Question

question 11
evaluate the limit
\lim_{t \to 16} \frac{16 - t}{4 - \sqrt{t}}
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Explanation:

Step1: Recognize indeterminate form

Substitute $t=16$: $\frac{16-16}{4-\sqrt{16}}=\frac{0}{0}$, indeterminate.

Step2: Rationalize the denominator

Multiply numerator/denominator by $4+\sqrt{t}$:
$$\lim_{t \to 16} \frac{(16-t)(4+\sqrt{t})}{(4-\sqrt{t})(4+\sqrt{t})}$$

Step3: Simplify denominator

Use $(a-b)(a+b)=a^2-b^2$:
$$\lim_{t \to 16} \frac{(16-t)(4+\sqrt{t})}{16-t}$$

Step4: Cancel common factor

Cancel $16-t$ (valid for $t
eq16$):
$$\lim_{t \to 16} (4+\sqrt{t})$$

Step5: Substitute $t=16$

$$4+\sqrt{16}=4+4$$

Answer:

$8$