Calculus Examples

$lim_{x \to 1} \frac{\cos (π x)}{x - 1}$

Step 1

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

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

Step 2

Since the numerator is negative and the denominator $x - 1$ approaches zero and is less than zero for $x$ near $1$ to the left, the function increases without bound.

$\infty$