Solving One-Sided Limit: lim_{x\rightarrow4^{-}} \frac{\sqrt{x}-2}{x-4}

[JennyInTheSky]

Homework Statement

lim$$_{x\rightarrow4^{-}}$$ $$\frac{\sqrt{x}-2}{x-4}$$

Homework Equations

Typical methods used in solving one-sided limit.

The Attempt at a Solution

I plug in something a little bit bigger than four, like 4.0000001 into x, and I get $$\frac{something a little less than zero}{something a little less than zero}$$ to equal 1. But the answer is 1/4. How is this so?

 

[altcmdesc]

Multiply both the top and the bottom by $$\sqrt{x}+2$$. This is called "multiplying by the conjugate" and is pretty standard for dealing with limits involving square roots