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DETAILS SCALC9 1.6.013.
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Evaluate the limit, if it exists. (If an answer does not exist, enter DNE.)
\[
\lim _{t \rightarrow 6} \frac{t^{2}-t-30}{t-6}
\]
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Answer
The limit of the function as t approaches 6 is \(\boxed{11}\).
Step 1 ：The function is not defined at t=6, but we can simplify the function to find the limit as t approaches 6.
Step 2 ：The numerator can be factored, and then we can cancel out the (t-6) term in the numerator and denominator.
Step 3 ：After simplifying, we can substitute t=6 to find the limit.
Step 4 ：\(t = t\)
Step 5 ：\(f = \frac{t^{2} - t - 30}{t - 6}\)
Step 6 ：\(f_{simplified} = t + 5\)
Step 7 ：\(limit = 11\)
Step 8 ：The limit of the function as t approaches 6 is \(\boxed{11}\).
