+oo (-1)"2n+1 2n +1 ITEMS: Consider tan for all r € [-1, 1]. n=0 2.x 1. By differentiating tan (r*), find a power series representation of f(r) = that is valid for all %3D rE(-1,1). (-1)"+1 2. Use the result in item 1 to find the exact value of 16" n=0 3. Approximate ( tan) using a 4th degree Maclaurin polynomial. Hint: Using the power series representation for tanr given above, write a tan-r as a power series.

Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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+oo
(-1)"12n+1
2n +1
ITEMS: Consider tan
for all r € [-1, 1].
n=0
2x
1. By differentiating tan (r*), find a power series representation of f(r) =
that is valid for all
%3D
1+r4
rE(-1, 1).
(-1)"+1
2. Use the result in item 1 to find the exact value of
16"
n=0
3. Approximate ( tan) using a 4th degree Maclaurin polynomial.
Hint: Using the power series representation for tanr given above, write a tan-r as a power series.
Transcribed Image Text:+oo (-1)"12n+1 2n +1 ITEMS: Consider tan for all r € [-1, 1]. n=0 2x 1. By differentiating tan (r*), find a power series representation of f(r) = that is valid for all %3D 1+r4 rE(-1, 1). (-1)"+1 2. Use the result in item 1 to find the exact value of 16" n=0 3. Approximate ( tan) using a 4th degree Maclaurin polynomial. Hint: Using the power series representation for tanr given above, write a tan-r as a power series.
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