# How can I find the following limit: $\lim\limits_{x\to \:4}\frac{\sqrt{x+5}-3}{x-4}$

Find the following limit:$$\lim\limits_{x\to \:4}\frac{\sqrt{x+5}-3}{x-4}$$

I tried to multiply by the conjugate and it did not work.

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It does work. Multiply by $\frac{\sqrt{x+5}+3}{\sqrt{x+5}+3}$. On top we end up with $x-4$. – André Nicolas Jan 4 '14 at 20:13

If you multiply by the conjugate, you should find

$$\frac{(x + 5) - 9}{(x - 4)(\sqrt{x + 5} + 3)} = \frac{x - 4}{(x - 4)\sqrt{x + 5} + 3}$$

Can you finish?

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thanks it worked. I don't know what happened it must be one of those days that my brain decides to not work. – Erick Jan 4 '14 at 20:21
@Erick Verify your result: you should get: $6^{-1}$ at the end. – user93957 Jan 4 '14 at 21:01
@Aðøbe thank you I got that answer – Erick Jan 5 '14 at 1:09

In case you are familiar with derivatives: this limit is the derivative of $f(x)=\sqrt{x+5}$ at $x=4$.

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no I'm not familiar with derivatives yet. I will soon be,I'm a first year college student. – Erick Jan 5 '14 at 1:12