Find the limi as xy approaches zero zero of (x^(2)+y^(2))/(x^(2)+y(^2)+1)^(.5)-1

Question

Please show work so I can follow along. Thank you!

Answer 1

Mandy, to show the work in determining the limit as xy approaches (0,0). Note: It looks like the limit does exist because it doesn't approach a number divided by zero.

 

lim→(0,0) (x^2+y^2)/(x^2+y^2+1)^(.5)-1=(0^2+0^2)/(0^2+0^2+1)^(.5)-1=0/(0+1)^(.5)-1 =0/1^(.5)-1=0-1=-1

 

Hope this helps.