hw6s - MAT 1330 Fall 2011 Assignment 6 Due November 23 at...

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Unformatted text preview: MAT 1330, Fall 2011 Assignment 6 Due November 23 at the beginning of class. Late assignments will not be accepted; nor will unstapled assignments. Instructor (circle one): Robert Smith? Jason Levy Olga Vassilieva Catalin Rada DGD (circle one): 1 2 3 4 Student Name Student Number By signing below, you declare that this work was your own and that you have not copied from any other individual or other source. Signature QUESTION 1. Consider the function f 2 m3 - 5m2 + 6x of a single real variable :13. Show that there exist two distinct solutions of f’ = O. WWKOd/L : EN) = 5X°Z~Im+é 625"- W’rsve :grm x : ’QLEF ~ [or-V2? i 6 7 X2, 6 chat/we dwfil‘e/e goluzéiuw off/x): WW5“ f”) 2 X5»Sx2+6x= Xfx~a)[>< *3) fat) §(o):§(&):gfi3)=o 3090 (swift/rim on [(9.23 W [52.37 M (toll Wat/“We (on/0,2)WZQKSJ) swarm W fzawflswem W ‘ Mzfi Q‘éwm’l) W 026} (3‘5) W+Lcwé ' W f’(€&):o (boo, [ab/magma) QUESTION 2. _ I 5‘ a) Fmd the Taylor polynomlal of degree n of f (at) = e”: near a: = 1. )QSQ for“ Polazwwu‘a) 0} Dagmar; WMiW{ 3 gorx we» {Cow Me {Mam/[Wop form: W” l H 2 Pm”); gm) + glofflxajr g (agff-al + .e M W ‘1 =1 (a): 704:5 +£ (OJ/X431) lmtsuwaczetg1 a lg :g h‘ )2 emu)” PHKx):g/+e,/)t<—I)+ >f-I +. T... £0!“ x W 1" §(¥>:&x% EHH) b) Approximate x/Eg using the Taylor polynomial obtained in (a) of degree n = 3. ESP 14:3 3 95 ()<): e + efx-” + QUE—[)2 Jr 81:4) : =e+e(m + 2mm gm} . )2 95 i. a 3:4 fléka 2; 33(3): away!) + 01 + i, + a,” [)3 r v Y733039 QUESTION 3. Complete the following steps needed to sketch the graph of the function -£Z+3X~l __.z2-3.z 1 & f(x>=e “if . = 6 a) Determine the domain of f Answer: b) Determine the vertical asymptotes of f 9) Compute the derivative f’ (11:), find the critical points of f (2:), and determine the Sign of f’(a3) and behavior of -><1+3X~I 3x—x2~l 6 01 an f’($) — Critical point(s): x 2. f) Compute the second derivative f”($), determine its Sign7 find the inflection points and determine the concavity of f Inflection points: $1 = and $2 2. g) Sketch the graph of f QUESTION 4. Determine the following limits: (3,) lim 1 u 005(3) m—+0 mtan(m) ‘ I ‘ ' (0 {Lug 6”” xtcm/X) 2M5 “we KS 3f 50”” 26”]- App kg eedg hwflx) , W$€ a! IXLao Xtanlx) (XL-(:3 SIIHX . Q N” skit-:2 IOX+ Egg?- OJ * X19? 4...... + l (2/ 7t~6t 90 é b {:90 L C : 6M;‘&‘6 3 £223- :(9 /§“//3 . 1~$+1n$ (“HEW . /~x+£m< /»/+6m Q A £50“ “ W < 0,1 .. O kw #003577“) ‘ /7‘W27/' Ii ...
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hw6s - MAT 1330 Fall 2011 Assignment 6 Due November 23 at...

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