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anonymous

  • one year ago

Help with calculus!

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  1. anonymous
    • one year ago
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    \[\frac{ \lim }{ x \rightarrow-7^{+} }f(x)=-\infty \]Graph this.

  2. jim_thompson5910
    • one year ago
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    how far did you get?

  3. jim_thompson5910
    • one year ago
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    I'm going to start a blank xy graph. Add to the graph what you have so far |dw:1441237470407:dw|

  4. jim_thompson5910
    • one year ago
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    click the pencil on my drawing to be able to draw on it

  5. anonymous
    • one year ago
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    I couldn't figure out where to start.

  6. anonymous
    • one year ago
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    How can you draw infinity?

  7. jim_thompson5910
    • one year ago
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    ok let's start by plotting a point at -7 on the x axis |dw:1441237530533:dw|

  8. jim_thompson5910
    • one year ago
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    then draw a vertical dashed line through -7 |dw:1441237577069:dw|

  9. jim_thompson5910
    • one year ago
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    the limit says "as x gets closer and closer and closer to -7 from the right side, the value of y heads off to negative infinity" so there are a number of ways to do this. You could have something like this |dw:1441237684271:dw|

  10. jim_thompson5910
    • one year ago
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    or something like this |dw:1441237697243:dw|

  11. jim_thompson5910
    • one year ago
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    or maybe something like this |dw:1441237713578:dw| the majority of this graph doesn't matter as long as you approach -infinity as you get closer to -7 from the right side

  12. anonymous
    • one year ago
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    Oh..that makes much more sense. Can you check my answers for some others? I think I might have them wrong.

  13. jim_thompson5910
    • one year ago
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    sure

  14. anonymous
    • one year ago
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    Thanks so much!\[\frac{ \lim }{ x \rightarrow5^{+} }f(x)=-8\]

  15. anonymous
    • one year ago
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    |dw:1441237595205:dw|

  16. anonymous
    • one year ago
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    That's what I put but I don't think it's right...

  17. jim_thompson5910
    • one year ago
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    I'm going to delete the horizontal line |dw:1441237965993:dw|

  18. jim_thompson5910
    • one year ago
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    the idea here is that as we get closer to x = 5 from the right side, the y value gets closer to -8 so here is one way to do it |dw:1441238039952:dw|

  19. jim_thompson5910
    • one year ago
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    here is an alternative way |dw:1441238056519:dw|

  20. anonymous
    • one year ago
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    So there is no line coming from the right?

  21. jim_thompson5910
    • one year ago
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    just like before, the majority of it doesn't matter as long as you end up at y = -8 when you approach from the right side of x = 5

  22. jim_thompson5910
    • one year ago
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    `So there is no line coming from the right?` what do you mean?

  23. anonymous
    • one year ago
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    *left

  24. anonymous
    • one year ago
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    I meant left sorry.

  25. jim_thompson5910
    • one year ago
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    oh, that could be possible, yes you could have |dw:1441238163678:dw| or |dw:1441238177135:dw| and I'm just realizing that your example is perfectly valid. You can approach x = 5 from the right and end up getting closer and closer to y = -8

  26. anonymous
    • one year ago
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    So why do they need a plus next to the 5 under the limit?

  27. jim_thompson5910
    • one year ago
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    that notation means "right hand limit" since we're approaching from the right side of that x value

  28. anonymous
    • one year ago
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    So how does that apply to the graph?

  29. jim_thompson5910
    • one year ago
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    for right hand limits, you don't need to worry about the left side so that's why we could stop at x = 5 and not continue on

  30. jim_thompson5910
    • one year ago
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    it allows us to graph more variety we could have graphs that stop at x = 5 or we could have graphs that continue on

  31. anonymous
    • one year ago
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    Okay I'm going to go with your answer just in case.

  32. anonymous
    • one year ago
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    \[\frac{ \lim }{ x \rightarrow \infty }f(x)=4\]

  33. Zarkon
    • one year ago
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    a little \(\LaTeX\) help for you \[\lim_{ x \to\infty }f(x)=4\] \lim_{ x \to\infty }f(x)=4

  34. anonymous
    • one year ago
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    |dw:1441238256310:dw|

  35. anonymous
    • one year ago
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    What is Latex?

  36. jim_thompson5910
    • one year ago
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    it's a tool to help write math notation

  37. anonymous
    • one year ago
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    Oh...

  38. jim_thompson5910
    • one year ago
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    that graph you drew is correct here is another possible answer for the limit \[\Large \lim_{x\to\infty}f(x) = 4\] |dw:1441238706491:dw|

  39. jim_thompson5910
    • one year ago
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    and another possible answer |dw:1441238735088:dw| the idea is to get closer to that horizontal line as x gets larger

  40. jim_thompson5910
    • one year ago
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    of course, we could cross that horizontal line like this |dw:1441238767240:dw| but notice how we still approach that horizontal line as x gets bigger

  41. anonymous
    • one year ago
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    Okay so if the number under the limit is + or - that number, would I just extend the line like what I did on the second problem?

  42. jim_thompson5910
    • one year ago
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    I'm not sure what you mean

  43. jim_thompson5910
    • one year ago
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    you mean like that \(\Large 5^{+}\) notation?

  44. anonymous
    • one year ago
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    Ya the notation on the top. If it is + and - (left and right) would you extend the line across the graph like what I did in the 2nd problem I gave?

  45. jim_thompson5910
    • one year ago
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    It's possible to extend it through, but also just as valid to stop at that x value. Both interpretations are valid for that one-sided limit If you were talking about a 2-sided limit, then you would have to extend it through because you would be approaching that x value from both sides (left and right)

  46. jim_thompson5910
    • one year ago
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    |dw:1441239084919:dw|

  47. jim_thompson5910
    • one year ago
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    |dw:1441239111134:dw|

  48. jim_thompson5910
    • one year ago
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    |dw:1441239138986:dw|

  49. anonymous
    • one year ago
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    Okay I understood that. Last one:\[\left(\begin{matrix}\lim \\ x \rightarrow-\infty\end{matrix}\right)f(x)=-2\]

  50. anonymous
    • one year ago
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    |dw:1441238954330:dw|

  51. anonymous
    • one year ago
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    Sorry the drawing board was malfunctioning

  52. anonymous
    • one year ago
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    It's suppose to be a straight line

  53. jim_thompson5910
    • one year ago
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    one last thing though, it's possible to evaluate a one-sided limit on a connected curve. Just approach from one side |dw:1441239320678:dw|

  54. anonymous
    • one year ago
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    Ohh ya! I forgot about that.

  55. jim_thompson5910
    • one year ago
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    as for your other problem, as long as you're approaching y = -2 as x heads off to negative infinity, then you have the proper graph another valid answer is this |dw:1441239584767:dw|

  56. jim_thompson5910
    • one year ago
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    something like this is also possible |dw:1441239609022:dw|

  57. anonymous
    • one year ago
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    Okay thanks! That's all I needed. :)

  58. jim_thompson5910
    • one year ago
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    you're welcome

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