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Math Help - Using limit laws to prove a limit

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    Using limit laws to prove a limit

    Using limit laws prove that:

    The limit as x approaches 0 of the function (x^4)(sin(1/x))=0

    Please state each law used.
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    Re: Using limit laws to prove a limit

    Quote Originally Posted by devilray1018 View Post
    Using limit laws prove that:

    The limit as x approaches 0 of the function (x^4)(sin(1/x))=0

    Please state each law used.
    The limit of a product is equal to the product of the limits. \displaystyle \begin{align*} \lim_{x \to 0}\sin{\frac{1}{x}} \end{align*} doesn't exist, but the function oscillates between -1 and 1. \displaystyle \begin{align*} \lim_{x \to 0}x^4 = 0 \end{align*}. The product of 0 with something that oscillates is still 0.
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