 31 23 17
16 12 14 16 11 5 0 (a) Find an upper estimate for
0 f (x) dx using 4 subintervals (n = 4). 16 (b) Find an upper estimate for
0 f (x) dx using 8 subintervals (n = 8). 4. (8 points) For a function f , you are given the graph of its derivative f ′ and that f (0) = 30.
10 5 f ’(t)
1 2 3 4 5 −5 −10 (a) On the interval 0 ≤ t ≤ 5, at what value of t does f appear to reach its maximum value? Its minimum value? (b) Estimate these maximum and minimum values. (c) Estimate f (5) − f (0). ...
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This note was uploaded on 01/26/2010 for the course MATH 3412341 taught by Professor Staff during the Winter '06 term at UCSD.
 Winter '06
 staff
 Math

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