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Math Help - limit help please!!

  1. #1
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    limit help please!!

    how do i prove lim (x^2) * (cos(1/x)) = 0
    as x approaches 0
    please can you list the steps
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  2. #2
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    Re: limit help please!!

    Note that cos(1/x) is bounded, no matter how rapidly it oscilates when x is near 0. Then apply the squeeze theorem.
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  3. #3
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    Re: limit help please!!

    Quote Originally Posted by johnsomeone View Post
    Note that cos(1/x) is bounded, no matter how rapidly it oscilates when x is near 0. Then apply the squeeze theorem.
    Or just the fact that the product of a function that goes to 0 with a bounded function is 0.
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  4. #4
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    Re: limit help please!!

    ok then how do i prove it on a 10 point free response question. can someone please list out the steps so that i can understand for future tests because i only got 3/10 for this question on the test
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    Re: limit help please!!

    Quote Originally Posted by ubhutto View Post
    ok then how do i prove it on a 10 point free response question. can someone please list out the steps so that i can understand for future tests because i only got 3/10 for this question on the test
    -1\le\cos\left(\tfrac{1}{x}\right)\le 1 thus -x^2\le x^2\cos\left(\tfrac{1}{x}\right)\le x^2

    Both \lim _{x \to 0}  - x^2  = 0 = \lim _{x \to 0} x^2 .
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