Question

Find the first four nonzero terms of the Taylor series for the function about $0 .$ $(1+x)^{3 / 2}$

Name: Problem 1, Chapter 10: Calculus Single Variable
Uploaded: 2021-05-24T14:58:40-08:00
Duration: 3 min 10 s
Channel: Manisha Sarker
Description: Find the first four nonzero terms of the Taylor series for the function about 0 . (1+x)^3 / 2

   Find the first four nonzero terms of the Taylor series for the function about $0 .$
$(1+x)^{3 / 2}$

Calculus Single Variable

Deborah… 7th Edition

Chapter 10, Problem 1

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Solved by Expert Manisha Sarker

05/24/2021

Step 1

The Taylor series for a binomial series $1+x^p$ about $x=0$ is given by: \[1+px+\frac{p(p-1)}{2!}x^2+\frac{p(p-1)(p-2)}{3!}x^3+...\] Show more…

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Find the first four nonzero terms of the Taylor series for the function about $0 .$ $(1+x)^{3 / 2}$

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Key Concepts

Taylor Series Expansion

A Taylor series expresses a function as an infinite sum of terms calculated from the function's derivatives at a specific point, typically around 0. This series approximation is useful for estimating function values by summing a finite number of terms, especially near the point of expansion.

Generalized Binomial Theorem

The generalized binomial theorem extends the traditional binomial expansion to cases where the exponent is not a positive integer. It provides a way to express (1 + x)^? as an infinite series in powers of x with coefficients derived from a generalized form of binomial coefficients, allowing the expansion of functions like (1 + x)^(3/2).

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