3-1t 4.) Iim 5x-4メト! 入ーレ Atuメ-X 5) メー3 メー0 2入+ (4x

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
3-1E
4.) lim
5x-4x+1
5)
lim
7メー3
ax+ (4x-5
Using the
definition
Transcribed Image Text:3-1E 4.) lim 5x-4x+1 5) lim 7メー3 ax+ (4x-5 Using the definition
Expert Solution
Part 4

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\lim _{x\to \infty }\left(\frac{5x^2-4x+1}{4+2x-x^2}\right)

divide by x2

=\lim _{x\to \infty }\left(\frac{\frac{5x^2}{x^2}-\frac{4x}{x^2}+\frac{1}{x^2}}{\frac{4}{x^2}+\frac{2x}{x^2}-\frac{x^2}{x^2}}\right)

=\lim _{x\to \infty }\left(\frac{5-\frac{4}{x}+\frac{1}{x^2}}{\frac{4}{x^2}+\frac{2}{x}-1}\right)

=\frac{5-\frac{4}{\infty }+\frac{1}{\infty ^2}}{\frac{4}{\infty ^2}+\frac{2}{\infty }-1}

=\frac{5-0+0}{0+0-1}

=\frac{5}{-1}

{\color{Red} =-5}

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