Question Number 414 by 123456 last updated on 25/Jan/15

$${f}\left({x},{y}\right)=\begin{cases}{\frac{\left({x}−\mathrm{1}\right)\left({y}−\mathrm{1}\right)\left({xy}−\mathrm{1}\right)+\left({x}^{\mathrm{2}} −\mathrm{1}\right)\left({y}^{\mathrm{2}} −\mathrm{1}\right)}{{x}^{\mathrm{2}} −{xy}}}&{\left({x},{y}\right)\neq\left(\mathrm{1},\mathrm{1}\right)}\\{\mathrm{0}}&{\left({x},{y}\right)=\left(\mathrm{1},\mathrm{1}\right)}\end{cases} \\ $$$$\mathrm{is}\:{f}\left({x},{y}\right)\:\mathrm{continuos}\:\mathrm{at}\:\left({x},{y}\right)=\left(\mathrm{1},\mathrm{1}\right)? \\ $$
Answered by prakash jain last updated on 31/Dec/14

$$\mathrm{The}\:\mathrm{function}\:\mathrm{is}\:\mathrm{not}\:\mathrm{continuous} \\ $$$$\mathrm{since}\:\mathrm{limit}\:\mathrm{does}\:\mathrm{not}\:\mathrm{exist}\:\mathrm{on} \\ $$$$\mathrm{line}\:{x}={y}. \\ $$