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# assig5sol - i fa/ufwkr l MAT 1322 A Assignment 5(Due Wed...

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Unformatted text preview: i fa/ufwkr l MAT 1322 A Assignment 5 (Due Wed. April 1st at 8:30) Student Number: 1 1 _ ac , ﬁnd the Maclaurin series of (i) ln(1 + \$2) and 1. Starting from the Maclaurin series for (ii) ln(1 + 1132) dx . For each, indicate on which open interval the series is guaranteed to be convergent and represent the given function. Work: C30 / - Z 2c“ )4 /7CI<i l’)‘ - [4:0 (>6 “:9. I - 2 mn- zenw" «4:» 4 WI .54 a. - ,_ - I+7L n—o "-0 If)!" “=0 " v) p, _‘ 'J‘o‘ - M Dani“ i , at jag/ma) — «4 — ﬂex U >4» w B A link? : C + a; QC“: :2) W% MM C in [04414 /W 74’”)? ﬁt(l): O :9 6:0 4%.5::o;bm) _ W "' QH)%“M+J / W /Z.[/+7L*)c%o~ f(n33 (2nd) )ﬂ/n = 1, + Answers: 2. Find the Maclaurin series of f (:8) = (1 + 3:2)1/3. Work: (7+1?) U3 : 3 (If) 9‘2" Aw ”I _' u; _ (1,33(,.2,3)(-5/3x.073)--.0,3,M.) «gs-u < 3- ”MM... V‘ n! (aw/96%) W) (“13w > ________________________...__._ n! M = (W "" valid“- ~~ (ax-'4) M 3“\ n“ ~ W wﬁs‘ﬁ“ m W“ 3“ n‘. (.296 + “:2: (j)w-':;)'f” '41‘311 )Ka" Answer: " 3 Mn M‘“; x2 43/2 3. Sketch, on the same graph, the level curves of I —- V = C for C = —-1,0, 1,4. Indicate the scale on your axes and label the contours. Answer: VA 5.3 I «q 4. Find all ﬁrst and second partial derivatives of the functions. (a) ﬂux, y) = 2532343 + 3;; — ln(2) (b) 90“: g) : T2 008(36) _ 83, (c) f(:c, t) =1n<ac2t _ _) 4}an XV- 9t) " (‘4 a}- I) (ﬁnaﬂl [71‘1~I£)2 - 3 = '- Rxwvh H (76" - 7L)" ,/\1 Answers: ...
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assig5sol - i fa/ufwkr l MAT 1322 A Assignment 5(Due Wed...

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