Estimate the limit, if it exists. If not, determine whether the one-sided limits exist (finite or infinite).
Recall the Quotient Law for evaluating limits given that and
exist. If
, then
exists and
.
For the given rational function , evaluate the limit of the numerator and denominator as x approaches 6.
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Since the rational function has an indeterminate form of the type at x = 6, we can find an equivalent expression for the function by factoring its numerator and denominator and cancelling like factors, however, that we keep the domain of the original rational function.
where z = .
Since the limit is being evaluated as x approaches 6 (meaning for all values of x near 6, but not equal to 6), we can try to evaluate by applying the Quotient Law for evaluating limits.
Evaluate the limit of the numerator and denominator as x approaches 6.
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Evaluate
=
(Round your answer to two decimal places.)