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3. Let T,(x)= f(a) + f '(a)(x-a)+ "(a 2(x-a)² +² a)(x-a)³ be the Taylor polynomial of degree three for the 2 function f(x), centered at the point x=a. a) Find T,'(x), T, "(x), and T,"(x). b) Evaluate T, '(x), T,"(x), and T,"''(x) at x=a to verify that: T;(a) = f(a), T, '(a) = f '(a), T",(a) = f"(a), T,""(a) = f""(a). and

3. Let T,(x)= f(a) + f '(a)(x-a)+ "(a 2(x-a)² +² a)(x-a)³ be the Taylor polynomial of degree three for the 2 function f(x), centered at the point x=a. a) Find T,'(x), T, "(x), and T,"(x). b) Evaluate T, '(x), T,"(x), and T,"''(x) at x=a to verify that: T;(a) = f(a), T, '(a) = f '(a), T",(a) = f"(a), T,""(a) = f""(a). and

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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3. Let T,(x)= f(a)+ f '(a)(x-a)+ f"(a) (x-a)² + 2 f'(a) (x-a) be the Taylor polynomial of degree three for the 6 function f(x), centered at the point x=a. a) Find T, '(x), T, "(x), and T,"'(x). b) Evaluate T '(x), T, "(x), and T,"'(x) at x=a to verify that: T;(a) = f(a), T, "(a) = f'(a), T",(a) =f"(a), and T,"'(a) = f"(a). %3D
Transcribed Image Text:3. Let T,(x)= f(a)+ f '(a)(x-a)+ f"(a) (x-a)² + 2 f'(a) (x-a) be the Taylor polynomial of degree three for the 6 function f(x), centered at the point x=a. a) Find T, '(x), T, "(x), and T,"'(x). b) Evaluate T '(x), T, "(x), and T,"'(x) at x=a to verify that: T;(a) = f(a), T, "(a) = f'(a), T",(a) =f"(a), and T,"'(a) = f"(a). %3D
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