5) Show that the function f(x) = {x³/ x2 if x < 1 if x ≥ 1 is continuous on the interval (-∞, ∞). 6) Compute the limit of the following as x approaches infinity. lim √√x²+1-x x-x 7) Find the horizontal and vertical asymptotes of the following. y = 2x²+x-1 x²+x-2

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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Calculus I

May I please have the solutions for the following questions?

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5) Show that the function
f(x) = {x³/
x2
if x < 1
if x ≥ 1
is continuous on the interval (-∞, ∞).
6) Compute the limit of the following as x approaches infinity.
lim √√x²+1-x
x-x
7) Find the horizontal and vertical asymptotes of the following.
y =
2x²+x-1
x²+x-2
Transcribed Image Text:5) Show that the function f(x) = {x³/ x2 if x < 1 if x ≥ 1 is continuous on the interval (-∞, ∞). 6) Compute the limit of the following as x approaches infinity. lim √√x²+1-x x-x 7) Find the horizontal and vertical asymptotes of the following. y = 2x²+x-1 x²+x-2
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