Question

7. Use Maclaurin's series of ( an ^{-1}(x) ) to evaluate ( lim _{x ightarrow 0} frac{3 x-x^{3}-3 an ^{-1}(x)}{x^{5}} ), Hint: ( an ^{-1}(x)=sum_{n=0}^{infty}(-1)^{n} frac{x^{2 n+1}}{2 n+1} ) (A) 0.03 (B) 0 (C) -0.02 (D) 0.07 (E) -0.6

          7. Use Maclaurin's series of ( 	an ^{-1}(x) ) to evaluate ( lim _{x 
ightarrow 0} frac{3 x-x^{3}-3 	an ^{-1}(x)}{x^{5}} ), Hint: ( 	an ^{-1}(x)=sum_{n=0}^{infty}(-1)^{n} frac{x^{2 n+1}}{2 n+1} )
(A) 0.03
(B) 0
(C) -0.02
(D) 0.07
(E) -0.6

$7. Use Maclaurin's series of ( an ^-1(x) ) to evaluate ( lim x ightarrow 0 frac3 x-x^3-3 an ^-1(x)x^5 ), Hint: ( an ^-1(x)=sumn=0^infty(-1)^n fracx^2 n+12 n+1 ) (A) 0.03 (B) 0 (C) -0.02 (D) 0.07 (E) -0.6$

Added by Sara A.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Zhumagali Shomanov

05/22/2024

Step 1

Step 1: Recall the Maclaurin series for $ \tan^{-1}(x) $: \[ \tan^{-1}(x) = \sum_{n=0}^{\infty} (-1)^n \frac{x^{2n+1}}{2n+1} \] This series expansion is valid for $ |x| \leq 1 $. Show more…

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