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
![(a) In this part of the question, you may assume any results that are proved
in Unit F1, but you should refer to any result that you use.
Prove each of the following statements.
(i) lim
a-1
(ii) lim
223-22-2x+1 2
x2 + 3x 4
26
1
a→0 sin (26)
2-4 logr
(iii) lim
24e-2r
(b) Prove that the function
f(x)
|x-2-x+2
2x - 4
does not tend to a limit as a tends to 2.
(c) Use the c-6 definition of continuity to prove that the function
f(x) = 3x² - x
is continuous at the point c= -1.
(d) Prove that the function
x
f(x)= x + 3
is uniformly continuous on the interval [0, 3], referring to any results
from the module that you use.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F78199da8-8819-492e-ab85-20d0b150b303%2Fcff3ccd6-0352-4d6c-9100-eb620380a335%2F4j4yyzq_processed.jpeg&w=3840&q=75)
Transcribed Image Text:(a) In this part of the question, you may assume any results that are proved
in Unit F1, but you should refer to any result that you use.
Prove each of the following statements.
(i) lim
a-1
(ii) lim
223-22-2x+1 2
x2 + 3x 4
26
1
a→0 sin (26)
2-4 logr
(iii) lim
24e-2r
(b) Prove that the function
f(x)
|x-2-x+2
2x - 4
does not tend to a limit as a tends to 2.
(c) Use the c-6 definition of continuity to prove that the function
f(x) = 3x² - x
is continuous at the point c= -1.
(d) Prove that the function
x
f(x)= x + 3
is uniformly continuous on the interval [0, 3], referring to any results
from the module that you use.
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