Taylor Series Approximation Formula f(x) = f(a) + f'(a)(x − a) + - f" (a) 2 _¡'¹' (a) (x − a)³ + ... 3! (x − a)² + - What is the second derivative of the function f(x) = -xe* ? What is the coefficient of the third term of the Taylor Series approximation for F(x) = -xex when a = Q?
Taylor Series Approximation Formula f(x) = f(a) + f'(a)(x − a) + - f" (a) 2 _¡'¹' (a) (x − a)³ + ... 3! (x − a)² + - What is the second derivative of the function f(x) = -xe* ? What is the coefficient of the third term of the Taylor Series approximation for F(x) = -xex when a = Q?
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.2: Graphs Of Equations
Problem 78E
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Question
Transcribed Image Text:Taylor Series Approximation Formula
_ƒ¹¹ (a) (x − a)² +
2
f(x) = f(a) + f'(a)(x − a) +
-
_ƒ''' (a) (x − a)³ + ...
3!
What is the second derivative of the function f(x) = -xe* ?
What is the coefficient of the third term of the Taylor Series approximation for
f(x) = -xex when a = 0?
Oa. (1/6)
Ob. (2/4!)
Oc. (-1/2)
Od. 3
Using substitution, calculate the approximate value of this function at x = 0.3,
using the fourth order Taylor series approximation of this function. Enter your
result up to five decimal places of accuracy.
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