Calculus Examples

$lim_{x \to 0} \frac{1}{\sqrt{1 + x^{2}} - \sqrt{1 - x^{2}}}$

Step 1

Since the numerator is positive and the denominator $\sqrt{1 + x^{2}} - \sqrt{1 - x^{2}}$ approaches zero and is greater than zero for $x$ near $0$ on both sides, the function increases without bound.

$\infty$