Use power series operations to find the Taylor series at x =0 for the following function. 9 (1-x)²

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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**Problem Statement:**

Use power series operations to find the Taylor series at \( x = 0 \) for the following function.

\[
\frac{9}{(1-x)^2}
\]

---

**Guidance:**

The Taylor series for \(\frac{1}{1-x}\) is a commonly known series. What is the Taylor series at \( x = 0 \) for \(\frac{1}{1-x}\)?

---

**Expression:**

\[
\sum_{n=0}^{\infty} \, [ \text{Type an exact answer.} ]
\]
Transcribed Image Text:**Problem Statement:** Use power series operations to find the Taylor series at \( x = 0 \) for the following function. \[ \frac{9}{(1-x)^2} \] --- **Guidance:** The Taylor series for \(\frac{1}{1-x}\) is a commonly known series. What is the Taylor series at \( x = 0 \) for \(\frac{1}{1-x}\)? --- **Expression:** \[ \sum_{n=0}^{\infty} \, [ \text{Type an exact answer.} ] \]
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