Problem

Find the Maclaurin series of $ f $ (by any method…

02:34

Problem 45 Medium Difficulty

Find the Maclaurin series of $ f $ (by any method) and its radius of convergence. Graph $ f $ and its first few Taylor polynomials on the same screen. What do you notice about the relationship between these polynomials and $ f? $

$ f(x) = \cos (x^2) $

Name: find the maclaurin series of f by any method and its radius of convergence graph f and its first few
Uploaded: 2018-04-07
Duration: 2 min 17 s
Channel: Numerade
Description: Find the Maclaurin series of $ f $ (by any method) and its radius of convergence. Graph $ f $ and its first few Taylor polynomials on the same screen. What do you notice about the relationship between these polynomials and $ f? $ $ f(x) = \cos (x^2) $

Answer

$\sum_{n=0}^{\infty}(-1)^{n} \frac{x^{4 n}}{(2 n) !}, \quad R=\infty$

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Discussion

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Video Transcript

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