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March 26, 2017

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By appropriate calculations, show that:
lim r(x)=5c^4
(x->c)

  • ? - ,

    I do not think you have given us the whole problem.

  • Precalc - ,

    In the problem before it says
    r(x)= (x^5 - c^5)/(x-c)
    Maybe it's referring to that?
    Does that help?

  • Precalc - ,

    now we are cooking

  • Precalc - ,

    I wish I could say that's why I don't understand this problem. But sadly, I still don't get it. Haha.

  • Precalc - ,

    Limit:

    Hide steps


    lim_(x->c) (x^5-c^5)/(x-c)
    Factor the numerator and denominator:
    = lim_(x->c) ((c-x) (-c^4-c^3 x-c^2 x^2-c x^3-x^4))
    /((c-x) (-1))
    Cancel terms, assuming c-x!=0
    (c^4+c^3 x+c^2 x^2+c x^3+x^4)
    The limit of c^4+c^3 x+c^2 x^2+c x^3+x^4 as x approaches c is 5 c^4

  • Precalc - ,

    I got that from
    http://www.wolframalpha.com/input/?i=limit+%28x^5+-+c^5%29%2F%28x-c%29++as+x-%3Ec

  • Precalc - ,

    click on "show steps" at upper right of box

  • Precalc - ,

    Thanks so much!

  • Precalc - ,

    I just divided the original numerator by (x-c) and got
    x^4 + cx^3 +c^2x^2 +c^3 x + c^4
    which is 5x^4 or 5c^4 as x-->c

  • Precalc - ,

    Ah. Alright, I think I understand.

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