1. Consider the function f(x): (a) Complete the following tables. Enter at least 8 decimal places for your answer. cos x 1 cos x 1 lim 1-0 x -0.1 -0.01 -0.001 -0.0001 X f(x) = cos x 1 = x X lim x-0+ X (c) Put a check mark in front of the correct answer. (c-1) Is f(0) defined? Yes (b) Based on your tables above, make a guess for the following limits: cos x 1 cos x 1 X cos x 1 0.1 0.01 the limit lim 2-0- x No! It is a guess only, not a proof. 0.001 0.0001 No f(x) = (c-2) Does this matter for the limits of lim lim 1-0 x-0+ Yes. For this reason, none of the above limit exists. lim x-0 cos x 1 X cos x 1 1 X X lim x-0 cos x 1 ? X No. What happens at "a' is irrelevant to the limit as x approaches a. (c-3) Does the table of values constitute a full proof of the limit value of lim cos - 1 ? I-0- X Yes! Full points would be awarded on a test if I use the above table to evaluate cos x 1

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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Can you please do question 1 letter b, c
1. Consider the function f(x):
(a) Complete the following tables. Enter at least 8 decimal places for your answer.
cos x 1
cos x 1
lim
x-0-
X
-0.1
-0.01
-0.001
-0.0001
X
cos x 1
f(x) =
X
X
lim
x-0+
COS X 1
X
(c) Put a check mark in front of the correct answer.
(c-1) Is f(0) defined?
Yes
(b) Based on your tables above, make a guess for the following limits:
cos x 1
cos x 1
X
0.01
the limit lim
x-0-
Xx
No! It is a guess only, not a proof.
0.1
0.001
0.0001
No
1
f(x)=
(c-2) Does this matter for the limits of lim
lim
x→0+
H-0-
X
Yes. For this reason, none of the above limit exists.
=
lim
x-0
cos x 1
X
cos x 1
7
X
X
lim
x-0
cos x
x
1
-?
No. What happens at "a' is irrelevant to the limit as x approaches a.
(c-3) Does the table of values constitute a full proof of the limit value of lim
COS X-
x-0-
X
Yes! Full points would be awarded on a test if I use the above table to evaluate
cos x 1
-?
Transcribed Image Text:1. Consider the function f(x): (a) Complete the following tables. Enter at least 8 decimal places for your answer. cos x 1 cos x 1 lim x-0- X -0.1 -0.01 -0.001 -0.0001 X cos x 1 f(x) = X X lim x-0+ COS X 1 X (c) Put a check mark in front of the correct answer. (c-1) Is f(0) defined? Yes (b) Based on your tables above, make a guess for the following limits: cos x 1 cos x 1 X 0.01 the limit lim x-0- Xx No! It is a guess only, not a proof. 0.1 0.001 0.0001 No 1 f(x)= (c-2) Does this matter for the limits of lim lim x→0+ H-0- X Yes. For this reason, none of the above limit exists. = lim x-0 cos x 1 X cos x 1 7 X X lim x-0 cos x x 1 -? No. What happens at "a' is irrelevant to the limit as x approaches a. (c-3) Does the table of values constitute a full proof of the limit value of lim COS X- x-0- X Yes! Full points would be awarded on a test if I use the above table to evaluate cos x 1 -?
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