ex2sol-a - MTH 133 —-—— Section 58 ~ Test Two...

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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 xaol—cosas “G I W: , ‘ , , .1 jay/K x493 x 1” 63% >4 </ a; W $“79G ” \ w“: ‘33?“ >1; Q L}! I :3; 3mm» ‘xémgfifiquv (5)324 «viogx ‘3»? L} K W” ~~~~ 5 C33 x ~ / 'f’ ,x ' X 1%; ff‘m if Er j L i 3.11 y/I ' ’2 W i.\ i ‘2, “7x gs, . hm ( m M > W wig/9"} 5 £544 ‘39:}: ’i x2 . gem L a} ‘ z B x W I?" X..>{7£3 X LA < if” :5; “N x [s j; : {I’M wig/M < 5“ g3 i 5<-?£>O W 2‘ '9 L1}; 3 2: ‘~ } a '32.»; k xaw (1W ,3 1‘ :2; 53’3’7’: N 3' M { wafié 5" i M: XL “’9 2. $3 231M xx " LMWM} Present your solutions clearly. 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”; ‘9” \il”(2?‘3‘1 55%: iii)" 4}» M 5 \5 §~ w M ? A ) I SW {fir’CSm a»? + Present your solutions clearly. 4 1 ‘”‘ 3 5 g b ————d V W ' ,, , 9x ( ) facQ+4as+7 ‘73 l ) Cxflfszgzg 85‘ aka/«5555435 sqaagéw] ; “LMWW §g( a3me Lazar % {j I r ‘ gig/L i a, f m M 2*” {Riff “Pay”? Km» ’4, {r $3 5; V .3?- you? W 5:2: {wk 31%? Wz’” ‘3?” C j ‘63 1 (d) /(arctan:c)(l+a:2) dx £57“ Carri “33%? 73 44:2: 65>: r: g“ g , M}; E u/ f in w ~43» C 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 K A r \ / ewe-“W” ,, g” V w ,2 (“3,99 6x $950 :2? 8 ,x: ~§,3§§1 6 a} C 5. (10 points) The graph of H is provided below. Note that H is one—to—one on the interval (—00, 12), 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 e x2e w H’Ce“): 3": z rev; 5: ...
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