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Math Help - basic calculus

  1. #1
    Junior Member turbod15b's Avatar
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    basic calculus

    can anyone answer these for me please



    thanks
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  2. #2
    Senior Member
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    Hello buddy

    Quote Originally Posted by turbod15b View Post
    can anyone answer these for me please



    thanks
    a) = 3*1 = 3

    b) = 5*e^{5t}+(-2)e^{-2t} = 5e^{5t}-2e^{-2t}

    c) = 2x-5

    d) = \frac{d}{dt} sin(t)/cos(t) = \frac{1}{cos^2(t)}

    This is because

    \frac{d}{dt} sin(t)/cos(t) = sin(t)*cos^{-1}(t)

    = cos(t)*cos(t)^{-1} + (-1)(-1) sin(x)*cos(x)^{-2}*sin(x)

    = 1 + sin^2(t)cos^{2}(t) = 1+tan^2(x) = \frac{1}{cos^2(t)}

    Im lazy, i wrote t instead of theta. Sorry for that.


    not sure, is  \frac{1}{cos^2(\theta)} = sec^2(\theta) ?

    Cheers,
    Rapha
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  3. #3
    Junior Member turbod15b's Avatar
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    thanks man

    can u show me step by step how to get to the end

    cheers
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  4. #4
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    e^(i*pi)'s Avatar
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    Quote Originally Posted by turbod15b View Post
    thanks man

    can u show me step by step how to get to the end

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

    \frac{d}{dx}tan(x) = \frac{d}{dx}\frac{sin(x)}{cos(x)}

    Use the quotient rule to solve this one
    Last edited by e^(i*pi); May 18th 2009 at 02:08 PM. Reason: Added math tags
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