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anonymous

  • 4 years ago

Does anyone know how to do limits? I have a few homework questions I can't figure out.

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  1. myininaya
    • 4 years ago
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    Post them! :)

  2. anonymous
    • 4 years ago
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    I figured out the answer to the first question. I got the answer 6.

  3. myininaya
    • 4 years ago
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    \[\lim_{x \rightarrow 9}\frac{x-9}{\sqrt{x}-3}\]

  4. myininaya
    • 4 years ago
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    oh you did the first one ok

  5. anonymous
    • 4 years ago
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    The rest I am clueless on. I don't even know where to start.

  6. myininaya
    • 4 years ago
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    \[\lim_{x \rightarrow 0^+}\frac{1}{\sqrt[10](x)}\] first of all the limit is not 2

  7. myininaya
    • 4 years ago
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    plug in even closer values to the right of 0 and you will see the number is getting really freaking huge so the limit is infinity also 1/(x^(1/10)) has a vertical asymptote at x=0 so we know it goes to infinity from the right

  8. anonymous
    • 4 years ago
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    Okay great, I was on the right track because I kept getting a large number also.

  9. myininaya
    • 4 years ago
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    the 2nd one is ln(9) because i remember \[f'(9)=\frac{1}{ \ln(a)} \lim_{x \rightarrow 0}\frac{9^x-9^0}{x-0}=\ln(9)\] where \[f(x)=\frac{a^x}{\ln(a)} \] But i'm not sure if you know this yet

  10. myininaya
    • 4 years ago
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    \[f'(x)=\frac{1}{ \ln(a)} \lim_{x \rightarrow 0}\frac{9^x-9^0}{x-0}=\ln(9)*\]

  11. myininaya
    • 4 years ago
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    and where a=9

  12. anonymous
    • 4 years ago
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    no I have not learned that yet.

  13. myininaya
    • 4 years ago
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    ok then just plug in values really close to 0 on both sides and see if it gets closer to anything

  14. anonymous
    • 4 years ago
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    I am getting close to 2. Am I way off? I am not sure if I am calculating correct.

  15. myininaya
    • 4 years ago
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    ln(9) is close to 2

  16. myininaya
    • 4 years ago
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    that is pretty close

  17. myininaya
    • 4 years ago
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    2.2 is a better number

  18. anonymous
    • 4 years ago
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    yes, I had 2.1972. We have only had whole number answers in our homework so far.

  19. myininaya
    • 4 years ago
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    well limits don't have to be whole numbers the numerical approach is okay but it only gives you approximations so if you want to put 2 i think that is close enough

  20. anonymous
    • 4 years ago
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    Thank you so much! I think I kind of knew what I was doing on these problems but didn't trust myself. Can you go over the 4th question with me.

  21. myininaya
    • 4 years ago
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    I would make a piecewise function here

  22. myininaya
    • 4 years ago
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    well you know what lets not do that

  23. anonymous
    • 4 years ago
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    I don't know what a piecewise function is.

  24. myininaya
    • 4 years ago
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    lets just say this \[f(x)=\frac{(x-8)(x+17)}{x-8}=\frac{x^2+17x-8x- 136}{x-8}=\frac{x^2+9x-136}{x-8}\]

  25. myininaya
    • 4 years ago
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    f is not defined at x=8 but tell me what happens as x->8 ?

  26. anonymous
    • 4 years ago
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    25

  27. myininaya
    • 4 years ago
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    that's right!

  28. myininaya
    • 4 years ago
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    you know how i came up with my function?

  29. anonymous
    • 4 years ago
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    So would I write down the function exists? I don't understand how to answer what they are asking. And yes please explain how you came up with the function.

  30. myininaya
    • 4 years ago
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    they want you to find a function f(x)=blah such that f(8) does not exist and as x->8, f->25

  31. myininaya
    • 4 years ago
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    so I knew I wanted this from the f(8) doesn't exist part \[f(x)=\frac{something}{x-8}\]

  32. myininaya
    • 4 years ago
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    but then i also since i wanted the limit to exist at x=8 so that means i wanted the x-8 on bottom to cancel out with one on top \[f(x)=\frac{(x-8)(something)}{x-8}\] but we still need a little more something on top since we don't just want 1 because we want as x->8, f->25

  33. myininaya
    • 4 years ago
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    so since the (x-8)/(x-8)->1 as x->8 we only need that something to go to 25 as x->8

  34. myininaya
    • 4 years ago
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    so I knew 8+17=25

  35. myininaya
    • 4 years ago
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    if x->8 then x+17->25

  36. myininaya
    • 4 years ago
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    since 8+17 is 25

  37. myininaya
    • 4 years ago
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    \[f(x)=\frac{(x-8)(x+17)}{x-8}\]

  38. anonymous
    • 4 years ago
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    I would have never figured that out. Thank you so much. And your explanation is awesome! You are one smart cookie! Too bad I couldn't have you tutor me for the res of the semester. It's very hard taking a math class online.

  39. myininaya
    • 4 years ago
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    i bet it is just keep coming back to openstudy and i or someone else will be here to help you out

  40. myininaya
    • 4 years ago
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    people are addicted to this site

  41. anonymous
    • 4 years ago
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    Well you are wonderful! You made my day! Thank you again!

  42. myininaya
    • 4 years ago
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    have a good day

  43. myininaya
    • 4 years ago
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    and thanks and welcome lol

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