Concept explainers
(a) What is wrong with the following equation?
(b) In view of part (a). explain why the equation
is correct.
(a)
To explain: The equation
Explanation of Solution
Let the function
Construct the table of
x | ||
−3 | ||
−2 | ||
−1 | ||
0 | ||
1 | ||
2 | ||
3 |
From the table, it is observed that,
The domain of
In general, the equation holds for all x not equal to 2. That is,
Therefore,
That is,
(b)
To explain: The equation
Explanation of Solution
From part (a), the equation holds for all real numbers except 2.
That is,
Thus, it can be concluded that both the limit functions are equal.
That is,
Chapter 2 Solutions
Single Variable Calculus: Concepts and Contexts, Enhanced Edition
Additional Math Textbook Solutions
Advanced Mathematical Concepts: Precalculus with Applications, Student Edition
Precalculus Enhanced with Graphing Utilities (7th Edition)
Calculus and Its Applications (11th Edition)
Precalculus: Concepts Through Functions, A Unit Circle Approach to Trigonometry (4th Edition)
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