Question

question 8 evaluate the limit \\( \lim_{s \to 3} \frac{\frac{1}{s} - \frac{1}{3}}{s - 3} \\) question help: video submit question

Explanation:

Step1: Combine numerator fractions

$\frac{1}{s} - \frac{1}{3} = \frac{3 - s}{3s}$

Step2: Rewrite the original limit

$\lim_{s \to 3} \frac{\frac{3 - s}{3s}}{s - 3} = \lim_{s \to 3} \frac{3 - s}{3s(s - 3)}$

Step3: Simplify the numerator

$3-s = -(s-3)$, so:
$\lim_{s \to 3} \frac{-(s - 3)}{3s(s - 3)} = \lim_{s \to 3} \frac{-1}{3s}$

Step4: Substitute $s=3$

$\frac{-1}{3 \times 3} = \frac{-1}{9}$

Answer:

$\frac{-1}{9}$