Find the limit as x approaches -1

- cassieforlife5

Find the limit as x approaches -1

- jamiebookeater

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- cassieforlife5

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- Jhannybean

\[\large \lim_{x\rightarrow -1} \frac{\dfrac{1}{\sqrt{1+x}}-1}{x}\]

- Jhannybean

Well, let's try a two sided limit approach.

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## More answers

- Jhannybean

So the first would be \(x\rightarrow (-1)^-\) and the second approach would be \(x\rightarrow (-1)^+\)

- 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

Well, you simply need to find a number that is incrementally smaller than -1 from the left,...like.... -0.9999

- Jhannybean

Then from the right, you could choose a number that incrementally bigger than -1, like... -1.00001

- Jhannybean

The value you get will essentially tell you whether your limit is approaching \(+\infty\) or \(-\infty\)

- 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

So how I would input into the calculator: \[\large \frac{((1)/(\sqrt{1-0.99999} ) -1))}{(-0.99999)}\]

- Jhannybean

Kind of like that?

- cassieforlife5

it says error which is the problem that I had before as well :(
I've tried phrasing the equation differently too

- Jhannybean

Might be the lack or the total amount of parenthesis.

- cassieforlife5

hmm i don't know. I can't think of any other way to insert it though

- Jhannybean

I'll show you in a second, let me just upload a picture so I can insert it here.

- Jhannybean

Take a look at that.

##### 1 Attachment

- Jhannybean

Hm.. as @iambatman stated earlier, what if we were to simplify the function a little?

- cassieforlife5

okay I got an answer from that and I'm working on a few of the other values

- cassieforlife5

wait wouldn't you need another parentheses after the -1? or is that what was messing me up before

- Jhannybean

yeah that's why I'm figuring out how to make this equation more manageable.

- Jhannybean

Let's see...

- 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

I've got to head off, good luck figuring this out!

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