Concept explainers
Whether the statement “The limit of a product is the product of the limits when each of the limits exists” is true or false.
Answer to Problem 1RE
Yes. The statement is true.
Explanation of Solution
Rule used:
Product rule:
Calculation:
Consider the function
Calculate the product of the functions
Take limit on both sides,
Thus,
Take limit for the functions
That is,
Product the functions
Thus,
From the equations (1) and (2), observe that
Thus, the statement is true.
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Chapter 3 Solutions
Calculus with Applications (11th Edition)
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