Concept explainers
(a)
To approximate: the limit by graphing utility.
(a)
Answer to Problem 57E
The function appears to approach
Explanation of Solution
Given:
Calculation:
In order to approximate this one-sided limit, graph the function and view it within a small window around
From the graph, the function appears to approach
Conclusion:
Therefore, the function appears to approach
(b)
To approximate: the limit by creating the table.
(b)
Answer to Problem 57E
Indeterminate | |
Explanation of Solution
Calculation:
Now, try to numerically approximate the limit by using a table of values of
Indeterminate | |
The table also shows that the function appears to approach the value
Conclusion:
Therefore, the table is created to approximate the limit.
(c)
To evaluate: the limit algebraically.
(c)
Answer to Problem 57E
The limit of this function is
Explanation of Solution
Calculation:
In order to evaluate this limit algebraically, first notice that direct substitution of
Instead, evaluate the limit by factoring the denominator, and dividing out common factors in the numerator and denominator in order to provide a function whose limit at
Before, the limit of this function as
Conclusion:
Therefore, the limit of this function is
Chapter 11 Solutions
Precalculus with Limits: A Graphing Approach
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