# Solved: Calculating derivatives f(x+h)f(x) a. or the ## Problem 50E Chapter 3.1

Calculus: Early Transcendentals | 1st Edition

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Problem 50E

Calculating derivatives f(x+h)?f(x) a.?? or the following functions, find f using the definition? f (x) = lim h . h?0 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) = x + 2; a = 7

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SOLUTION STEP 1 (a). Given f(x) = x+2. 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(x) = lim h h0 f(x+h) = (+h)+2 (x+h)+2 x+2 Thus f (x) =h0m h To solve this we have to multiply the numerator and the denominator with the conjugate of the numerator. (x+h)+2 x+2 (x+h)+2 x+2 (x+h)+2+ x+2 Therefore f(x) = lim h = lim h × (x+h)+2+ x+2 h0 h0 =lim (x+h)+2(x+2)= lim h = h0 h (x+h)+2+ x+2 h0 h (x+h)+2+ x+2 = 1 = 1 x+2+ x+2 2 x+2 Therefore...

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##### ISBN: 9780321570567

The answer to “Calculating derivatives f(x+h)?f(x) a.?? or the following functions, find f using the definition? f (x) = lim h . h?0 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) = x + 2; a = 7” is broken down into a number of easy to follow steps, and 50 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. Calculus: Early Transcendentals was written by and is associated to the ISBN: 9780321570567. The full step-by-step solution to problem: 50E 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. Since the solution to 50E from 3.1 chapter was answered, more than 273 students have viewed the full step-by-step answer.

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