Limits
9.0 L'Hospital's Rule for evaluation of limits:
9.0 L'Hospital's Rule for evaluation of limits:
L'Hospital's rule states that for functions $f(x)$ and $g(x)$ which are differentiable on an open interval $I$ except possibly at a point $c$ contained in $I$.
If $\mathop {\lim }\limits_{x \to c} f(x) = \mathop {\lim }\limits_{x \to c} g(x) = 0$ or $ \pm \infty $, $g'(x) \ne 0$ for all $x$ in $I$ with $x \ne c$
and
$\mathop {\lim }\limits_{x \to c} \frac{{f'(x)}}{{g'(x)}}$ exists, then $\mathop {\lim }\limits_{x \to c} \frac{{f(x)}}{{g(x)}} = \mathop {\lim }\limits_{x \to c} \frac{{f'(x)}}{{g'(x)}}$.
ie; If $\mathop {\lim }\limits_{x \to c} \frac{{f(x)}}{{g(x)}}$ is in the form of $\frac{0}{0}$ or $\frac{\infty }{\infty }$ and $f(x)$ & $g(x)$ are differentiable functions, $g'(x) \ne 0$ then $\mathop {\lim }\limits_{x \to c} \frac{{f(x)}}{{g(x)}} = \mathop {\lim }\limits_{x \to c} \frac{{f'(x)}}{{g'(x)}}$
Note:
For using L'Hospital Rule, Basic knowledge of differentiation is required. So one is advised to revisit Limits after completing Differentiation Chapter.
