I need help finding this limit.

- anonymous

I need help finding this limit.

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- anonymous

\[\lim_{x \rightarrow 0} \left( x+Deltax^2-2(x+Deltax)+1-(x^2+2x+1)/Deltax \right)\]

- 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

Yes, sorry for not inputting it correctly.

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## More answers

- thomas5267

\(\Delta\) can be inputed by typing \Delta

- anonymous

Thank you!

- thomas5267

Put a space after the command so the software can recognize it.

- anonymous

np. and is \(x\) or \(\Delta x\) approaching 0?

- anonymous

just x is approaching 0, not \Delta

- 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

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

It looked like the definition of the derivative, but it would have to be \(\Delta x\) approaching 0

- anonymous

Oh, I'm sorry, it is \[\Delta x\]

- anonymous

ok, so you should start by multiplying everything out in the numerator. Using foil and distribution.

- anonymous

Okay, I'll start out by doing that and but what am I going to do about \[\Delta x\]

- anonymous

Treat it as just another variable. For example that middle term would be
\[-2(x +\Delta x)= -2x-2\Delta x\]

- anonymous

Oh okay, so we wouldn't be doing final minus initial. That's what I was confused about. Thank you so much!

- anonymous

you're welcome. keep it as \(\Delta x\) because once you're done simplifying the numerator, the denominator will cancle out

- 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

- anonymous

can you post the picture?

- anonymous

yes, one moment, my school's internet is very slow.

- 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

you're welcome

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