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Question Number 187730 by otchereabdullai last updated on 20/Feb/23
 Evaluate   lim(x,y)→(0,0) ((x^2 (y−1)^2 )/(x^2 +(y−1)^2 ))
$$\:{Evaluate}\: \\ $$$${lim}\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)\:\frac{{x}^{\mathrm{2}} \left({y}−\mathrm{1}\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} +\left({y}−\mathrm{1}\right)^{\mathrm{2}} } \\ $$
Answered by mr W last updated on 21/Feb/23
lim_((x,y)→(0,0)) ((x^2 (y−1)^2 )/(x^2 +(y−1)^2 ))=((0^2 (0−1)^2 )/(0^2 +(0−1)^2 ))=(0/1)=0
$$\underset{\left({x},{y}\right)\rightarrow\left(\mathrm{0},\mathrm{0}\right)} {\mathrm{lim}}\frac{{x}^{\mathrm{2}} \left({y}−\mathrm{1}\right)^{\mathrm{2}} }{{x}^{\mathrm{2}} +\left({y}−\mathrm{1}\right)^{\mathrm{2}} }=\frac{\mathrm{0}^{\mathrm{2}} \left(\mathrm{0}−\mathrm{1}\right)^{\mathrm{2}} }{\mathrm{0}^{\mathrm{2}} +\left(\mathrm{0}−\mathrm{1}\right)^{\mathrm{2}} }=\frac{\mathrm{0}}{\mathrm{1}}=\mathrm{0} \\ $$
Commented by otchereabdullai last updated on 21/Feb/23
thank you my supper prof W
$${thank}\:{you}\:{my}\:{supper}\:{prof}\:{W} \\ $$

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