Calculus Examples

$lim_{x \to 0} \frac{\sqrt{3 + x^{2}}}{x}$

Step 1

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

$lim_{x \to 0^{-}} \frac{\sqrt{3 + x^{2}}}{x}$

Step 2

Since the numerator is positive and the denominator $x$ approaches zero and is less than zero for $x$ near $0$ to the left, the function decreases without bound.

$- \infty$