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Limit Problem

  1. Feb 21, 2008 #1
    I'm having trouble with this one. How do I get h out of the denominator?

    [tex]lim_{h\rightarrow0}\left(\frac{\frac{1}{(a+h)^{2}}-\frac{1}{x^{2}}}{h}\right)[/tex]

    [tex]lim_{h\rightarrow0}\left(\frac{1}{h(a+h)^2}-\frac{1}{hx^{2}}\right)[/tex]

    [tex]lim_{h\rightarrow0}\left(\frac{hx^2-h(a+h)^2}{h^2x^2(a+h)^2}\right)[/tex]

    [tex]lim_{h\rightarrow0}\left(\frac{x^2-(a+h)^2}{hx^2(a+h)^2}\right)[/tex]

    I keep getting a divide by zero. Am I wrong?
     
  2. jcsd
  3. Feb 21, 2008 #2
    Are you trying to find the derivative of 1/x^2 using the def. of the derivative???????
     
  4. Feb 21, 2008 #3
    that should be an 'a' where it is an 'x', sorry.
     
  5. Feb 21, 2008 #4
    lol, a=x.
     
  6. Feb 21, 2008 #5
    and, yes, I am suppose to solve it using algebra.
     
  7. Feb 21, 2008 #6
    i do not know whether u did the algebra good up to the last part, i won't be checking that. here at the last part you can rearrange the numerator like this

    : a^2-(a+h)^2=(a-a-h)(a+a+h)=-h(2a+h)
    so you will get rid of the h on the denominator.
     
  8. Feb 21, 2008 #7
    very clever, thanks
     
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