Results 1 to 4 of 4

Math Help - most urgent please

  1. #1
    Newbie
    Joined
    Oct 2008
    Posts
    17

    most urgent please

    please urgent step by step solution
    thanks
    Attached Thumbnails Attached Thumbnails most urgent please-untitled.bmp   most urgent please-untitled1.bmp  
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Senior Member Peritus's Avatar
    Joined
    Nov 2007
    Posts
    397
    <br />
\begin{gathered}<br />
  g(x) = \sqrt x f(x) \hfill \\<br />
   \Rightarrow g'(x) = \frac{1}<br />
{{2\sqrt x }}f(x) + \sqrt x f'(x) \hfill \\ <br />
\end{gathered} <br />

    now use the given data.


    \begin{gathered}<br />
  \frac{{d^2 }}<br />
{{dx^2 }}\left( {\frac{1}<br />
{{\sin x}}} \right) =  - \frac{d}<br />
{{dx}}\sin ^{ - 2} x\cos x =  - 2\sin ^{ - 3} x\cos x\sin x =  \hfill \\<br />
   =  - 2\sin ^{ - 2} x\cos x \hfill \\ <br />
\end{gathered} <br />
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,657
    Thanks
    598
    hELLO, ea12345!

    These are straight-forward . . . exactly where is your difficulty?


    \text{Given: }\:y \:=\:\csc x.\qquad\text{ Find: }\:\frac{d^2y}{dx^2}
    . . \frac{dy}{dx} \;=\;\underbrace{-\csc x\cdot\cot x}_{\text{product}}

    \frac{d^2y}{dx^2} \;=\;(-\csc x)(-\csc^2\!x) + (+\csc x\cot x)(\cot x) \;=\;\csc^3\!x + \csc x\cot^2\!x




    \text{If }\,f(4) = 3\,\text{ and }\,f'(4) = \text{-}5,\;\text{ find }g'(4),\;\text{ where }\:g(x) \:=\:\sqrt{x}\!\cdot\!f(x)
    We have: . g(x) \;=\;x^{\frac{1}{2}}\cdot f(x) . . . a product

    Then: . g'(x) \;=\;x^{\frac{1}{2}}\!\cdot\!f'(x) + \tfrac{1}{2}x^{\text{-}\frac{1}{2}}\!\cdot\!f(x) \;=\;\sqrt{x}\!\cdot\!f'(x) + \frac{1}{2\sqrt{x}}\!\cdot\!f(x)


    Hence: . g'(4) \;=\;\sqrt{4}\!\cdot\!f'(4) + \frac{1}{2\sqrt{4}}\!\cdot\!f(4)

    . . . . . . . . . = \quad 2\!\cdot(-5) + \tfrac{1}{4}\cdot(3) \;=\;-10 + \tfrac{3}{4} \;=\;-\frac{37}{4}

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Oct 2008
    Posts
    17
    Thanks soroban you are great
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Urgent!!!help with attempted questions - urgent
    Posted in the Statistics Forum
    Replies: 2
    Last Post: February 28th 2010, 12:29 AM
  2. I need urgent urgent hel with this parabola question
    Posted in the Pre-Calculus Forum
    Replies: 1
    Last Post: December 14th 2008, 04:48 PM
  3. Very urgent!
    Posted in the Algebra Forum
    Replies: 2
    Last Post: September 30th 2008, 01:01 PM
  4. Urgent HW help
    Posted in the Discrete Math Forum
    Replies: 2
    Last Post: March 14th 2008, 05:52 AM
  5. urgent HELP
    Posted in the Statistics Forum
    Replies: 1
    Last Post: July 12th 2007, 04:34 AM

Search Tags


/mathhelpforum @mathhelpforum