cassieforlife5
  • cassieforlife5
Find the limit as x approaches -1
Mathematics
jamiebookeater
  • jamiebookeater
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cassieforlife5
  • cassieforlife5
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Jhannybean
  • Jhannybean
\[\large \lim_{x\rightarrow -1} \frac{\dfrac{1}{\sqrt{1+x}}-1}{x}\]
Jhannybean
  • Jhannybean
Well, let's try a two sided limit approach.

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Jhannybean
  • Jhannybean
So the first would be \(x\rightarrow (-1)^-\) and the second approach would be \(x\rightarrow (-1)^+\)
cassieforlife5
  • cassieforlife5
okay I normally plug these into the calculator and use the table, but I'm not sure how I should insert it into the calculator
Jhannybean
  • Jhannybean
Well, you simply need to find a number that is incrementally smaller than -1 from the left,...like.... -0.9999
Jhannybean
  • Jhannybean
Then from the right, you could choose a number that incrementally bigger than -1, like... -1.00001
Jhannybean
  • Jhannybean
The value you get will essentially tell you whether your limit is approaching \(+\infty\) or \(-\infty\)
cassieforlife5
  • cassieforlife5
I'm having trouble including the actual equation. Now i'm putting in: \[\left( \left( 1\div \sqrt{1+\chi} \right))\div \chi \right)-(1\div \chi)\] But I don't think it's right
Jhannybean
  • Jhannybean
So how I would input into the calculator: \[\large \frac{((1)/(\sqrt{1-0.99999} ) -1))}{(-0.99999)}\]
Jhannybean
  • Jhannybean
Kind of like that?
cassieforlife5
  • cassieforlife5
it says error which is the problem that I had before as well :( I've tried phrasing the equation differently too
Jhannybean
  • Jhannybean
Might be the lack or the total amount of parenthesis.
cassieforlife5
  • cassieforlife5
hmm i don't know. I can't think of any other way to insert it though
Jhannybean
  • Jhannybean
I'll show you in a second, let me just upload a picture so I can insert it here.
Jhannybean
  • Jhannybean
Take a look at that.
Jhannybean
  • Jhannybean
Hm.. as @iambatman stated earlier, what if we were to simplify the function a little?
cassieforlife5
  • cassieforlife5
okay I got an answer from that and I'm working on a few of the other values
cassieforlife5
  • cassieforlife5
wait wouldn't you need another parentheses after the -1? or is that what was messing me up before
Jhannybean
  • Jhannybean
yeah that's why I'm figuring out how to make this equation more manageable.
Jhannybean
  • Jhannybean
Let's see...
Jhannybean
  • Jhannybean
\[\begin{align} \lim_{x\rightarrow (-1)^-} \frac{\dfrac{1}{\sqrt{1+x}}-1}{x} \qquad &\implies\lim_{x\rightarrow (-1)^-} \frac{1-\sqrt{1+x}}{x\sqrt{1+x}} \\ & \implies \lim_{x\rightarrow (-1)^-} \frac{1}{x\sqrt{1+x}} -\frac{1}{x} \end{align} \]
Jhannybean
  • Jhannybean
I've got to head off, good luck figuring this out!

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