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Limits help!

  1. Aug 29, 2005 #1
    I just started calculus and we are doing limits. I was doing fine until I ran across this problem:

    lim ( (x+∆x)^2 - x^2 ) / x
    ∆x approaches 0

    I substituted delta x for a and ended up with 2x + a

    I dont think this is right for some reason, but I think I did everything right, can someone please verify my answer so that I know Im on the right track? thanks!
     
  2. jcsd
  3. Aug 29, 2005 #2
    Just expand it out. (note that [itex] a = \Delta x) [/itex] [itex] (x+a )^{2} - x^{2} = 2ax + a^{2} [/itex]. So we have [itex] \frac{2ax + a^{2}}{x} [/itex]. Divide through by [itex] x [/itex]. What do you notice when you substitute [itex] a = 0 [/itex].
     
    Last edited: Aug 29, 2005
  4. Aug 29, 2005 #3
    I actually messed up when I typed that problem. It should all be over delta x. I'm so sorry! So I divided through by a and got a + 2x. Then substituted o in for a, so I'm left with 2x. Right?
     
  5. Aug 29, 2005 #4
    2x, you are right !
    Remember this calculation, since you will learn soon that 2x is the derivative of x².
     
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