## cassieforlife5 one year ago Find the limit as x approaches -1

1. cassieforlife5

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2. anonymous

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

3. anonymous

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

4. anonymous

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

5. 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

6. anonymous

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

7. anonymous

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

8. anonymous

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

9. 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

10. anonymous

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

11. anonymous

Kind of like that?

12. cassieforlife5

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

13. anonymous

Might be the lack or the total amount of parenthesis.

14. cassieforlife5

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

15. anonymous

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

16. anonymous

Take a look at that.

17. anonymous

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

18. cassieforlife5

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

19. cassieforlife5

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

20. anonymous

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

21. anonymous

Let's see...

22. anonymous

\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}

23. anonymous

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