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Math Help - limit to infinity !!

  1. #1
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    limit to infinity !!

    what is the value of the limit as the function cosx/x tends to infinity??...
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by anme View Post
    what is the value of the limit as the function cosx/x tends to infinity??...
    zero.

    use the squeeze theorem
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  3. #3
    Rhymes with Orange Chris L T521's Avatar
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    Quote Originally Posted by anme View Post
    what is the value of the limit as the function cosx/x tends to infinity??...
    The squeeze theorem is necessary.

    Recall that -1\leqslant\cos x\leqslant 1.

    Modifiying the inequality, we see that -\frac{1}{x}\leqslant\frac{\cos x}{x}\leqslant\frac{1}{x}

    Taking the limit of each of these terms as x approaches infinity, we see that

    \lim_{x\to\infty}-\frac{1}{x}\leqslant\lim_{x\to\infty}\frac{\cos x}{x}\leqslant\lim_{x\to\infty}\frac{1}{x}\implies 0\leqslant\lim_{x\to\infty}\frac{\cos x}{x}\leqslant0.

    This then suggests that \color{red}\boxed{\lim_{x\to\infty}\frac{\cos x}{x}=0}

    Does this make sense?
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  4. #4
    Like a stone-audioslave ADARSH's Avatar
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    Directly put the Limit
    Hint:Since cos(x) is somewhere in beteen +/- 1 and x is infinity
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