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Math Help - Squeeze Theorem

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    Squeeze Theorem

    Use the squeeze theorem to show that lim as n goes to infinity arctan(n^2)/Sqrt(n) = 0
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Link88 View Post
    Use the squeeze theorem to show that lim as n goes to infinity arctan(n^2)/Sqrt(n) = 0
    note that - \frac {\pi}2 \le \arctan x \le \frac {\pi}2 for all x, thus we have

    - \frac {\pi}{2 \sqrt{n}} \le \frac {\arctan (n^2)}{\sqrt{n}} \le \frac {\pi}{2 \sqrt{n}}

    can you finish?

    (also, note that we can make the left side zero, but this looks nice for symmetry )
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    Im just kinda confused on how you end up with zero from that : /
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by Link88 View Post
    Im just kinda confused on how you end up with zero from that : /
    the next step is to take the limit of the system...

    \lim_{n \to \infty} - \frac {\pi}{2 \sqrt{n}} \le \lim_{n \to \infty} \frac {\arctan (n^2)}{\sqrt{n}} \le \lim_{n \to \infty} \frac {\pi}{2 \sqrt{n}}


    which means?
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    k gotcha i see how it goes to zero
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