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Math Help - Question about limits

  1. #1
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    Question about limits

    the question involves lim x->0 (x cot x)
    Sorry if the notation isnt so good but its the limit of x as it approaches 0

    the book goes on to prove that the answer is 1 by doing the following steps that confuse me:

    lim(x cot x) = lim(x (cosx/sin x)) = lim ((x/sin x)cos x)

    =(lim(x/sin x))(lim cos x)

    =((lim cos x)/(lim (sin x/x))) = 1/1 = 1


    the bold part highlights my confusion, I dont understand what happened there, why the denominator went to x, and was removed by cos x

    its very possible its just a simple mistake on my part, but for some reason im just lost.

    thanks, and sorry about the notation, I dont know how to use the forum that well
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  2. #2
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    Re: Question about limits

    Quote Originally Posted by NecroWinter View Post
    the question involves lim x->0 (x cot x)
    Sorry if the notation isnt so good but its the limit of x as it approaches 0

    the book goes on to prove that the answer is 1 by doing the following steps that confuse me:

    lim(x cot x) = lim(x (cosx/sin x)) = lim ((x/sin x)cos x)

    =(lim(x/sin x))(lim cos x)

    =((lim cos x)/(lim (sin x/x))) = 1/1 = 1


    the bold part highlights my confusion, I dont understand what happened there, why the denominator went to x, and was removed by cos x

    its very possible its just a simple mistake on my part, but for some reason im just lost.

    thanks, and sorry about the notation, I dont know how to use the forum that well
    x\cot{x} = x\cdot \frac{\cos{x}}{\sin{x}} = \frac{x}{\sin{x}} \cdot \cos{x} = \cos{x} \cdot \frac{x}{\sin{x}} = \cos{x} \div \frac{\sin{x}}{x}
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  3. #3
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    Clarksville, ARk
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    Re: Question about limits

    x\frac{\cos(x)}{\sin(x)}=\frac{x\cos(x)}{\sin(x)}=  \frac{x}{\sin(x)}\cos(x)
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