exam1_wi06

# exam1_wi06 - 4 6 8 10 12 14 16 f x 80 52 40 31 23 17 11 5(a...

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Name: Section Number: TA Name: Section Time: Math 10B. Midterm Exam 1 January 30, 2006 Turn of and put away your cell phone. 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. 1. (4 points) Suppose that f and g are continuous functions such that Z 5 0 f ( x ) dx = 5 , Z 5 4 f ( x ) dx = 11 , Z 5 0 g ( x ) dx = 3 , and Z 5 4 g ( x ) dx = - 3 . Find the value of each of the following de±nite integrals: (a) Z 4 0 f ( x ) dx (b) Z 5 4 [ g ( x ) - f ( x )] dx (c) Z 5 - 5 f ( x ) dx , given that f is an even function (d) Z 4 - 4 g ( x ) dx , given that g is an odd function # Score 1 2 3 4 Σ

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2. (4 points) Values of a function f for 0 x 16 are tabulated below. x 0 2

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Unformatted text preview: 4 6 8 10 12 14 16 f ( x ) 80 52 40 31 23 17 11 5 (a) Find an upper estimate for Z 16 f ( x ) dx using 4 subintervals ( n = 4). (b) Find an upper estimate for Z 16 f ( x ) dx using 8 subintervals ( n = 8). 3. (4 points) Let f ( x ) be a function whose derivative is graphed below. 1 2 3 4 5 6-2-1 1 2-1 f ’ (x) (a) At what value(s) of x does the graph of f (not shown) have a local minimum? (b) Suppose f (0) = 3. Use the graph to compute the value of f (5). 4. (4 points) Find the area of the region between the curves y = 3 cos( x ) and y = 3 sin( x ) for π 4 ≤ x ≤ π 2 ....
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## This note was uploaded on 04/02/2010 for the course MATH 10b taught by Professor Lender during the Spring '08 term at UCSD.

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exam1_wi06 - 4 6 8 10 12 14 16 f x 80 52 40 31 23 17 11 5(a...

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