Question

attempt 1: 5 attempts remaining. evaluate the following limit. give an exact answer if the limit is a number. otherwise, enter $-infty$ or $infty$ if the limit is infinite, or enter dne if the limit does not exist in another way. $limlimits_{t \to 8} \frac{\frac{1}{t} - \frac{1}{8}}{t - 8} = $

Explanation:

Step1: Combine numerator fractions

$\frac{1}{t} - \frac{1}{8} = \frac{8 - t}{8t}$

Step2: Rewrite the original limit

$\lim_{t \to 8} \frac{\frac{8 - t}{8t}}{t - 8} = \lim_{t \to 8} \frac{8 - t}{8t(t - 8)}$

Step3: Simplify the expression

$\frac{8 - t}{8t(t - 8)} = \frac{-(t - 8)}{8t(t - 8)} = -\frac{1}{8t}$

Step4: Evaluate the simplified limit

$\lim_{t \to 8} -\frac{1}{8t} = -\frac{1}{8 \times 8}$

Answer:

$-\frac{1}{64}$