Question

Evaluate lim┬((x,y)→(4,5))⁡〖(√(x+y)-3)/(x+y-9)〗

Answer 1

$\lim_{(x,y)\to(4,5)}\frac{\sqrt{x+y}-3}{x+y-9}=\lim_{(x,y)\to(4,5)}\frac{\sqrt{x+y}-3}{(\sqrt{x+y}-3)(\sqrt{x+y}+3)}=$

$=\lim_{(x,y)\to(4,5)}\frac{1}{\sqrt{x+y}+3}=\frac{1}{\sqrt{4+5}+3}=\frac{1}{3+3}=\frac{1}{6}.$