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adam32885

Limit Help lim as x approches -4 ((1/4)+(1/x)/(4+x)

  • one year ago
  • one year ago

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  1. adam32885
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    Does that make sense or should i draw it?

    • one year ago
  2. zepdrix
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    \[\huge \lim_{x \rightarrow -4}\frac{\frac{1}{4}+\frac{1}{x}}{4+x}\] It makes sense c: But I wanted to format it anway, heh.

    • one year ago
  3. adam32885
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    yes that is it we have only covered limit laws so far.

    • one year ago
  4. zepdrix
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    Ok this one isn't too bad.. it's just to test your silly math skills. So first let's get a common denominator on top.

    • one year ago
  5. adam32885
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    My "silly" math skills are slowly coming back I took precalc 5 years ago

    • one year ago
  6. zepdrix
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    Remember how to get a common denominator? We'll just multiply them both together, that will be the easiest way to do it. So our common denominator will be 4x. It looks like the first term is missing an x, while the second term is missing a 4, So let's fix that. \[\huge \lim_{x \rightarrow -4}\frac{\left(\color{cornflowerblue}{\frac{x}{x}}\cdot \frac{1}{4}\right)+\left(\frac{1}{x}\cdot \color{cornflowerblue}{\frac{4}{4}}\right)}{4+x}\]Understand that part ok? :D

    • one year ago
  7. zepdrix
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    \[\huge \lim_{x \rightarrow -4}\frac{\left(\frac{4+x}{4x}\right)}{4+x}\]

    • one year ago
  8. adam32885
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    okay so now can the denominator of the whole problem cancel out the numerator on the top leaving 4x?

    • one year ago
  9. zepdrix
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    oh well, um let's be careful a sec :)

    • one year ago
  10. zepdrix
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    We can write our problem like this,\[\large \lim_{x \rightarrow -4}\frac{\left(\frac{4+x}{4x}\right)}{4+x} \qquad =\qquad \lim_{x \rightarrow -4} \left(\frac{4+x}{4x}\right)\cdot \frac{1}{4+x}\]

    • one year ago
  11. zepdrix
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    Maybe this will help you see what's going on better. So what happens when we cancel those out? :O

    • one year ago
  12. adam32885
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    it is 1/4x so the lim will be -1/16

    • one year ago
  13. zepdrix
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    Yay good job \c:/

    • one year ago
  14. adam32885
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    thank you!

    • one year ago
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