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anonymous

  • one year ago

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

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  1. anonymous
    • one year ago
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    \[\lim_{x \rightarrow 5} \frac{ \sqrt{x+4}-3 }{ x-5 }\]

  2. zepdrix
    • one year ago
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    Hey Mojo :) You would start by applying an algebraic trick, multiplying the top and bottom by the `conjugate` of the numerator.

  3. zepdrix
    • one year ago
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    \[\large\rm \lim_{x\to5}\frac{\sqrt{x+4}-3}{x-5}\color{royalblue}{\left(\frac{\sqrt{x+4}+3}{\sqrt{x+4}+3}\right)}\]

  4. anonymous
    • one year ago
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    yup did that got \[\lim_{x \rightarrow 5}\frac{ x+1 }{ (x-5)(\sqrt{x+4}-3) }\]

  5. anonymous
    • one year ago
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    sorry mean to have +3 not negative

  6. zepdrix
    • one year ago
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    Hmmm that numerator looks a big messed up :O

  7. anonymous
    • one year ago
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    oooh i see what id id wrong lol

  8. zepdrix
    • one year ago
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    Recall that when you multiply conjugates, you get the difference of `squares`. You have to square that 3! :)

  9. anonymous
    • one year ago
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    thanks for pointing that out

  10. anonymous
    • one year ago
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    yay the got an answer of 1/9

  11. anonymous
    • one year ago
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    thanks again

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