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Math Help - Limits of Trig Functions

  1. #1
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    Limits of Trig Functions

    ...again.


    1. lim sec x - 1 / xsecx (x--->0)
    2. lim (1-cosx)^2 / x (x--->0)
    3. lim 5x / sin 4x (x--->0)

    Sometimes I get these, and sometimes I don't. Is there any specific way I'm supposed to look at these trig. functions? I keep getting marked off for the way I've been solving them. =/

    Any help is greatly appreciated!
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  2. #2
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    Krizalid's Avatar
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    Quote Originally Posted by alreadyinuse View Post
    1. lim sec x - 1 / xsecx (x--->0)
    2. lim (1-cosx)^2 / x (x--->0)
    3. lim 5x / sin 4x (x--->0)
    1) Multiply up & down by \cos x

    2) Use that (1-\cos x)^2=(1-\cos x)(1-\cos x)

    3) Classic, there're many types of these ones, just use the fact \lim_{x\to0}\frac{\sin x}x=1
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  3. #3
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    Thanks!

    The last one, I know I have to use sin x/x = 1, but every time I use that to justify my answer...I get marked off. ...
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  4. #4
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    Quote Originally Posted by alreadyinuse View Post
    3. lim 5x / sin 4x (x--->0)
    \lim_{x\to0}\frac{5x}{\sin4x}=\frac54\lim_{x\to0}\  frac{4x}{\sin4x}

    That's all
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  5. #5
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    That's exactly what I did on my last quiz and she still marked me off. Hmmm. I think I'll just ask her exactly what she wants from me, heh.

    Thanks a ton!
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