Use the Squeeze Theorem to evaluate the limit: Student solution. which is true for all x values except x = Then we can multiply all sides by to obtain the double inequality L From the definition of the cosine function, we know that it satisfies the following double inequality: 53 -1≤cos (58) Then limit at 0 of the left side above equals and the right side equals Then by Squeeze Theorem if follows that = lim x¹² x→0 lim x→0 lim 0←x COS lim x→0 = = 53 x = VI 12 X

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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Use the Squeeze Theorem to evaluate the limit:
Student solution.
which is true for all x values except x =
From the definition of the cosine function, we know that it satisfies the following double inequality:
-1≤cos
(53)
Then we can multiply all sides by
to obtain the double inequality
L = lim x¹2 COS
x →0
Then limit at 0 of the left side above equals
and the right side equals
Then by Squeeze Theorem if follows that
lim
x →0
lim
x→0
lim
x →0
||
=
(53)
=
VI
12
X
Transcribed Image Text:Use the Squeeze Theorem to evaluate the limit: Student solution. which is true for all x values except x = From the definition of the cosine function, we know that it satisfies the following double inequality: -1≤cos (53) Then we can multiply all sides by to obtain the double inequality L = lim x¹2 COS x →0 Then limit at 0 of the left side above equals and the right side equals Then by Squeeze Theorem if follows that lim x →0 lim x→0 lim x →0 || = (53) = VI 12 X
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