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Math Help - Limits Problem

  1. #1
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    Limits Problem

    Hi everyone this is what the problem asks:

    Evaluate the Limit and Justify each step by indicating the appropriate Limit Law(s).

    Lim
    X→0 (cos4x)/( 5+2x3 )
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  2. #2
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    Quote Originally Posted by Asuhuman18 View Post
    Hi everyone this is what the problem asks:

    Evaluate the Limit and Justify each step by indicating the appropriate Limit Law(s).

    Lim
    X→0 (cos4x)/( 5+2x3 )
    Is this what you're asking?

    \lim_{x \to 0}\frac{\cos{4x}}{5 + 2x^3}.


    If so, first note that the numerator and denominator are both continuous at x = 0, and the denominator does not \to 0.


    These are the limit laws you will use...

    1. If f(x) is continuous at x = a, then \lim_{x \to a}f(x) = f(a).

    2. \lim_{x \to a}\frac{f(x)}{g(x)} = \frac{\lim_{x \to a}f(x)}{\lim_{x \to a}g(x)} if g(x) does not \to 0.

    Thus

    \lim_{x \to 0}\frac{\cos{4x}}{5 + 2x^3} = \frac{\lim_{x \to 0}\cos{4x}}{\lim_{x \to 0}5 + 2x^3}

     = \frac{\cos{4\cdot 0}}{5 + 2(0)^3}

     = \frac{1}{5}.
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  3. #3
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    yeah thanks a lot man.
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