Question

Please help me find the limit:

lim x--> 2
((1/3)-1/sqrt(x))/)x-9)

Answer 1

1/3 - 1/sqrt 2 = (sqrt 2 -3)/3 sqrt 2

divide that by 2-9 = -7

(sqrt 2 -3)/-21

Answer 2

I recognize this as

Lim ( 1/3 - 1/√x)/(x-9) , as x -->9

But for yours x --->2

Most teachers would tell you that the first step in any limit question is to actually sub in the restricted value into your expression.
If you get 0/0, then you have some work to do
If you get an actual real number, that is your answer and you are done!

so if x = 2 we get

(1/3 - 1/√3)/(-7) which is a real number

so that's it! We are done
All you have to do is simplify the answer

= (√3 - 3)/(-21√3)
= (3 - √3)/(21√3) *(√3/√3)
= (√3-1)/21

Answer 3

go with Damon's

I really don't know how my 1/√2 became 1/√3