CUET Preparation Today
Evaluate $\underset{x→2}{\lim}\frac{\sqrt{x^2+x-3}-\sqrt{x+1}}{x-2}$. |
$\frac{1}{\sqrt{3}}$ $\sqrt{3}$ $\frac{2}{\sqrt{3}}$ $2\sqrt{3}$ |
$\frac{2}{\sqrt{3}}$ |
$\underset{x→2}{\lim}\frac{\sqrt{x^2+x-3}-\sqrt{x+1}}{x-2}=\frac{x^2-4}{(x-2)(\sqrt{x^2+x-3}-\sqrt{x+1})}$(Rationalise) $\underset{x→2}{\lim}\frac{x+2}{(\sqrt{x^2+x-3}-\sqrt{x+1})}=\frac{4}{2\sqrt{3}}=\frac{2}{\sqrt{3}}$ |
