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Math Help - Prove (Limit)

  1. #1
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    Prove (Limit)

    Can someone help me prove this?

    sqrt(x)e^sin(pi/x) = 0 , x--> 0+ (from the right)
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  2. #2
    MHF Contributor Drexel28's Avatar
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    Quote Originally Posted by l flipboi l View Post
    Can someone help me prove this?

    sqrt(x)e^sin(pi/x) = 0 , x--> 0+ (from the right)
    \left|\sqrt{x}e^{\sin\left(\frac{\pi}{x}\right)}\r  ight|\leqslant e\sqrt{x}
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  3. #3
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    sin(\pi/x) lies between -1 and 1 for all x so e^{sin(\pi/x)} lies between e^{-1} and e^1 for all x. The important point is that it is bounded. Since \sqrt{x} goes to 0, the limit of this function is 0.
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