Calculus Examples

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

Step 1

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

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

Step 2

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

$- \infty$