The function is [tex]Limit \text (x,y)→ (0,0) \frac{{x^{10} -y^{10}}}{x^5-y^5}[/tex]
⇒[tex]Lim(x,y)\rightarrow (0,0)\frac{{x^5}^2-{y^5}^2}{{x^5-y^5}}[/tex]
→[tex]Lim(x,y)\rightarrow (0,0)\frac{(x^5-y^5)\times(x^5+y^5)}{(x^5-y^5)}[/tex]
→[tex]Lim(x,y)\rightarrow (0,0){(x^5+y^5)}[/tex]
=0+0
=0
Hence the value of the given function i.e [tex]\frac{{x^{10} -y^{10}}}{x^5-y^5}[/tex] when (x,y)→(0,0) is 0.
