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Math Help - Squeeze theorem

  1. #1
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    Exclamation Squeeze theorem

    Use the squeeze theorem to solve the limit.

    limit when x approaches 0

    x^4 cos (3/x)
    Last edited by mr fantastic; October 8th 2009 at 04:29 PM. Reason: Changed post title
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  2. #2
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    Quote Originally Posted by math123456 View Post
    Use the squeeze theorem to solve the limit.

    limit when x approaches 0

    x^4 cos (3/x)
    since -1 \le \cos\left(\frac{3}{x}\right) \le 1 and x^4 \ge 0 ,

    x^4(-1) \le x^4 \cos\left(\frac{3}{x}\right) \le x^4(1)

    squeeze it.
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  3. #3
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    Exclamation squeeze theorem

    I am not sure what you mean by this. Can you help me solve it.
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  4. #4
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    Quote Originally Posted by skeeter View Post
    since -1 \le \cos\left(\frac{3}{x}\right) \le 1 and x^4 \ge 0 ,

    x^4(-1) \le x^4 \cos\left(\frac{3}{x}\right) \le x^4(1)

    squeeze it.
    Quote Originally Posted by math123456 View Post
    I am not sure what you mean by this. Can you help me solve it.
    What is the limit of each side as x --> 0? Therefore ....
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