Problem

Find the Taylor series for $ f(x) $ centered at t…

03:27

Problem 18 Medium Difficulty

Find the Maclaurin series for $ f(x) $ using the definition of a Maclaurin series. [ Assume that $ f $ has a power series expansion. Do not show that $ R_n (x) \to 0. $] Also find the associated radius of convergence.

$ f(x) = \cosh x $

Name: find the maclaurin series for fx using the definition of a maclaurin series assume that f has a po 8
Uploaded: 2018-03-13
Duration: 2 min 3 s
Channel: Numerade
Description: Find the Maclaurin series for $ f(x) $ using the definition of a Maclaurin series. [ Assume that $ f $ has a power series expansion. Do not show that $ R_n (x) \to 0. $] Also find the associated radius of convergence. $ f(x) = \cosh x $

Answer

The Maclaurin series is $\sum_{n=0}^{\infty} \frac{x^{2 n}}{(2 n) !}$
which has radius of convergence $=\infty$ .

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

find my corn serious for half of ax using the definition of met Lauren Siri's. Okay, So gonna farm. We're going first. Find the primes. The rhythms for that's so zero at zero equals half of eat with zero. Plus, it was not a zero, which is zero, and it goes to one, and a crime at zero is gonna be That's six zero is going to zero and so on were going to find that so forty even order of the derivative at zero is gonna be zero. And for the old number for the other of us is going to one. So we plug in this data into over definition of McLaren, Siri's, and we're going to have This is our definition, and we know that for your r. O. C. It is the affinity because it converts for the whole realign end. With plugging this data, it becomes one purse. So for the even, Order of threw him is just a one and for all, Member, it's just a zero. So Okay, it wasn't this I got So which is equals to K equals two in King. Sorry, Kay. From zero to infinity, Extra pole of two in over two K to Victoria. Yeah, that's all the answer

Yiming Z.

University of Illinois at Urbana-Champaign

Topics

Sequences

Series

Calculus: Early Transcendentals

Chapter 11

Infinite Sequences and Series

Section 10

Taylor and Maclaurin Series

Problem

Find the Taylor series for $ f(x) $ centered at t…

Problem 18 Medium Difficulty

Find the Maclaurin series for $ f(x) $ using the definition of a Maclaurin series. [ Assume that $ f $ has a power series expansion. Do not show that $ R_n (x) \to 0. $] Also find the associated radius of convergence.

$ f(x) = \cosh x $

Answer

The Maclaurin series is $\sum_{n=0}^{\infty} \frac{x^{2 n}}{(2 n) !}$
which has radius of convergence $=\infty$ .

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Grace H.

Kayleah T.

Samuel H.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 11

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Grace H.

Kayleah T.

Samuel H.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Problem

Find the Taylor series for $ f(x) $ centered at t…

Problem 18 Medium Difficulty

Find the Maclaurin series for $ f(x) $ using the definition of a Maclaurin series. [ Assume that $ f $ has a power series expansion. Do not show that $ R_n (x) \to 0. $] Also find the associated radius of convergence. $ f(x) = \cosh x $

Answer

The Maclaurin series is $\sum_{n=0}^{\infty} \frac{x^{2 n}}{(2 n) !}$which has radius of convergence $=\infty$ .

Topics

Calculus: Early Transcendentals

Discussion

Top Calculus 2 / BC Educators

Grace H.

Kayleah T.

Samuel H.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Watch More Solved Questions in Chapter 11

Video Transcript

Topics

Calculus: Early Transcendentals

Top Calculus 2 / BC Educators

Grace H.

Kayleah T.

Samuel H.

Joseph L.

Calculus 2 / BC Bootcamp

Integration Review - Intro

Definite vs Indefinite

Recommended Videos

Find the Maclaurin series for $ f(x) $ using the definition of a Maclaurin series. [ Assume that $ f $ has a power series expansion. Do not show that $ R_n (x) \to 0. $] Also find the associated radius of convergence.

$ f(x) = \cosh x $

The Maclaurin series is $\sum_{n=0}^{\infty} \frac{x^{2 n}}{(2 n) !}$
which has radius of convergence $=\infty$ .