Take the 2-minute tour ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

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.

share|improve this question
4  
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 at 20:13
add comment

2 Answers

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?

share|improve this answer
    
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 at 20:21
1  
@Erick Verify your result: you should get: $6^{-1}$ at the end. –  user93957 Jan 4 at 21:01
    
@Aðøbe thank you I got that answer –  Erick Jan 5 at 1:09
add comment

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

share|improve this answer
    
no I'm not familiar with derivatives yet. I will soon be,I'm a first year college student. –  Erick Jan 5 at 1:12
add comment

Your Answer

 
discard

By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.