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Sol-165E2-F2004

# Sol-165E2-F2004 - MA 165 EXAM 2 Fall 2004 Page 1/4 NAME M...

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Unformatted text preview: MA 165 EXAM 2 Fall 2004 Page 1/4 NAME M STUDENT ID RECITATION INSTRUCTOR RECITATION TIME DIRECTIONS 1. 9° (16) 1. Write your name, student ID number, recitation instructor’s name and recitation time in the space provided above. Also write your name at the top of pages 2, 3 and 4. The test has four (4) pages, including this one. Write your answers in the boxes provided. You must Show sufﬁcient work to justify all answers unless otherwise stated in the problem. Correct answers with inconsistent work may not be given credit. Credit for each problem is given in parentheses in the left hand margin. No books, notes or calculators may be used on this exam. Find the derivatives of the following functions. (It is not necessary to simplify). (a) y: (1+cos2 \$),6. ye NF’C but 41>)t i} first owswm in Carved: . 5 than: (I: am ervov in (“slaying av simplyy'mb . 2 ' 5:3... : 6(i+cos x) 2cmx(.smx) dux _ '19., sinx cm): (1. + 03395— (b) f (93) = sin—V2162) 4x g’m = 1 W. {23(1) (c) ('1 + \$2) tan“1 :17. 1+7: ‘ H [(9 -.—.- (t +1?) MA 165 EXAM 2 I Fall 2004 Page 2/4 (6) 2. Find an equation of the tangent line to the curve 3/3 — x2 : 4 at the point (2, 2). a \$3..)(2: 4- 0 @ OT :: x1+4 2 2 —/ 3‘52 if: " (2“ 3.3% :: J- (x‘+4> 32.x @ 2 .. iii:—'2£I 2%8y3'2A2:—11-® At (x)16)=(‘27‘2.): :-.. _.____. =._.. 2. °" 3‘2“ 3 9 \g-Z‘: \$3642) [6] 99. 0% tom. line: «3-2 -: ~—%L>‘-9~) (9). 3. If xsiny + cos 2y 2 cosy, ﬁnd 3% by implicit differentiation. xcaink) 1— 00523 :cos @ W—~——~«@ Q) /X C65 Ll! . , . iskﬂ *2 (ha _v_.\ i . “a Ax-i—Smka +( \ ‘20 d3 -asmxb‘iti 4% - 4"“? oLx "' Xmsng —2ssn2~3 +5in X 0393 -—-2 {meta +S\'Vna 6 4. Find the ﬁrst and second derivatives of the function h cc 2 x2 + 1. ( ) v (8) 5. Find the derivative of the function y = (1n - - l 4w: eww’;ewna ea ﬂ— : e M MA 165 EXAM 2 Fall 2004 Page 3/4 (9) 6. Find the exact value of each expression. (a) sin"1<-%>= “A <———;> 9mg =42 9 ’55 ‘39”; NFC 1 . :— G __ 3%; @ (b) tan”11 :: :1 <2: tamxézi/ Ja'k «3413 a = 3-; :5 ‘9 (0) #102084?) = \$603, WW ta: cos-L35; . b8 ': (138—251;, @ “0033': 35':— Jas'j é‘n' :g— (3) - —2. ( 8mg 2+m=W= 33 ’5 +V— MW». 54"?) 20 whan o .5 \$5111) 6 (6) 7. Find the differential of the function y = . 0L3: Q(X+L)ng)x wzu (map. x—‘L (x—L)‘ , _ 1‘ 5 i J ,- (Xﬂifz. x (10) 8" (a) Find the linearizaﬁon LC”) of the function f = x/E at a = 1. W = saw * mm (a) ~ E (x) = R to) = ’5. © «was; m=é L<w>= L + 2%“) in (b) Use a linear approximation to estimate the number \/1.1. £0034 Lb), )Lor x wear 1 \5? :8 1+ %(x~t),+°" Mamet . Nch \(‘m 9:, 1 + %(1.1—1):1+é(o.1)='1,0:7 Vl-l z 1.0 E (6) 9. Suppose that x and y are functions of t and are related by the equation 51:2 + y2 = 1_ dy (1.7: f — = _ — = —1— 1 . I ,dt 2, ﬁnd dt when (m,y) ( ) MA 165 ‘ EXAM 2 Fall 2004 Page 4/4 (12) 10. Gravel is being dumped from a conveyor belt at a rate of 30 ft3 / min and its coarseness is such that it forms a pile in the shape of a cone whose base diameter and height are always equal. How fast is the height of the pile increasing when the pile is 10 ft high? LAC V laJ. 'UNL \lolmmr. of UM Coming File.) Y m mAJ'Mcplt-m em (ml hﬂrmkai Givemv. ALCEPw §t7m;w, in?» d1” Front 0:1"— mlmun Mtﬁ'oft oh? 2 VtJi'WV-zln “ﬂan-h. ,ln ’5 V—Iﬁh (12) 11. A balloon was released at point A on level ground and is rising at a rate of 140 ft / min. The balloon is observed by a telescope located on the ground at point B which is 500 ft from point A. How fast is the telescope’s angle of elevation changing when the balloon is 500 ft above ground? Q») "f (\$va %”1140 {if/m». k Fuvud. .42.. wkw ln:SOO§t l. a dot A 500 a tame =JI.._» 500 @ 2 \$236.4ﬁciél‘. _;_ at; .5 cm 9 4h 0‘1 5°”; 0U: 5'00 our WM '73?ch 6:?)m\$e:é &“ J2: a -" Li. —-.Z wood ‘Y, 0U: ’ 5'00 140 ' H30 50 /W' ...
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