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Unformatted text preview: MTH 133 m Section 1—4 —— Test Two DEPARTMENT OF MATHEMATICS
Michigan State University October 13, 2005 NAME: <3 “i” :53?“ ID NUMBER: SIGNATURE: SECTION: 1. This exam has 5 pages including this cover. There are 6 questions. 2. Include units in your answers whenever appropriate. 3. You may NOT use your calculator. 4. Sines, cosines, and tangents of simple angles are to be written out. For example, if you have a cos(%), you should write 5. Present your solutions to each problem in a clear and orderly fashion. Include enough steps, including diagrams, to permit the grader to follow your method. Your method must justify your
answer. PROBLEM POINTS SCORE 1 20
2 20
3 40
4 5
5 10
6 5 TOTAL 100 Present your solutions clearly. 2 1. (20 points) Find the following limits. Mark each instance in which L’Hépital’s rule is used. (a) hm arctansc {if 3
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w” { (W Present your solutions clearly. 2. (20 points)
Differentiate, but DO NOT SIMPLIFY each of the following functions. (a) f (a?) = 35m , 33%»; 5
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3. (40 points)
Find each of the following indeﬁnite integrals.
(20/ 1 d3:
. V1—2w2
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g: ‘{ z/‘jz‘w’? 31;? X LA ‘22
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1
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"3“ {31’1" 44% m4: C :2. ﬁfe/Egg? C  4. (5 points) gig/39.3» x Which one of the following two functions has a faster rate of growth? Justify your answer. (In 93)2 330‘1 /Cvki ; 4 wéx‘?
WM ‘24 L g»? A?“ (:3; g X p
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$43
2. Present your solutions clearly. 5 ' 5. (10 points) Let f(.’13) = sinm, so that f‘1(:c) :— arcsincc. Note that f(»%) = %. Find the derivative of f “1(93) at a: = —% using two different methods: (a) directly take the derivative of f '1 and evaluate; .., i (i
<4“? {0; WM)! 1 3 L ’3
So (9;); Z I 35%
i“ a (b) use the inverse function theorem.
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6. (5 points) a?"
The graphs of f and g(a:) and their tangent lines at (4,0) are provided below. 9 f (93) Find lim —.
364 9(93) MI“? Wig “33 "€16 3%?" {we};
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 Fall '07
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 ObjectOriented Programming, Following, Inverse function, following indeﬁnite integrals

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