Home » mcq » Engineering maths » Calculus » The value of $$\mathop {\lim }\limits_{\left( {{\text{x,}}\,{\text{y}}} \right) \to \left( {0,\,0} \right)} \frac{{{{\text{x}}^2} – {\text{xy}}}}{{\sqrt {\text{x}} – \sqrt {\text{y}} }}$$ is A. 0 B. $$\frac{1}{2}$$ C. 1 D. 100
The value of $$\mathop {\lim }\limits_{\left( {{\text{x,}}\,{\text{y}}} \right) \to \left( {0,\,0} \right)} \frac{{{{\text{x}}^2} – {\text{xy}}}}{{\sqrt {\text{x}} – \sqrt {\text{y}} }}$$ is A. 0 B. $$\frac{1}{2}$$ C. 1 D. 100
To solve this limit, we can use L’Hôpital’s rule. L’Hôpital’s rule states that if $\lim_{x\to a} \frac{f(x)}{g(x)}$ exists and $\lim_{x\to a} \frac{f'(x)}{g'(x)}$ also exists, then $\lim_{x\to a} \frac{f(x)}{g(x)} = \lim_{x\to a} \frac{f'(x)}{g'(x)}$.