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M1550-Exam2-Sol

# M1550-Exam2-Sol - W£§y.—.—— Math 1550(30 EXAM 2...

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Unformatted text preview: W£§y_.—.——_ Math 1550 (30) 10/07/2010 EXAM 2 Instructions: You must Show your work to receive credit. Scratch paper will not be collected, so you must write all your work that you wish to have graded on the exam. No calculators! There are problems 011 both sides of the paper! Problem 1 [10 points] Find all values of a: where the tangent lines to y : 2:2:2 and y = 9e are perpendicular. M1(X)= 9 "I: ma. ="l 4X61 : —| 9e:ﬁk -= -I X:_.l.i \$6 Problem 2 [10 points] Use the deﬁnition of the derivative to ﬁnd f’(:c), for: f(x) = 2:2 ,3 Sim: 15m“ mm— l‘rm : “m (mm’ia — (xi-3) _ #0 h h-QD ——""‘——"—“—"h .. = \im ﬁth+h1-/¥_ ﬁg \‘ MZX-l-h) he '-——-—-——- = rm h h-z-o )il/ =h‘m (2mm = @ h—m Problem 3 [10 points] Find the equation for the line tangent to the graph of: f(x) = x/5 at the point (a, f(a)), for a = 4. Express this equation in the form 3,: = mm+b. 5;“) = 9—14.12 => [it-,2.) ﬂuid: on Hat “me 24— 2s 2?. 4 202mm ~2 = JA-CXJO 3-2, = {pa—l )3 = {—x-H Problem 4 [10 points] Suppose that: ﬁx + h) — ﬂat) = m3 — 4th + 1159: + 3:533: — 9h? Find f’(:r:). - 3 1 \1“ 3h“ ah) \$00 = L13:— HHV‘: 57700 _= E3: w =h‘m.(8)(3 406+ h:K+3h:x—— Dir—ﬁh) H—EX Lth l h-‘ro Problem 5 [10 points] Find g for the following: In 4:17 a). y = 2:1: arcsintr) b)’ y : 51:1: ) O). Proclucf Rule: j'= Zarcsin ()0 + 2x. ‘ = Zarasin 00* 2X \JHG V HG. b). Quoﬁenfﬂgfzf C‘Min Rule 1' ‘_ [\nMXﬂ- AK— \nUDO'UtXY (4)0" ' l (H.4).w—ln(ax\.4 = “—‘—"———‘-————‘____..____ mx’ {-AX—Alnﬂtx) le. XL 4 — #111000 15x1 g ___d \— ln (‘00 A x‘. / Problem 6 [10 points] Find dy/dx for the following: a). y = (a: + sin(x))3 b). y = V 2:1: + V33": a). % = mm salmon)2 (Henna) Problem 7 [10 points] What is the velocity of an object being dropped from a height of 16ft when it hits the ground? Recall that for an object in vertical motion, its height 3(t) at time t is given by: l 3(t) = so + out — 5th where 39 = 3(0) is the initial position at time t = 0, v0 = v(0) is the initial velocity at time t = 0, and g is the constant: g=9.8§=32§ SWG a sea: It— we: V0 =0 (3:92 .momexd: when. _ f a— mews. Odomtm-ol Sﬂzl=0 => lQ-le’c1=0 -> \tslet‘w» t1=l=> ﬁnal Velocity ad is a! : Problem 8 [10 points] For the function: ﬁnd: A23}, x‘1 3 q Ax“ —e (x-eX—l + e 2M0 = “CK“HX) 9 3%: e‘fxﬂax) + 6*(2193 -- ‘06-» We) Problem 9 [10 points] Find g3 for: ? l 3 x fj= X ___[ am] _ elnmq ! no a“ £3; = e n [\an) an]! n "I“ = ex (>0 [31(qu+ Moog“, \n(ﬁ)] _ 9 .314: lnCX)- \nqu] Problem 10 [10 points] Find g? for: 323?; + Smy" = y + me” if {X37+7X)"'] = ﬁiwxeﬂ ?’X2)’+ 33—1 + a)“ + '7'X- H33“ d—‘L- ﬁ- + eh xe" ? (X +IZX73)(ﬂ) + gx1y+ 2,)“: 33% +8}:- XQDK (X5 “9093-“ 0A :32} = E’. +xexh'ax1y—?7H 10 Bonus [10 points] Show that the function: ffiv) = [ml is continuous at a: = 0, but is not differentiable at a: = 0. ¥ is eoniimouSoi Xr—O hm. \$(x\=1im\x\—o } =>Hm£txi= .CCO) x90 K90 X'PO Hobo gig net oU-Fferen’ﬁabié’ (xi Xt-O LNJ image +‘ne side limits are Aiﬁemn‘i: ll ...
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M1550-Exam2-Sol - W£§y.—.—— Math 1550(30 EXAM 2...

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