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Math Help - limits and converges or diverges.

  1. #1
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    limits and converges or diverges.

    Hello,
    plz try to solve these question.
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  2. #2
    Grand Panjandrum
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    Quote Originally Posted by m777 View Post
    Hello,
    plz try to solve these question.
    Question 1:

    Find the limit: \lim_{x \to 3} \frac{(x-3)}{3x^2-13x+12}

    Factorise the denominator:

    \lim_{x \to 3} \frac{(x-3)}{3x^2-13x+12}=\lim_{x \to 3} \frac{(x-3)}{(x-3)(3x-4)}=\lim_{x \to 3} \frac{1}{3x-4}=1/5


    Question 2:

    Determine if the following series converges or diverges:

    \sum_1^{\infty}4^{k-1}

    As an absolute minimum requirement for convergence of a series, the
    terms must go to zero as the sumation index goes to infinity. This series
    fails this most basic requirement and thus diverges.

    RonL
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