Textbook ExpertVerified Tutor
16 Oct 2021
Given information
Here given a function 
.
We have to Show that 
is continuous on 
.
Step-by-step explanation
Step 1.
By theorem 7, the trigonometric function are continuous. Thus, 
on 
and 
on 
are continuous.
Thus, 
is continuous on 
.
To check continuity of at 
, we will evaluate left hand limit and right hand limit.
as the sine function is continuous at 
.
by continuity of cosine function at .
Thus, 
Therefore, is continuous at , so is continuous on .
Single Variable Calculus: Early Transcendentals
4th Edition, 2018
Stewart
ISBN: 9781337687805
Solutions
Chapter
Section
- Problem 1
- Problem 2
- Problem 3a
- Problem 3b
- Problem 4
- Problem 5
- Problem 6
- Problem 7
- Problem 8
- Problem 9
- Problem 9a
- Problem 9b
- Problem 10a
- Problem 10b
- Problem 10c
- Problem 10d
- Problem 10e
- Problem 11
- Problem 11
- Problem 12
- Problem 13
- Problem 14
- Problem 15
- Problem 16
- Problem 17
- Problem 18
- Problem 19
- Problem 20
- Problem 21
- Problem 22
- Problem 23
- Problem 24
- Problem 25
- Problem 26
- Problem 27
- Problem 28
- Problem 29
- Problem 30
- Problem 31
- Problem 31E
- Problem 32
- Problem 33
- Problem 34
- Problem 34E
- Problem 35
- Problem 36
- Problem 37a
- Problem 37b
- Problem 37c
- Problem 38
- Problem 39
- Problem 40
- Problem 41
- Problem 42
- Problem 43
- Problem 44
- Problem 45a
- Problem 45b
- Problem 46a
- Problem 46b
- Problem 47a
- Problem 47b
- Problem 48a
- Problem 48b
- Problem 49
- Problem 50
- Problem 51
- Problem 52
- Problem 53
- Problem 54a
- Problem 54b
- Problem 54c
- Problem 55