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  1. #1
    Junior Member
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    Question

    Hi everybody,

    I have two questions:

    1)- $\displaystyle \lim_{x\to 0}\frac{sinKx}{x}= K ??? \$

    2)-$\displaystyle \lim_{x\to 0} \frac{1-cosKx}{x^2}= \frac{K}{2} ???$

    Thank you anyway.
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  2. #2
    MHF Contributor

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    Quote Originally Posted by lehder View Post
    Hi everybody,

    I have two questions:

    1)- $\displaystyle \lim_{x\to 0}\frac{sinKx}{x}= K ??? \$

    2)-$\displaystyle \lim_{x\to 0} \frac{1-cosKx}{x^2}= \frac{K}{2} ???$

    Thank you anyway.
    As before, use L'Hopital's rule. The derivative of sin(Kx) is K cos(Kx) and the derivative of x is 1. The limit is $\displaystyle \lim_{x\to 0}K cos(Kx)$.

    The derivative of 1- cos(Kx) is K sin(Kx) and the derivative of $\displaystyle x^2$ is 2x. Since those both go to 0, do it again.
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