Methods to Find Limit of Rational Function> Substitution Method

If \[\lim_{x\to a}f\left(x\right)=l,\], where l is a real number, then l is the limit of the function.

If \[\lim_{x\to a}\frac{f(x)}{g(x)}\] is of the form \[\frac{0}{0}\mathrm{or}\frac{\infty}{\infty}\], then \[\lim_{x\to a}\frac{\mathrm{f}(x)}{\mathrm{g}(x)}=\lim_{x\to a}\frac{\mathrm{f}^{\prime}(x)}{\mathrm{g}^{\prime}(x)}\] Process is continued till the indeterminate form remains.