## anonymous one year ago Applied Calculus 1 question. How would you go about finding the limit of the following function without using a calculator?

1. anonymous

$\lim_{x \rightarrow 5} \frac{ \sqrt{x+4}-3 }{ x-5 }$

2. zepdrix

Hey Mojo :) You would start by applying an algebraic trick, multiplying the top and bottom by the conjugate of the numerator.

3. zepdrix

$\large\rm \lim_{x\to5}\frac{\sqrt{x+4}-3}{x-5}\color{royalblue}{\left(\frac{\sqrt{x+4}+3}{\sqrt{x+4}+3}\right)}$

4. anonymous

yup did that got $\lim_{x \rightarrow 5}\frac{ x+1 }{ (x-5)(\sqrt{x+4}-3) }$

5. anonymous

sorry mean to have +3 not negative

6. zepdrix

Hmmm that numerator looks a big messed up :O

7. anonymous

oooh i see what id id wrong lol

8. zepdrix

Recall that when you multiply conjugates, you get the difference of squares. You have to square that 3! :)

9. anonymous

thanks for pointing that out

10. anonymous

yay the got an answer of 1/9

11. anonymous

thanks again