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Math Help - Limit x-> 0

  1. #1
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    Limit x-> 0

    lim x->0 ( X2-x+sinx)/(2x)

    I can't seem to figure this one out, thanks
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  2. #2
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    Hello, Soulwraith56!

    You're expected to know that: . \lim_{\theta\to0} \frac{\sin\theta}{\theta} \:=\:1



    \lim_{x\to0}\frac{x^2-x+\sin x}{2x}

    We have: . \lim_{x\to0}\left(\frac{x^2}{2x} - \frac{x}{2x} + \frac{\sin x}{2x}\right)

    . . =\;\;\lim_{x\to0}\left(\frac{1}{2}x - \frac{1}{2} + \frac{1}{2}\!\cdot\!\frac{\sin x}{x}\right) \;\;=\;\;\frac{1}{2}(0) - \frac{1}{2} + \frac{1}{2}(1) \;\;=\;\;0

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