Whether the statement, is true or false.
The statement is false.
Quotient Law: Suppose that the limits and exist.
Let the function where and .
Then, by the Quotient Law, the given statement is true only if the limit of the denominator is not equal to zero as x approaches 1.
That is, is true whenever is not equal to zero.
The limit as x approaches 1 is computed as follows,
Thus, the limit exists and it is equal to zero.
Since the denominator is equal to zero as x approaches 1, the Quotient law cannot be used here.
Therefore, the statement is false.
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