Results 1 to 4 of 4

Math Help - Continuity of Functions

  1. #1
    Newbie
    Joined
    Feb 2008
    Posts
    10

    Continuity of Functions

    Hey everyone! I have these two online problems that I cannot figure out for the life of me. Please help!! I understand continuity but these are terrible.

    1.) The function f is given by the formula
    when and by the formula


    when .

    What value must be chosen for a in order to make this function continuous at -4?

    2.) For what value of the constant c is the function f continuous on where

    Thank you so much guys!
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Behold, the power of SARDINES!
    TheEmptySet's Avatar
    Joined
    Feb 2008
    From
    Yuma, AZ, USA
    Posts
    3,764
    Thanks
    78
    For the first one...

    f(x)=\frac{4x^3+15x^2+4x+32}{x+4} \iff \frac{(x+4)(4x^2-x+8)}{(x+4)}=(4x^2-x+8)

    so evaluate the above expression at -4 and set equal to
    3x^2-2x+a evaluated at -4 and solve for a.

    Do same thing for part 2 except use x=5.


    Good luck.
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Super Member

    Joined
    May 2006
    From
    Lexington, MA (USA)
    Posts
    11,825
    Thanks
    713
    Hello, funnylookinkid!

    1) The function f(x) is given by: . f(x) \;=\;\begin{Bmatrix}\dfrac{4x^3+15x^2+4x+32}{x+4} & x < -4 \\  \\[-1mm] 3x^2 - 2x + a & x \geq -4\end{Bmatrix}

    What value must be chosen for a in order to make this function continuous at -4?

    For x < -4 the first function is: . \frac{(x+4)(4x^2-x+8)}{x+4} \;=\;4x^2 - x + 8

    So we have: . f(x)\;=\;\begin{Bmatrix}4x^2 - x + 8 & x < -4 \\ 3x^2 - 2x + a & x \geq -4 \end{Bmatrix}


    To be continuous at x = -4, the two branches must be equal.

    . . 4(\text{-}4)^2 - (\text{-}4 ) + 8 \;=\;3(\text{-}4)^2 - 2(\text{-}4) + a \quad\Rightarrow\quad\boxed{ a \:=\:20}




    2) For what value of the constant c is the function f(x) continuous?

    . . f(x) \;=\;\begin{Bmatrix}cx + 4 & x \leq 5 \\ cx^2-4 & x > 5 \end{Bmatrix}

    To be continuous at x = 5, the two branches must be equal.

    . . 5x + 4 \:=\:25x - 4\quad\Rightarrow\quad\boxed{ c \:=\:\frac{2}{5}}

    Follow Math Help Forum on Facebook and Google+

  4. #4
    Newbie
    Joined
    Feb 2008
    Posts
    10
    Thank you guys so much! The problem was in me not knowing how to factor the first and me not opening my eyes for the second, haha!
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. more continuity of functions
    Posted in the Differential Geometry Forum
    Replies: 1
    Last Post: April 9th 2009, 12:26 AM
  2. continuity of multivariable functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: February 10th 2009, 01:37 AM
  3. Continuity of Functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: May 1st 2008, 02:14 PM
  4. piecewise functions and continuity.
    Posted in the Calculus Forum
    Replies: 14
    Last Post: January 14th 2008, 12:48 AM
  5. Continuity Functions
    Posted in the Calculus Forum
    Replies: 2
    Last Post: September 11th 2007, 08:12 PM

Search Tags


/mathhelpforum @mathhelpforum