Question

find the limit.
lim(f→4) (1/f - 1/4)/(f - 4)

Explanation:

Step1: Combine fractions in numerator

First, find a common - denominator for the fractions in the numerator. The common denominator of $f$ and $4$ is $4f$. So, $\frac{1}{f}-\frac{1}{4}=\frac{4 - f}{4f}$.
The original limit becomes $\lim_{f
ightarrow4}\frac{\frac{4 - f}{4f}}{f - 4}$.

Step2: Simplify the complex - fraction

We can rewrite $\frac{\frac{4 - f}{4f}}{f - 4}$ as $\frac{4 - f}{4f(f - 4)}$. Notice that $4 - f=-(f - 4)$. So, $\frac{4 - f}{4f(f - 4)}=\frac{-(f - 4)}{4f(f - 4)}$.

Step3: Cancel out common factors

Cancel out the common factor $(f - 4)$ (since $f
eq4$ when taking the limit), we get $\lim_{f
ightarrow4}-\frac{1}{4f}$.

Step4: Evaluate the limit

Substitute $f = 4$ into $-\frac{1}{4f}$. We have $-\frac{1}{4\times4}=-\frac{1}{16}$.

Answer:

$-\frac{1}{16}$