Question

How do you find the lim (-7x^2-8y^2)/(sqrt(-7x^2-8y^2+1)-1)
(x,y)->(0,0)? The hint is to rationalize the denominator but I have tried this and it only seems to make things complicated.

Answer 1

Multiple numerator and denominator by conjugate. I'll work it out now.

Answer 2

I tried that but it made things complicated because of the -1. Did I do something wrong?

Answer 3

I got...\[\sqrt{1}+1\]

Answer 4

2

Answer 5

:)

Answer 6

Perfect!

Answer 7

ur left with sqrt(-7x^2 - 8x^2 + 1) + 1 , so solving for the limit yields 2