Concept explainers
Suppose the following limits exist:
Then
These formulas can be stated verbally as follows: The limit of a sum is the ______ of the limits, and the limit of a product is the _______ of the limits.
To fill: The conditions of formula for limit of a sum and limit of a product.
Answer to Problem 1E
The formula for addition and product of limits is,
Explanation of Solution
If the following limits exist, the limits are
According to limit laws, if limits exist then the limit of sum of these limits is sum of the limits because both sides have same result, and limit of a product is the product of these limits because both sides have same result.
In the given statement of limit of the value of Right-Hand Side is equal to the value of Left-Hand Side for both addition and product of limits.
Thus, the formula for addition and product of limits is,
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