anonymous
  • anonymous
I need help finding this limit.
Calculus1
  • Stacey Warren - Expert brainly.com
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SOLVED
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schrodinger
  • schrodinger
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anonymous
  • anonymous
\[\lim_{x \rightarrow 0} \left( x+Deltax^2-2(x+Deltax)+1-(x^2+2x+1)/Deltax \right)\]
anonymous
  • anonymous
this? \[\lim_{x \rightarrow 0} \left( \frac{(x+\Delta x)^2-2(x+\Delta x)+1-(x^2+2x+1)}{\Delta x} \right)\]
anonymous
  • anonymous
Yes, sorry for not inputting it correctly.

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More answers

thomas5267
  • thomas5267
\(\Delta\) can be inputed by typing \Delta
anonymous
  • anonymous
Thank you!
thomas5267
  • thomas5267
Put a space after the command so the software can recognize it.
anonymous
  • anonymous
np. and is \(x\) or \(\Delta x\) approaching 0?
anonymous
  • anonymous
just x is approaching 0, not \Delta
thomas5267
  • thomas5267
\frac{a}{b} \[ \frac{a}{b} \] \lim_{x \to 0} \left( \frac{x+\Delta x^2-2(x+\Delta x)+1-(x^2+2x+1)}{\Delta x} \right) \[ \lim_{x \to 0} \left( \frac{x+\Delta x^2-2(x+\Delta x)+1-(x^2+2x+1)}{\Delta x} \right) \]
thomas5267
  • thomas5267
Does the limit has anything to do with derivatives? This is the definition of the derivative except the definition of the derivative has \(\Delta x\to 0\) not \(x\to 0\).
anonymous
  • anonymous
It looked like the definition of the derivative, but it would have to be \(\Delta x\) approaching 0
anonymous
  • anonymous
Oh, I'm sorry, it is \[\Delta x\]
anonymous
  • anonymous
ok, so you should start by multiplying everything out in the numerator. Using foil and distribution.
anonymous
  • anonymous
Okay, I'll start out by doing that and but what am I going to do about \[\Delta x\]
anonymous
  • anonymous
Treat it as just another variable. For example that middle term would be \[-2(x +\Delta x)= -2x-2\Delta x\]
anonymous
  • anonymous
Oh okay, so we wouldn't be doing final minus initial. That's what I was confused about. Thank you so much!
anonymous
  • anonymous
you're welcome. keep it as \(\Delta x\) because once you're done simplifying the numerator, the denominator will cancle out
anonymous
  • anonymous
Do you know how to find limits by looking at a graph and discussing the continuity of the function? I'm lost on a (1-6) on this page in my textbook.
anonymous
  • anonymous
Do you know how to find limits by looking at a graph and discussing the continuity of the function? I'm lost on a (1-6) on this page in my textbook.
anonymous
  • anonymous
Do you know how to find limits by looking at a graph and discussing the continuity of the function? I'm lost on a (1-6) on this page in my textbook.
anonymous
  • anonymous
can you post the picture?
anonymous
  • anonymous
yes, one moment, my school's internet is very slow.
anonymous
  • anonymous
I'm sorry for some reason, it just won't send, but I have to go to class. I'll ask my instructor and see if he can clarify. Thank you so much for all your help, it really means a lot to me!
anonymous
  • anonymous
you're welcome

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