Use Taylor's formula with n=2 to find the quadratic approximation of f(x) = (1 + x)k at x = 0 (k a constant). If k= 4, for approximately what values of x in the interval [0,1] will the error in the quadratic approximation be less than 100?

College Algebra
10th Edition
ISBN:9781337282291
Author:Ron Larson
Publisher:Ron Larson
Chapter5: Exponential And Logarithmic Functions
Section: Chapter Questions
Problem 39CT: The population P (in millions) of Texas from 2001 through 2014 can be approximated by the model...
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a. Use Taylor's formula with n=2 to find the quadratic approximation of f(x) = (1 + x)k at x = 0 (k a constant).
b. If k = 4, for approximately what values of x in the interval [0,1] will the error in the quadratic approximation be less than
1/100?
a. What is the quadratic approximation of f(x) = (1 + x)k at x = 0?
k(k-1)
2
b. If k= 4, for approximately what values of x in the interval [0,1] is the error less than 1/100?
Q(x) = 1 + kx +
- 1/3
A. 0≤x<25
B. 0<x< 100-1/3
C. 0≤x<800
D. 0≤x≤1
-x²
- 1/3
Transcribed Image Text:a. Use Taylor's formula with n=2 to find the quadratic approximation of f(x) = (1 + x)k at x = 0 (k a constant). b. If k = 4, for approximately what values of x in the interval [0,1] will the error in the quadratic approximation be less than 1/100? a. What is the quadratic approximation of f(x) = (1 + x)k at x = 0? k(k-1) 2 b. If k= 4, for approximately what values of x in the interval [0,1] is the error less than 1/100? Q(x) = 1 + kx + - 1/3 A. 0≤x<25 B. 0<x< 100-1/3 C. 0≤x<800 D. 0≤x≤1 -x² - 1/3
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