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Math Help - two calculus problems

  1. #1
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    two calculus problems

    hey all i'm having alot of bother with these two questions. any comments would be very much appreciated!!!

    1)
    show that the derivative of

    arctan(a + x/1 -ax) is independent of a and explain why


    2)
    use the substitution x-p = 1/u to show the integral of

    1/(x-p)sqrt((x-p)(x-q)) = 2/(q-p) . sqrt((x-q)/(x-p))

    thanks muchly!!!!!
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  2. #2
    Super Member Matt Westwood's Avatar
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    First one:

    First you note that \frac d {dx} \left({\tan^{-1} z}\right) =  \frac 1 {1 + z^2} \frac {dz}{dx} where z = f \left({x}\right) where here z = \frac {a + x}{1 - ax}.

    Yuch. The algebra's messy, but when you flog through it you'll find that a does not appear in the final equation.
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  3. #3
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    Quote Originally Posted by laura90 View Post
    hey all i'm having alot of bother with these two questions. any comments would be very much appreciated!!!

    1)
    show that the derivative of

    arctan(a + x/1 -ax) is independent of a and explain why


    2)
    use the substitution x-p = 1/u to show the integral of

    1/(x-p)sqrt((x-p)(x-q)) = 2/(q-p) . sqrt((x-q)/(x-p))

    thanks muchly!!!!!
    \tan^{-1}\frac{a+x}{1-ax} = \tan^{-1} a + \tan^{-1} x + k\pi, k\in \mathbb{Z}
    Last edited by mr fantastic; September 19th 2009 at 01:21 AM. Reason: Restored original reply
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