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Math Help - Problem Finding A Limit

  1. #1
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    Problem Finding A Limit

    I am just starting Calculus II, and I have thrown everything I know at this thing, to no avail

    \lim_{x \to \infty} (x sin\frac{\Pi}{x})

    Also, is there a guide for [,math] [/.math]? I swear the amount of time it took me to figure it out... you're damn lucky I am going into Computer Science! =P

    Any assistance is greatly appreciated.
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  2. #2
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    Lexington, MA (USA)
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    Hello, wm_hunter!

    It looks suspiciously like: . \lim_{\theta\to0}\frac{\sin\theta}{\theta} \:=\:1


    \lim_{x \to \infty} \left(x\cdot\sin\tfrac{\pi}{x}\right)

    We have: . x\cdot\sin\tfrac{\pi}{x} \:=\:\frac{\sin\frac{\pi}{x}}{\frac{1}{x}} \:=\:\frac{\pi}{\pi}\cdot\frac{\sin\frac{\pi}{x}}{  \frac{1}{x}} \:=\:\pi\cdot\frac{\sin\frac{\pi}{x}}{\frac{\pi}{x  }}

    Now, as x\to\infty,\;\frac{\pi}{x} \to 0


    So we have: . \lim_{\frac{\pi}{x}\to0}\left(\pi\cdot\frac{\sin\f  rac{\pi}{x}}{\frac{\pi}{x}}\right) \:=\:\pi\cdot1 \:=\:\pi


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  3. #3
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    Thank you. I can see the solution and I understand, it does seem a little complicated, but if it wasn't I wouldn't be on here asking for help
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