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7. Let f(x)=64x² ln (2x) −16x¹. Findƒ(e)-f(€) 2

7. Let f(x)=64x² ln (2x) −16x¹. Findƒ(e)-f(€) 2

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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7. Let f(x)=64x² ln (2x)-16x². Find f(e)-f
Transcribed Image Text:7. Let f(x)=64x² ln (2x)-16x². Find f(e)-f
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f\left(x\right)=64x^4\ln \left(2x\right)-16x^4

f\left(x\right)=4\cdot16x^4\ln \left(2x\right)-16x^4

f\left(x\right)=16x^4\left(4\ln \left(2x\right)-1\right)

take x=e

f\left(e\right)=16e^4\left(4\ln \left(2\cdot e\right)-1\right)

f(e)=16e^4\left(4\left(\ln \left(2\right)+\ln \left(e\right)\right)-1\right)

f(e)= 16e^4\left(4\left(\ln \left(2\right)+1\right)-1\right)

f(e)= 16e^4\left(4\ln \left(2\right)+4-1\right)

f(e)= 16e^4\left(4\ln \left(2\right)+3\right)

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