Calculus Examples

$lim_{x \to 2^{-}} \frac{\ln (2 - x)}{x}$

Step 1

Split the limit using the Limits Quotient Rule on the limit as $x$ approaches $2$ .

$\frac{lim_{x \to 2^{-}} \ln (2 - x)}{lim_{x \to 2^{-}} x}$

Step 2

As $x$ approaches $2$ from the left side, $\ln (2 - x)$ decreases without bound.

$\frac{- \infty}{lim_{x \to 2^{-}} x}$

Step 3

Evaluate the limit of $x$ by plugging in $2$ for $x$ .

$\frac{- \infty}{2}$

Step 4

Infinity divided by anything that is finite and non-zero is infinity.

$- \infty$