{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# 3 - (ac—2" k l 2(15 pts For the power series 2 k-o...

This preview shows page 1. Sign up to view the full content.

This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: (ac—2)" k+l 2.(15 pts) For the power series 2 ' k-o , determine the precise interval of convergence (don't forget to check the endpoints!). (la—2)1m (k+1) (k+2) (x—2)* lx — 2| <1 :> absolute convergence lx— 2| > 1 => divergence ‘“ 1 x=3: —— diver es §k+l ‘ g w(_1)k x==l 21H] 1:! The interval of convergence is [L3J . 3.02 pts) Compute the Taylor polynomial 30:) for the function f (x) = tan‘1 x _ Take a = 0 (i.e., use powers of x). —l _x d! __x _2 _22 tan Jr_"[l+tz_£(l+(1).“r) _ x3 sol“;(:t)-—x——3 _ k+l _ k “Ix"2|[m]-lx—2l 2 converges by the alternating series test 1+l ->|x-2| as k—MD 1+; 5 +...)d:=x—£+x——... 3 5 Alternatively, you may ﬁnd P3(x) by computing the coefﬁcients directly. f’(x)=(1+x1)", f'(x)=—2x(l+x2)=2, f”(x)=—2(l+x2)'2+8x2(1+x2)" —2 1 x3 :— thusan=0, a,=l, (12:0, a3=—=——,so 193(x)=x—— 't ‘ x , 3! 3 3 , i 2' 4’ \$ ‘| ”‘1'..ng ; \ ab! 2 t!-—K"""" (H [- He{‘ J § 1 t _?l -I- 3:, ' -" : 1 5' S “F DonalLTt'UHOL \ ...
View Full Document

{[ snackBarMessage ]}

Ask a homework question - tutors are online