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Chain rule proof help me dunno what's wrong

  1. Mar 14, 2013 #1
    1. The problem statement, all variables and given/known data
    this is kinda funny i've been strugglnig with the proof for 3 hours straight today
    long story short(<--sorry couldn't find the best way t o say this ) i made it to this statement
    lim(x->a) g(x) if this is equal to g(x) then my proof is done
    lim(x->a) f(a) if this is equal to f(x) then my proof is done
    what's on my mind : this is obviously NOT correct ,after 3 hours of pain i decided to check the txtbook found everything that ive doneto this part and they just write
    lim(x->a) g(x)=g(x) and lim(x->a) f(a)=f(x) vthis made me pretty mad i have no idea how they've done this , i was good at limits i have no idea how is this correct if someone can help explain it to me please

    forgot to metion i don't think this is important though they use h instead of x-a
    chain rule = d/dx (f*g) = df/dxf*g+dg/dxg*f

    2. Relevant equations
    without reading the above why lim(x->a) g(x)=g(x)
    and why lim(x->a) f(a)=f(x)


    3. The attempt at a solution
    what i've said up
     
    Last edited: Mar 14, 2013
  2. jcsd
  3. Mar 14, 2013 #2

    Fredrik

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    ##\lim_{x\to a}g(x)## is not equal to g(x). Note that this wouldn't even make sense, since x is a dummy variable in ##\lim_{x\to a}g(x)##. This expression means the same thing as ##\lim_{t\to a}g(t)##. It's equal to g(a) if and only if g is continuous at a. (Note that if g is differentiable at a, it is also continuous at a).
     
  4. Mar 15, 2013 #3
    Oh i totally missed this part g is actually continous at a thanks
     
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