Sol-165E2-F2010

# Sol-165E2-F2010 - (16 MA 165 EXAM 2 Fall 2010 Page 1/4 NAME...

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Unformatted text preview: (16) MA 165 EXAM 2 Fall 2010 Page 1/4 NAME QBHDWZ’E KEV Page 1 / 16 STUDENT ID Page 2 /31 P 3 27 l RECITATION INSTRUCTOR age / Page 4 /26 l i [ RECITATION TIME TOTAL /100 l E DIRECTIONS 1. Write your name, 10—digit PUID, recitation instructor’s name and recitation time in 03 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, calculators or any electronic devices may be used on this exam. 1. Find the derivatives of the following functions. (It is not necessary to simplify). (a) y = m W52- ‘3 I: My will 4“ (2 a??? 4’ (é) (b) f(\$) = ewcm gxww (mama’s rt“ msm) ” ' if}? (c) y = tan2 (3:13) 3 a?) Ci: 6 \$23 72%;) a “‘3 53%;) (d) y = [1n(1 + 6‘”)? g QM (:3. a e“) 2; wt @ln MA 165 EXAM 2 Fall 2010 Name Page 2/4 (6) 2. The position function of a particle is given by s : t3 — (4.5)t2 — 7t, t Z 0. (a) When does the particle reach a velocity of 5 m/sec? Mﬁ) :5: 3‘?1L —- 9t w“? ‘6? (Va) 2:: 5 ms» 312L931 m7 :2 3t1w9i"12:0 w, fingfvm4iﬂ i (fr/ﬁr)(t+i)::() «a E4“) 1 (b) When is the acceleration 0? (la? a)%) 3:; G17” 9 agam ; é‘tw ? :rrO WM d (6) 3. Find 3% by implicit differentiation, if sinx+cosy : sinwcosy. er“ '1, ' we} I226 '“-’ M, , guy, Jim) , Cﬂggfm» mug : insknx( Elna) +0; W (gi'n‘x‘giwg m 5mm @skiﬂxﬂ “ {ix ’ in __ m\$x(cm‘§ml) d2: — git-n (8) 4. Find the equation of the tangent line to the curve 3:2 + 2mg — 3/2 + at = 2 at the point (1, 2). g: x my) M ' rs ~— A/Uﬁ r: .. t (it? 2:1 + i 0 e; Wynn): 2-1424 All. +2v2 mfg-2 =% £30 WWW 2:52p "a2 m, 3' I, ’4! a Q/kh w Lg A ngﬁgCM-mi) —0.015 (6) 5. Use a linear approximation to estimate 6 iii??? EEK) J? j) (Ewe) A (fame ﬁx “any? on L (it?) ﬁxéfmtd, a, i? 8%} gay an ‘%5 £0 .34 MAMA Q x l 624‘ “1’6”? m. 0,0153" ("2,69% (5) 6. Find the differential dy of y : ln(secw + tan m cm _ L W, a 7? x i “’“wmmmmw “mew-w S V A; d s ,_ > I g Rm +MW ( mart 2m» 2%» i» H WW, ': (“fem Ska t a; gifﬁffiy €947? W vi {Chi}! t} w é—j, 7km" missing; , £25: 6’ it dy : C5) (9) (6) (12) MA 165 EXAM 2 Fall 2010 Name Page 3/4 7. Find the exact value (in radians) of NPC -— f ___., ... 3__ - (a)1(73)~“23« Wgsgma ) 3, —1 1 __ 1 M“ K i etw ee-g<:§;gwMwaiiwe :17: C; (c)s1n (s1n3) gm 3 ﬁxi‘jeg 3:11 3 8. Simplify the expression sin(2 sin“1 and write it in terms of a: Without using trigono— metric and inverse trigogometric functions. LaT 3:3[6474 ngl'hta 7 :3 LNLN—x i f \$(n(?wsiwni7i)) == Sin 2, L3 2: 2 S»an may: 77%, Sl‘ntg (3,05% j;\ 1—3:;371‘5 3% irmL/ﬂ WMAWWM, l\ “X if ‘. efri(Q tariffs? a: 21W]? \@ 9. Find the derivatives of the following functions. (It is not necessary to simplify). (a) y = sin“1 (x/sinx) .L i k r W 7W WW“ W 035% i 1, , i “‘ ~ #53:”; , WW « Wm” - CQiy’ﬁ V] m As Miriam E ww» dx 1 (ﬂ is) 2 mm s; m. ,y \Flwwe'mw 31‘"in (b) y : tan“1(sin”1(\/E)) Slit Wigwam. . a 1L “3% t? sitin‘ E, ﬁﬁﬁasniﬁarsvv \_ NW? QT, TQM); stigma)” (C) yzzva’l” ﬁfe m) m 8 (A 2 (it, ’MQMWDW _ am i Haw} W n ,g ; Egan: 6 Ly 2 3% j 7% W L21“? +(Qmﬂ ;( saw; u (13) (13) MA 165 EXAM 2 Fall 2010 Name Page 4/4 10. Gravel is being dumped from a conveyer 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? LA {LI v V oﬁumxg g Y” “: “(YUM um .55; if} Wax gym? ~ e an Maw , viz-£2 f MW h :40 Ei my h g} WM. ab» mg?) . f»? ‘23 a if?) M was its. ea in.“ r“ h “if” 6M [.30 a: iii/mm mm 5,} Wiféms rift rﬂi'm (2. rr ' 11. An airplane is ﬂying at 150 ft / sec at an altitude of 2000 ft in a direction that will take it directly over the observer at the ground level. Find the rate of change of the angle between the line from the observer to the plane and the horizontal, when the plane is directly over a point on the ground that is 2000 ft from the observer. ...
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Sol-165E2-F2010 - (16 MA 165 EXAM 2 Fall 2010 Page 1/4 NAME...

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