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Unformatted text preview: FINAL EXAMINATION. MAT 2010
April 28. 2011 Write your solutions in a blue book. To receive fuil credit you must show all work. You are
allowed to use an approved graphing calculator unless otherwise indicated. Simplify your answer
when possible, but use the precise value rather than an approximation when you have a choice.
(Example: If the actual answer is at, then write 71', not 3.14.) There are 15 problems worth a
total of 200 points. The time limit is 2% hours. 1. (10 points) Use the definition of the derivative to differentiate the following function. f (33) = W» + 2
2. (7 points each) Find the exact value of each of the following limits. Write ”00," ”—00,"
or “does not exist" if appropriate. It is particularly important to show your work on this
problem.
(10393
a I'm «—
( ) 21—»0 sinm— 1 (b) Iim ace7’ _ 111(93/3)
(c) 21:13; 3: — 3 3. Differentiate the following functions. (a) (7 pointS) f0”) = fin; (b) (8 points) 9(3) 2 sin(4a:)
(c) (7 points) Mm) = 51331113: (Cl) (5 points) m(a:) = f: 6'52 dt 4. (8 points each) Evaluate the following integrals.
(a) / «5+ 3
1 — $2
2
(b) /2 x4+3$ d3; (c) ] eczema da; da: Version 1 10. (10 points) A car travels at the speed of 10+3t2 feet per second where t is time, measured
in seconds. (a) What are the speeds at t = 1 and t = 3?
(b) What is the average acceleration during this interval? (c) What is the instantaneous acceleration at t :2: 2?
Express your answers in proper units. 11. (10 points) in a rectangle the length is increasing at 2 inches per minute, and the width is
decreasing at 1 inch per minute. What is the rate of change of the length of the diagonal
when the length is 20 inches and the width is 15 inches? 12. (10 points) The graph of the function f is shown below. The function g is defined by
a:
gas) =fo at) at, a s m s s. (3) Find 9(0). 9(2). 9(3). 9(6) and 9(3)
(b) Sketch the graph of 9 showing all local maxima and minima. ...
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 Spring '11
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