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HW22 - Math 160 Kouba Worksheet 10 1 Use any...

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Unformatted text preview: Math 160 Kouba Worksheet 10 1.) Use any method (repeated differentiation method or short cuts using well know Maclaurin series) to find the first four nonzero terms of the Taylor series centered at c for each of the following functions. a.) f(m)=x2+3+sin(a:2) and (:20 b.) f(:1:)=e‘$—cos :3 and 020 c.) f(:c)::c3cos2x and 020 d.) f(a:):(1+:c+a:2)-ln(1+a:) and 0:0 f.) f(:z:) =x+¢m and c: —3 g.) f(:r) : tan(7ra:/4) and c = 1 2.) Determine the common function represented by (equal to) each of the following Taylor series. a.) 1+23+zr2/2!+$3/3l+x4/4l+-~ b.) x2+x3+x4/2l+£5/3l+a:6/4l+-~ c.)1+m+a:2+:c3+m4+$5+... d.) x4-x6+w8—$10+x12—~- G _ 3 -2x24,3_: q_,_‘_‘:x4_ ] —x D 3x #5 .. 3 5" 1 7 "I q _ _ -—,2 +.,>< .— + X X 3 ‘45“ I 2. 3 4) ~——:\+x+>< +><+--' A1,— ‘ \---X K I : : \—x+x"——>(3 ”v3— (M) l+>< 1-L—x) 3 4.4 ~ _ X1 25, _— 31+.” W MCl+x2v X 3: + 3 q 4&0: (\+x+x’~) XMLNX) A x x44 . : U+x+><‘) (x~%+§—-;—+-°) (W) 2 3 q - _ x x 5, - ’ X 35+?" <+ + + x"~ 5+3,”— 2. 3 q +x3v 31+ 1 : .1,ka £3___§/ <4 X +¢X 1.1x + f X 5 l e ~Hx : — X ) 2 PM3 14:06) —. x’[\+2><3+q><“+ gxfi+~.] x54» 92x57 + qx” + Xx”+-~ ‘ —I 4') ~\‘—(><): X+ Cxufl/‘L —» ~(1‘CX): 1+ ile—q) 6* / n - ~3/ ~b' +00: mm) '1, 4%) : .3,C><+<4) 4} ) (m) : ‘Q— (—3) Ad" “0 _ $03) : ‘3 .. __2 ‘4‘ O]. I j -; 4963) _. ‘39: = E. a : “$63)- ”3‘ ~ :_L 1! 7" a.) ’1 2; ' T ' 5’ 2 ll!_ 3 3 fl : i - J, m 3g 4, ” ICp ’ 4M): X+(X+q) : ’24— 3(x+3)— SEQ-+314. $84,323....” 3) 4-00: m (LIX) ‘3 4900: gmlch) ) 400: g:— l<§>§).m1<§x)'g L +§—M(§X) 2MC§X)-MCEX)M(~EX)- LI- 3 3 : g5 m€gx)+%m*(§x)m1(3x)) ) an: 4W0) M a _ 40): MG)‘ _l__ :1 m ° o} I ‘ \ J a — £91 - I: ’49-’02 Li) I: .2 _ T * H ' I ’ ‘i' ‘ 3: ) \\ _ w 1 4y it 2%M‘(§)m<% = 77: 2 " ”E32 ~4“» 3 4 3 “3° 7"“ %[§%MC§ + %M1C§}MZ(§)] 3 +132 = 7:, [31; 4, «9 *Lthkaw ~(x—)+ 3’ q .’ 0?.) A.) \+X-(— fi-l—l-LL-FH' _ e, an 3\_ q 3 x w+v ‘0.) XZ+X+—r+ 01! all *4! {iv/{(54); + q 9‘ X :X1[‘+X+K+_+__,+ 3 \l X n Tr3 w 2c: ...
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