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Unformatted text preview: MTH 133 ——— Section 58 ~ Test Two DEPARTMENT or MATHEMATICS
Michigan State University October 11, 2005 f S ‘7 ﬂ
NAME: be 3 mi“ ‘ ID NUMBER: SIGNATURE: SECTION: 1. This exam has 5 pages including this cover. There are 5 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
(303%), 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 10
5 10
TOTAL 100 Present your solutions clearly. 1. (20 points) Find the following limits. Mark each instance in which L’Hopital’s rule is used. (a) 11m ————$Sin$ A
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2. (20 points) Differentiate, but DO NOT SIMPLIFY each of the following functions. (a) f(:c)=arctan(3m)
Vi %) t . g (1») gas) = L5; 5,3,; X14661”; égﬁyﬁ '9 ,éw X : "ﬁ'mﬁé’x g. (“f/AA )4: , g _
l, 2 slot? ' i X ~+ Ems Sag/X 53:; § § '%iliﬁ‘;< i f 2 754%“ y: 3. (40 points) Find each of the following indeﬁnite integrals. (a) / is ,i‘ %v2élf “:3”;
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3,, ﬁfﬁ’kaﬂ 3" f f 4. (10 points) (a) What does it mean for a positive function ﬁns) to have a faster rate of growth (as
at —~> 00) than another positive function g(:c)? Ei‘ag‘é {é ‘V£?€W 3 JM Y \3 a.» *%& oéx> Present your solutions Clearly. 5 (b) Which one of the following two functions has a. faster rate of growth? Justify your
answer. sinh 32: ex ﬁiﬁlw 3* 3893} <3§nq§ e I :5»: way , 5m 3:53: 4% x, we A W ,5 2;; i m
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hence is invertible on that domain. (24, 14) x=l2 Use the information given in the graph to ﬁnd the derivative of H _1(a:) at :c 2 8. image “gynéézén ss‘ﬂi‘é Email/f3 {95)Y3>: (g WW). MK??? {3 w 336?? W eavawli‘w if? H
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