Results 1 to 5 of 5

Math Help - advanced calc diffrential prob

  1. #1
    Newbie
    Joined
    Nov 2009
    Posts
    13

    Post advanced calc diffrential prob

    can someone please help me with this

    let g(x) be such that l g(x) l <= M for all x in [-1,1]
    let h(x) = (x^2)g(x) if x is not equal to 0
    = 0 if x is equal to 0
    show that h(x) is diffrentiable at x = 0 and find h'(0)
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Super Member
    Joined
    Apr 2009
    From
    México
    Posts
    721
    0 \leq \vert \frac{h(x)}{x} \vert = \vert xg(x) \vert \leq M\vert x \vert so taking x\rightarrow 0 we have h'(0)=0
    Follow Math Help Forum on Facebook and Google+

  3. #3
    Newbie
    Joined
    Nov 2009
    Posts
    13
    can u break down a little more please
    Follow Math Help Forum on Facebook and Google+

  4. #4
    Super Member
    Joined
    Apr 2009
    From
    México
    Posts
    721
    Remember that h'(0)= \lim_{x\rightarrow 0} \frac{h(x)-h(0)}{x-0} =\lim_{x\rightarrow 0} \frac{h(x)}{x} and to evaluate the limit we use the squeeze theorem.
    Follow Math Help Forum on Facebook and Google+

  5. #5
    Newbie
    Joined
    Nov 2009
    Posts
    13
    thanks so much
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. advanced calc prob Darboux's Property
    Posted in the Calculus Forum
    Replies: 0
    Last Post: November 21st 2009, 10:40 PM
  2. Replies: 0
    Last Post: September 23rd 2009, 07:26 PM
  3. Replies: 0
    Last Post: September 23rd 2009, 07:26 PM
  4. Advanced Calc I
    Posted in the Calculus Forum
    Replies: 1
    Last Post: September 18th 2007, 11:01 AM
  5. Advanced Calc help
    Posted in the Calculus Forum
    Replies: 7
    Last Post: January 7th 2007, 09:27 AM

Search Tags


/mathhelpforum @mathhelpforum