anonymous
  • anonymous
Limit Help lim as x approches -4 ((1/4)+(1/x)/(4+x)
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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jamiebookeater
  • jamiebookeater
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anonymous
  • anonymous
Does that make sense or should i draw it?
zepdrix
  • zepdrix
\[\huge \lim_{x \rightarrow -4}\frac{\frac{1}{4}+\frac{1}{x}}{4+x}\] It makes sense c: But I wanted to format it anway, heh.
anonymous
  • anonymous
yes that is it we have only covered limit laws so far.

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zepdrix
  • zepdrix
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.
anonymous
  • anonymous
My "silly" math skills are slowly coming back I took precalc 5 years ago
zepdrix
  • zepdrix
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
zepdrix
  • zepdrix
\[\huge \lim_{x \rightarrow -4}\frac{\left(\frac{4+x}{4x}\right)}{4+x}\]
anonymous
  • anonymous
okay so now can the denominator of the whole problem cancel out the numerator on the top leaving 4x?
zepdrix
  • zepdrix
oh well, um let's be careful a sec :)
zepdrix
  • zepdrix
We can write our problem like this,\[\large \lim_{x \rightarrow -4}\frac{\left(\frac{4+x}{4x}\right)}{4+x} \qquad =\qquad \lim_{x \rightarrow -4} \left(\frac{4+x}{4x}\right)\cdot \frac{1}{4+x}\]
zepdrix
  • zepdrix
Maybe this will help you see what's going on better. So what happens when we cancel those out? :O
anonymous
  • anonymous
it is 1/4x so the lim will be -1/16
zepdrix
  • zepdrix
Yay good job \c:/
anonymous
  • anonymous
thank you!

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