erms of the Taylor Series for Vx centered at x = es for f(x) = x³ – 10x² + 6 at x = 3. the Taylor series for the following functions: a = 1

College Algebra
7th Edition
ISBN:9781305115545
Author:James Stewart, Lothar Redlin, Saleem Watson
Publisher:James Stewart, Lothar Redlin, Saleem Watson
Chapter2: Functions
Section2.4: Average Rate Of Change Of A Function
Problem 2E
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1. Determine the true error and relative true error when approximating the
derivative of f(x) = -x² + 5x at x = 2 with h = 0.1.
2. Use the formula *+1)-7® to approximate the derivative of f(x) = 3x² at
f(x+h)-f(x)
h
x = 1 using h = 0.1. Compute both the absolute true error and absolute
relative true error.
3. Write out the first five terms of the Taylor Series for Vx centered at x =
1.
4. Evaluate the Taylor Series for f(x) = x³ – 10x² + 6 at x = 3.
5. Find the first 4 terms of the Taylor series for the following functions:
a. Inx centered at a = 1
b. - centered at a = 1
C. sin x centered at a =
4
Transcribed Image Text:1. Determine the true error and relative true error when approximating the derivative of f(x) = -x² + 5x at x = 2 with h = 0.1. 2. Use the formula *+1)-7® to approximate the derivative of f(x) = 3x² at f(x+h)-f(x) h x = 1 using h = 0.1. Compute both the absolute true error and absolute relative true error. 3. Write out the first five terms of the Taylor Series for Vx centered at x = 1. 4. Evaluate the Taylor Series for f(x) = x³ – 10x² + 6 at x = 3. 5. Find the first 4 terms of the Taylor series for the following functions: a. Inx centered at a = 1 b. - centered at a = 1 C. sin x centered at a = 4
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