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In E.urcise.r I 12. o malrir and liS dwractuistic

Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence ISBN: 9780131871410 187

Solution for problem 1 Chapter 5.2

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

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Elementary Linear Algebra: A Matrix Approach | 2nd Edition | ISBN: 9780131871410 | Authors: Lawrence E. Spence

Elementary Linear Algebra: A Matrix Approach | 2nd Edition

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Problem 1

In E.urcise.r I 12. o malrir and liS dwractuistic [HJiytUHIIial [-: -4 art' gil't'n. Find t/r(' t'igenmlllt'S of t'aclr matrix and dt'tennint' a 7. 2 -4] 4 . -(/ - 6){/ + 2)1 basis for eoclr t'lflt'nSIHICI!. I. [i

Step-by-Step Solution:
Step 1 of 3

Product Rule If F(x)=f(x)g(x), Then F’(x)=f(x)g’(x) + f’(x)g(x) Ex. d/dx [ (4x^3 - x^2 -1)(x^3 -2x^2 + 3x +1)] = (4x^3 - X^2 - 1) (3x^2- 4x + 3) = (12x^2 -2x)(x^3 - 2x^2 + 3x + 1) However the product rule is more useful for the product of different types of functions Ex. f(x)= x^2cos(x) g(x) = e^x arctan(x) Proof of the Product Rule Let F(x) = f(x)g(x) F’(x) = lim ((F(x + h ) - F(x))/h) h 0 =lim ((f(x + h )g( x + h) - f(x)g(x))/h) h 0 Subtract and add f(x + h)g(x) = lim ((f( x + h)g(x + h) - f(x + h)g(x) + f(x + h) - g(x) - f(x)g(x))/h) h 0 = lim ((f( x + h)(g( x + h) - g(x)) + g(x)(f( x + h) - f(x))/h) h 0 = lim ((f ( x+ h)(g( x + h) - g(x))/h) + (g(x)f(x + h) - f(x)/h) h 0 = lim (f( x + h) lim ((g(x + h) - g(x))/h

Step 2 of 3

Chapter 5.2, Problem 1 is Solved
Step 3 of 3

Textbook: Elementary Linear Algebra: A Matrix Approach
Edition: 2
Author: Lawrence E. Spence
ISBN: 9780131871410

This textbook survival guide was created for the textbook: Elementary Linear Algebra: A Matrix Approach, edition: 2. The full step-by-step solution to problem: 1 from chapter: 5.2 was answered by , our top Math solution expert on 12/27/17, 07:57PM. Elementary Linear Algebra: A Matrix Approach was written by and is associated to the ISBN: 9780131871410. This full solution covers the following key subjects: . This expansive textbook survival guide covers 34 chapters, and 2741 solutions. Since the solution to 1 from 5.2 chapter was answered, more than 273 students have viewed the full step-by-step answer. The answer to “In E.urcise.r I 12. o malrir and liS dwractuistic [HJiytUHIIial [-: -4 art' gil't'n. Find t/r(' t'igenmlllt'S of t'aclr matrix and dt'tennint' a 7. 2 -4] 4 . -(/ - 6){/ + 2)1 basis for eoclr t'lflt'nSIHICI!. I. [i” is broken down into a number of easy to follow steps, and 39 words.

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