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