Please explain thank you! Find lim f(x) if, for all x > 1,X→∞20e* - 21 < f-4exf(x) <5√x√x-1

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Answered: Please explain thank you!

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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Question

Please explain thank you!

Find lim f(x) if, for all x > 1,
X→∞
20e* - 21 < f
-
4ex
f(x) <
5√x
√x-1

Expert Solution

Step 1: Squeeze Theorem

$table row cell limit as x rightwards arrow infinity of fraction numerator open parentheses 20 e to the power of x minus 21 close parentheses over denominator 4 e to the power of x end fraction end cell equals cell limit as x rightwards arrow infinity of 1 fourth open parentheses 20 minus 21 over e to the power of x close parentheses end cell row blank equals cell 1 fourth open parentheses 20 minus 21 over e to the power of infinity close parentheses end cell row blank equals cell 1 fourth open parentheses 20 minus 21 over infinity close parentheses end cell row blank equals cell 1 fourth open parentheses 20 minus 0 close parentheses end cell row blank equals 5 end table$