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cassieforlife5

  • one year ago

Find the limit as x approaches -1

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  1. cassieforlife5
    • one year ago
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    |dw:1444032099173:dw|

  2. Jhannybean
    • one year ago
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    \[\large \lim_{x\rightarrow -1} \frac{\dfrac{1}{\sqrt{1+x}}-1}{x}\]

  3. Jhannybean
    • one year ago
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    Well, let's try a two sided limit approach.

  4. Jhannybean
    • one year ago
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    So the first would be \(x\rightarrow (-1)^-\) and the second approach would be \(x\rightarrow (-1)^+\)

  5. cassieforlife5
    • one year ago
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    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. Jhannybean
    • one year ago
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    Well, you simply need to find a number that is incrementally smaller than -1 from the left,...like.... -0.9999

  7. Jhannybean
    • one year ago
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    Then from the right, you could choose a number that incrementally bigger than -1, like... -1.00001

  8. Jhannybean
    • one year ago
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    The value you get will essentially tell you whether your limit is approaching \(+\infty\) or \(-\infty\)

  9. cassieforlife5
    • one year ago
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    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. Jhannybean
    • one year ago
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    So how I would input into the calculator: \[\large \frac{((1)/(\sqrt{1-0.99999} ) -1))}{(-0.99999)}\]

  11. Jhannybean
    • one year ago
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    Kind of like that?

  12. cassieforlife5
    • one year ago
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    it says error which is the problem that I had before as well :( I've tried phrasing the equation differently too

  13. Jhannybean
    • one year ago
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    Might be the lack or the total amount of parenthesis.

  14. cassieforlife5
    • one year ago
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    hmm i don't know. I can't think of any other way to insert it though

  15. Jhannybean
    • one year ago
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    I'll show you in a second, let me just upload a picture so I can insert it here.

  16. Jhannybean
    • one year ago
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    Take a look at that.

  17. Jhannybean
    • one year ago
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    Hm.. as @iambatman stated earlier, what if we were to simplify the function a little?

  18. cassieforlife5
    • one year ago
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    okay I got an answer from that and I'm working on a few of the other values

  19. cassieforlife5
    • one year ago
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    wait wouldn't you need another parentheses after the -1? or is that what was messing me up before

  20. Jhannybean
    • one year ago
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    yeah that's why I'm figuring out how to make this equation more manageable.

  21. Jhannybean
    • one year ago
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    Let's see...

  22. Jhannybean
    • one year ago
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    \[\begin{align} \lim_{x\rightarrow (-1)^-} \frac{\dfrac{1}{\sqrt{1+x}}-1}{x} \qquad &\implies\lim_{x\rightarrow (-1)^-} \frac{1-\sqrt{1+x}}{x\sqrt{1+x}} \\ & \implies \lim_{x\rightarrow (-1)^-} \frac{1}{x\sqrt{1+x}} -\frac{1}{x} \end{align} \]

  23. Jhannybean
    • one year ago
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    I've got to head off, good luck figuring this out!

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