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Sol-165E2-F2008

# Sol-165E2-F2008 - MA 165 EXAM 2 Fall 2008 Page 1/4 NAME...

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Unformatted text preview: MA 165 EXAM 2 Fall 2008 Page 1/4 NAME GRADING RE ———-——— Page 1 / 16 STUDENT ID ___—— Page 2 / 30 P 3 26 RECITATION INSTRUCTOR L—L Page 4 / 28 RECITATION TIME — TOTAL MO DIRECTIONS 1. Write your name, 10—digit PUID, 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. 2. The test has four (4) pages, including this one. 3. Write your answers in the boxes provided. 4. 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. 5. Credit for each problem is given in parentheses in the left hand margin. 6. No books, notes, calculators or any electronic devices may be used on this exam. (16) W 1. Find the derivative of the following functions. (It is not necessary to simplify). (a) y=sin\/1+4wl (c) y = tan2(30) sign—3 2 tam(39).sec2(3<9).3 (d) F(y) = yln(1 + 6y) F (a ma .1.» MA 165 EXAM 2 Fall 2008 Name —_—_ Page 2/4 (7) 2- HEW) = f(g(\$)), Where f(-2) = 8, f’(-2) = 4, f’(5) = 3, 9(5) = —2, and g’(5) = 6, ﬁnd F’(5). F’m a g’gmm’m @l 4 we =¥Qgﬁﬁ§wé = +6 =25 Ln (8) 3. Find the slope of the tangent line to the curve sinx = cos y at the point (g, ‘55:"??? - If . _, COSOIDC? M “'3455’3 )' 31”?" swig) @ 2. (9) 4. Find the exact value of each expression: a sin—1 @ I (> < )( WC 2 \ h l _ 3 3:9“ SLﬁ‘é'E 9*g-‘5‘3EI-2r E: “3"? a C3) .. L 3:008 '65 <==> 00321:”? 9 0‘4” 2:: _ ,, 217 N 3 Cg) “J: "é‘ (c) tan—1(tan 13 = [Cm—'1Ct4m‘ ¢==> tang Titan ZE,-E<"g<£ If, 6) _ 11' 6 ~ '6— (6) 5. Find the second derivative of y = :123 1n‘(4\$). ,3 It %:X%2Jn(+x) 93; LQZXQ/H‘ii'bﬁ ‘3’ =x3_,i..,4 1- 3x7'Xm(4x) 4x 7. “<1 + 373%(479 @ v: m +23%}...4 +9349“ 4X N :sx +63<JZMM>O @ ov/7 E» y": S'X +6'x/em(4><) E +3X (Ink :31W47+w2+~37’11m* <3 ‘2 {hex (boar +2>< *3)? i; +9763” ‘3 MA 165 EXAM 2 Fall 2008 Name —___ Page 3/4 (12) 6. Find the derivatives of the following functions. (It is not necessary to simplify). (a) y = sin—1 x/E (b) y = tan—1(cos2 0) &- J...»— ' Q-L’DSBC‘SW) 9) .— M 1 +(cos‘9)2 K (N V , *5. __ 2.3%)st .n-p :L + @549 _ v 1 (c) y—(tanx)”, 0<\$<g 01x (8) 7. Use a linear approximation to estimate (8.06)”3 ® W s Hr») + Siam-co, for 3W on; em: W3, cps) Ra): + , 5:00:23” 9c"? , § @w’ezML-‘gwwwwﬁ 0?. 402 m 2' f: + I . 6&m)% 4‘ +%(%’06 '8):4+%(0.6) =+oz© i (6) 8. Find the differential dy of each of the functions: (a) y = a: sina: : Woosx +sfhx A’X (Us ( ) and; liar rm‘ssihg CL): @ i 1 atoll? 0 V" ___._————; 1V1: 2W Kr“ s—i Pt +0? mksina an; _v =J—lmfI+-t°‘) gr I ‘4 dy=-—‘—~'T_’ it ﬂ=éw2tdr a 1” ® MA 165 EXAM 2 Fall 2008 Name __—_ Page 4/4 (14) 9. 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? Let \/ lot. U/Lo. «legume 0} t0“ oom’ooi Figé In be TL? height cmol *r hell/Lavagljus cymbdggl Giumi twat sighs gthm V9)“ (\$22k «h V-lnhzk “'5 3 IV’ z ﬂ) "’3 '5) d1;%k“é[email protected] d't ‘Lt i so _; 6 t WW I'm-.10 a 30:.g100g‘iﬁ—a ouzm—‘E‘njg/MIH The height of the pile is increasing at the rate of _§... ft / min «— Srr U4 (14) 10. A block of ice in the shape of a cube with initial volume 1000 cm3 is melting in such a way that the length of each edge is decreasing at the rate of 1 cm/ hr. Assuming that the block of ice maintains its cubical shape, at what rate is its surface area decreasing when the volume is 27 cm3? Let ‘1 Lu titu— {Jail-km o ﬂu; ice mile.) 3 loll its surfed, Mm mad X he Misﬁt/l1 0}» 2.4014 0}. edﬁes, Given SEE. =«1Cm/hw C?) Fin 1%; WW v: 27”" ...
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Sol-165E2-F2008 - MA 165 EXAM 2 Fall 2008 Page 1/4 NAME...

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