Results 1 to 6 of 6
Like Tree1Thanks
  • 1 Post By kalyanram

Math Help - Need answer soon please

  1. #1
    Newbie
    Joined
    Sep 2012
    From
    sydney
    Posts
    6

    Need answer soon please

    find the value of the constants a and b to ensure the following function is differentiable for all real values of x:

    f(x) = { (ax / sqrtx) + b , x less than or equal to 1

    and x^2 - 1 , x is greater than 1
    Last edited by fibonacci007; September 14th 2012 at 03:46 AM.
    Follow Math Help Forum on Facebook and Google+

  2. #2
    MHF Contributor MarkFL's Avatar
    Joined
    Dec 2011
    From
    St. Augustine, FL.
    Posts
    1,988
    Thanks
    734

    Re: Need answer soon please

    What two conditions must be met?
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Sep 2012
    From
    sydney
    Posts
    6

    Re: Need answer soon please

    updated sorry didn't know it would look like that
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Sep 2012
    From
    sydney
    Posts
    6

    Re: Need answer soon please

    also find a and subsequently the limit of lim (x->-2)[ 3x^2 + ax + a + 3/ x^2 + x - 2] which i found a to be 15 after some trial and error and established that the end result would be lim (x->-2) [(3x + 9)(x+2)/(x-1)(x+2)] = -1 but would like better reasoning for the deduction of a
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Member kalyanram's Avatar
    Joined
    Jun 2008
    From
    Bangalore, India
    Posts
    142
    Thanks
    14

    Re: Need answer soon please

    Quote Originally Posted by fibonacci007 View Post
    find the value of the constants a and b to ensure the following function is differentiable for all real values of x:

    f(x) = { (ax / sqrtx) + b , x less than or equal to 1

    and x^2 - 1 , x is greater than 1
    Given
    f(x) = \left \{ \begin{matrix} \frac{ax}{\sqrt{x}} + b & x \le 1 \\ x^2 -1 & x > 1 \end{matrix} \right.

    1. Continuity at x=1
     \lim_{h \rightarrow 0} \frac{a(1-h)}{\sqrt{(1-h)}} + b = \lim_{h \rightarrow 0} (1+h)^2 -1 \implies a+b =0

    2. Derivative at x=1
     \lim_{h \rightarrow 0} \frac{1}{2} \frac{a}{\sqrt{(1-h)}} = \lim_{h \rightarrow 0} 2(1+h) \implies \frac{a}{2} = 2

     a= 4, b = -4
    Thanks from fibonacci007
    Follow Math Help Forum on Facebook and Google+

  6. #6
    Newbie
    Joined
    Sep 2012
    From
    sydney
    Posts
    6

    Re: Need answer soon please

    Much love
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. Replies: 5
    Last Post: March 3rd 2013, 07:17 PM
  2. Converting my answer into the books answer
    Posted in the Algebra Forum
    Replies: 6
    Last Post: March 10th 2011, 02:06 PM
  3. Replies: 1
    Last Post: October 4th 2010, 04:46 PM
  4. checking my answer with another answer...
    Posted in the Pre-Calculus Forum
    Replies: 4
    Last Post: November 30th 2009, 07:12 AM

Search Tags


/mathhelpforum @mathhelpforum