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

Question

anonymous · Answer

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

zepdrix · Answer

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

zepdrix · Answer

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

anonymous · Answer

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

anonymous · Answer

sorry mean to have +3 not negative

zepdrix · Answer

Hmmm that numerator looks a big messed up :O

anonymous · Answer

oooh i see what id id wrong lol

zepdrix · Answer

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

anonymous · Answer

thanks for pointing that out

anonymous · Answer

yay the got an answer of 1/9

anonymous · Answer

thanks again