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Limits help!

  • Thread starter kendal12
  • Start date
  • #1
kendal12
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!
 

Answers and Replies

  • #2
1,235
1
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:
  • #3
kendal12
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?
 
  • #4
1,227
2
2x, you are right !
Remember this calculation, since you will learn soon that 2x is the derivative of x².
 

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