Problem 31
Page 104
Section 2.2: The Limit of a Function
Chapter 2: Limits and Derivatives
Given information
Given :- The expression is 
To find :-
The graph of 
has a vertical tangent or a vertical cusp at c
Step-by-step explanation
The function is 
...(1)
The vertical tangent means that the derivative at that point approaches infinity
Since the slope is infinitely large
Test one point in each of the region formed by the graph
If the point satisfies the function then shade the entire region to denote that every point in the region satisfies the function .
|
|
0 |
-1 |
1 |
-2.19 |
|
y-axis |
4 |
6 |
2 |
0.05 |
The required graph of the given function is:
When we zoom the region of the graph around 
, we can see that in order to be within 
of 
, 
must be within the range 
. Thus must be at most 
away from 
.
Again we zoom the region of the graph around , we can see that in order to be within 
of , must be within the range 
. Thus must be at most 
away from .
Single Variable Calculus: Early Transcendentals
Solutions
Chapter
Section
- Problem 1
- Problem 2
- Problem 3a
- Problem 3b
- Problem 3c
- Problem 3d
- Problem 3e
- Problem 4a
- Problem 4b
- Problem 4c
- Problem 4d
- Problem 4e
- Problem 5a
- Problem 5b
- Problem 5c
- Problem 5d
- Problem 5e
- Problem 5f
- Problem 5g
- Problem 5h
- Problem 6a
- Problem 6b
- Problem 6c
- Problem 6d
- Problem 6e
- Problem 6g
- Problem 6h
- Problem 6h
- Problem 6i
- Problem 6j
- Problem 6k
- Problem 6l
- Problem 7
- Problem 8
- Problem 9a
- Problem 9b
- Problem 9c
- Problem 10a
- Problem 10b
- Problem 10c
- Problem 11a
- Problem 11b
- Problem 11c
- 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 25a
- Problem 25b
- Problem 26a
- Problem 26b
- Problem 27a
- Problem 27b
- Problem 28
- Problem 29a
- Problem 29b
- Problem 30a
- Problem 30b
- Problem 30c
- Problem 30c
- Problem 30d
- Problem 31
- Problem 32a
- Problem 32b