Question

1. - / 1 points evaluate the limit, if it exists. (if an answer does not exist, enter dne.) $lim_{x \to 4}\frac{\frac{1}{x}-\frac{1}{4}}{x - 4}$ resources read it

Explanation:

Step1: Combine fractions in numerator

First, combine $\frac{1}{x}-\frac{1}{4}$ in the numerator. $\frac{1}{x}-\frac{1}{4}=\frac{4 - x}{4x}$. So the limit becomes $\lim_{x
ightarrow4}\frac{\frac{4 - x}{4x}}{x - 4}$.

Step2: Simplify the complex - fraction

Rewrite the complex - fraction $\frac{\frac{4 - x}{4x}}{x - 4}$ as $\frac{4 - x}{4x(x - 4)}$. Notice that $4 - x=-(x - 4)$. Then the expression is $\lim_{x
ightarrow4}\frac{-(x - 4)}{4x(x - 4)}$.

Step3: Cancel out common factors

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

Step4: Evaluate the limit

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

Answer:

$-\frac{1}{16}$