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I got 3 questions!

  1. Mar 11, 2007 #1
    1. Suppose that f(a)=g(a) and the left-hand derivative of f at a equals the right-hand derivative of g at a. Define h(x)=f(x) for x<=a, and h(x)=g(x) for x>=a. Prove that h is differentiable at a.

    2. Let 0<B<1. Prove that if f satisfies /f(x)/ >= /x/^B and f(0)=0, then f is not differentiable at 0.

    the sign / / is absolute value.

    3. Let f(x)=x^n for x>=0 and let f(x)=0 for x<=0. Prove that f^(n-1)exists and find a formula for it, but that f^(n) (0) does not exist.


    Can someone help me out with these problems? thx a lot!!!
     
  2. jcsd
  3. Mar 11, 2007 #2

    cristo

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    You need to show some work on homework questions before we can help you.
     
  4. Mar 11, 2007 #3

    Tom Mattson

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    Yep. That, and homework goes in the Homework Help section, not the Math section.

    So, antibody, let's see whatcha got so far.
     
  5. Mar 11, 2007 #4
    for the second one , i know how to prove the converse, like let B>1, if f satisfies /f(x)/ <=/x/^B, prove that f is differentiable at 0,

    this one will be easier, first let x=0 then f(0)=0, and i know to prove some fn is differentiable at some point x, it means to prove lim(h->0) f(x+h)-f(x) /h = some number( here is 0 since the prob has given)

    i guess i can do the same thing to the second one, but i m not sure how to write a religious proof.
     
  6. Mar 11, 2007 #5
    and same thing happens to quesntion no.3 .......

    if the question gives me some precise function, i probably can solve it,
    but this one i am still working on it, my idea is
    x^n when x>=0
    f(x)=
    0 when x<=0

    so the f ' (x) = n x^(n-1) when x>0 and f ' (x)=0 when x<0 then use the left and right limit to see if f ' (x) exists when x=0. Right?

    and again..i am not very familiar with this kind of proof right now,, since we just spent a week on this topic, and i am not sure when we need to use delta-epsilon proof on the question...
     
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