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Solved: Calculating derivatives a. or the following

Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett ISBN: 9780321570567 2

Solution for problem 52E Chapter 3.1

Calculus: Early Transcendentals | 1st Edition

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Calculus: Early Transcendentals | 1st Edition | ISBN: 9780321570567 | Authors: William L. Briggs, Lyle Cochran, Bernard Gillett

Calculus: Early Transcendentals | 1st Edition

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Problem 52E

Calculating derivatives a.?? or the following functions, find f using the definition? f (x) = lim f(x+h)?f(x). h?0 h b.? ?Determine an equation of the line tangent to the graph of f at? (?a?, ?f?(?a?)) ?for the given value of a. f(x) = ;a =? 5 x

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Step 1 of 3

SOLUTION STEP 1 (a). Given f(x) = 1 . x We need to find the derivative of f(x) using the definition of the derivative f(x+h)f(x) The definition of the derivative is f (x) = lim h h0 f(x + h) = 1 x+h 1 1 xxh Thus f (x) = lim x+h x= lim x(x+h= lim h h0 h h0 h h0 hx(x+h) 1 1 = h0 x(x+h)= x2 STEP 2 (b). Determine an equation of the line tangent to the graph of f at (a, f(a)) ,{ie,(-5,f(-5))} for the given value a=-5. Equation of a tangent line at (a,f(a)) is y y =1m(x x ) 1 1 1 Slope is the m here which is given by the equation m = f (a) = f 5) = (5) = 25 1 1 f(a) = f( 5) = 5 = 5 Therefore the line tangent to the graph of f at (-5,- ) for the given value a=-5 is 5 1 1 1 5 y ( )5= 25 (x ( 5)) = 25 x 25 1 1 1 y + 5 = 25 x 5 y = 1 x 1 1 = 1x 2 25 5 5 25 5 The equation of the line is 1 2 y = 25x 5

Step 2 of 3

Chapter 3.1, Problem 52E is Solved
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Textbook: Calculus: Early Transcendentals
Edition: 1
Author: William L. Briggs, Lyle Cochran, Bernard Gillett
ISBN: 9780321570567

Since the solution to 52E from 3.1 chapter was answered, more than 375 students have viewed the full step-by-step answer. The answer to “Calculating derivatives a.?? or the following functions, find f using the definition? f (x) = lim f(x+h)?f(x). h?0 h b.? ?Determine an equation of the line tangent to the graph of f at? (?a?, ?f?(?a?)) ?for the given value of a. f(x) = ;a =? 5 x” is broken down into a number of easy to follow steps, and 47 words. This full solution covers the following key subjects: Calculating, definition, Derivatives, determine, equation. This expansive textbook survival guide covers 85 chapters, and 5218 solutions. The full step-by-step solution to problem: 52E from chapter: 3.1 was answered by , our top Calculus solution expert on 03/03/17, 03:45PM. This textbook survival guide was created for the textbook: Calculus: Early Transcendentals, edition: 1. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567.

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Solved: Calculating derivatives a. or the following