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adam32885

  • 2 years ago

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

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  1. adam32885
    • 2 years ago
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    Does that make sense or should i draw it?

  2. zepdrix
    • 2 years ago
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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.

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

  4. zepdrix
    • 2 years ago
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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.

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

  6. zepdrix
    • 2 years ago
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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

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

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

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

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

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

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

  13. zepdrix
    • 2 years ago
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    Yay good job \c:/

  14. adam32885
    • 2 years ago
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    thank you!

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