anonymous
  • anonymous
Applied Calculus 1 question. How would you go about finding the limit of the following function without using a calculator?
Mathematics
  • Stacey Warren - Expert brainly.com
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\lim_{x \rightarrow 5} \frac{ \sqrt{x+4}-3 }{ x-5 }\]
zepdrix
  • zepdrix
Hey Mojo :) You would start by applying an algebraic trick, multiplying the top and bottom by the `conjugate` of the numerator.
zepdrix
  • zepdrix
\[\large\rm \lim_{x\to5}\frac{\sqrt{x+4}-3}{x-5}\color{royalblue}{\left(\frac{\sqrt{x+4}+3}{\sqrt{x+4}+3}\right)}\]

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anonymous
  • anonymous
yup did that got \[\lim_{x \rightarrow 5}\frac{ x+1 }{ (x-5)(\sqrt{x+4}-3) }\]
anonymous
  • anonymous
sorry mean to have +3 not negative
zepdrix
  • zepdrix
Hmmm that numerator looks a big messed up :O
anonymous
  • anonymous
oooh i see what id id wrong lol
zepdrix
  • zepdrix
Recall that when you multiply conjugates, you get the difference of `squares`. You have to square that 3! :)
anonymous
  • anonymous
thanks for pointing that out
anonymous
  • anonymous
yay the got an answer of 1/9
anonymous
  • anonymous
thanks again

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