Calculus Examples

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

Step 1

Change the two-sided limit into a right 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 greater than zero for $x$ near $1$ to the right, the function increases without bound.

$\infty$