Calculus Examples

$lim_{x \to 1} \frac{x}{\ln (x)}$

Step 1

Change the two-sided limit into a left sided limit.

$lim_{x \to 1^{-}} \frac{x}{\ln (x)}$

Step 2

Since the numerator is positive and the denominator $\ln (x)$ approaches zero and is less than zero for $x$ near $1$ to the left, the function decreases without bound.

$- \infty$