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Math Help - Limits

  1. #1
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    Question Limits

    How does

    lim (x --> 0) [tan^2(4x)] / (2x)^2

    equal 4?
    Last edited by agl89; January 29th 2014 at 03:05 PM.
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  2. #2
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    Re: Limits

    It doesn't unless you wrote the problem wrong.
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  3. #3
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    Re: Limits

    Quote Originally Posted by SlipEternal View Post
    It doesn't unless you wrote the problem wrong.
    I did... I have corrected my mistake.
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  4. #4
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    Re: Limits

    Then, are you familiar with the limit:

    Limit (x -> 0) sin x / x = 1?

    Now, tan^2(4x) / (2x)^2 = [sin(4x)/(4x)] * [sin(4x)/(4x)] * [4/cos^2(4x)]

    Use the product rule. As x approaches zero, so does 4x, so the limit can be broken up as the product of three limits. The first two will evaluate to 1 and the last will evaluate to 4.
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  5. #5
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    Re: Limits

    Quote Originally Posted by SlipEternal View Post
    Then, are you familiar with the limit:

    Limit (x -> 0) sin x / x = 1?

    Now, tan^2(4x) / (2x)^2 = [sin(4x)/(4x)] * [sin(4x)/(4x)] * [4/cos^2(4x)]

    Use the product rule. As x approaches zero, so does 4x, so the limit can be broken up as the product of three limits. The first two will evaluate to 1 and the last will evaluate to 4.
    Got it. Thank you.
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