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For the next two exercises, determine the Taylor series generated by the function f at x = a.

For the next two exercises, determine the Taylor series generated by the function f at x = a.

Calculus: Early Transcendentals
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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### Taylor and Maclaurin Series Exercises **Instructions:** All computations in this section must be done by the definition of Taylor series (taking derivatives, establishing a pattern…). #### 1. Determine the Taylor polynomials of orders 0, 1, 2, and 3 generated by \( f(x) = \sqrt{1-x} \) at \( x = 0 \). ### Maclaurin Series Exercises For the next two exercises, determine the Maclaurin series for the given function. #### 2. \( \sin(x/2) \) #### 3. \( \frac{e^x - e^{-x}}{2} \) ### Taylor Series Exercises For the next two exercises, determine the Taylor series generated by the function \( f \) at \( x = a \). #### 4. \( f(x) = 2x^3 + x^2 + 3x - 8 \), \( a = 1 \). #### 5. \( f(x) = 2^x \), \( a = 1 \).
Transcribed Image Text:### Taylor and Maclaurin Series Exercises **Instructions:** All computations in this section must be done by the definition of Taylor series (taking derivatives, establishing a pattern…). #### 1. Determine the Taylor polynomials of orders 0, 1, 2, and 3 generated by \( f(x) = \sqrt{1-x} \) at \( x = 0 \). ### Maclaurin Series Exercises For the next two exercises, determine the Maclaurin series for the given function. #### 2. \( \sin(x/2) \) #### 3. \( \frac{e^x - e^{-x}}{2} \) ### Taylor Series Exercises For the next two exercises, determine the Taylor series generated by the function \( f \) at \( x = a \). #### 4. \( f(x) = 2x^3 + x^2 + 3x - 8 \), \( a = 1 \). #### 5. \( f(x) = 2^x \), \( a = 1 \).
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