lim Square root of (x)- 3 over x-9

Question

x->9

thanks.

Answer 1

[x^.5 -3] / (x-9) is of course 0/0 so use
derivative of top/derivative of bottom
= [.5 x^-.5 ] /1
= as x-->9
[.5/3 ]/1
= .16666666666666.......
check
let x = 8.9
x^.5 -3 = -.0167
8.9-9 = -.1
ratio = .167
let x = 8.99
x^.5 - 3 = -.00167
8.99 - 9 = .01
ratio = .167
sure enough