Limit of x/(sqrt(1+3x)-1) as x approaches 0

[KiwiKid]

Homework Statement

Find the limit of x/(sqrt(1+3x)-1) as x approaches 0.

Homework Equations

The limit laws.

The Attempt at a Solution

I'm really stuck. I've tried multiplying all of it by (sqrt(1+3x)+1)/(sqrt(1+3x)+1), but that didn't work. I can't seem to get that 0 out of the denominator. What am I missing?

 

[micromass]

What did you get after doing that multiplication?

 

[KiwiKid]

What did you get after doing that multiplication?

(x(sqrt(1+3x)+1))/3x. Or (x*sqrt(1+3x)+x)/3x if you will. But the 3x still goes to 0, so that doesn't seem to work.

 

[micromass]

(x(sqrt(1+3x)+1))/3x. Or (x*sqrt(1+3x)+x)/3x if you will. But the 3x still goes to 0, so that doesn't seem to work.

You can simplify it: you have x is numerator and denominator.

 

[KiwiKid]

You can simplify it: you have x is numerator and denominator.

Oh, wait! I realize what I did wrong. I'd seen that, yes, but made the stupid mistake of presuming that there would still be '2x' (instead of '3') left in the denominator. *slaps head* Thank you, micro.