Question

I need help finding this limit.

Answer 1

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

Answer 2

this?
\[\lim_{x \rightarrow 0} \left( \frac{(x+\Delta x)^2-2(x+\Delta x)+1-(x^2+2x+1)}{\Delta x} \right)\]

Answer 3

Yes, sorry for not inputting it correctly.

Answer 4

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

Answer 5

Thank you!

Answer 6

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

Answer 7

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

Answer 8

just x is approaching 0, not \Delta

Answer 9

\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)
\[
\lim_{x \to 0} \left( \frac{x+\Delta x^2-2(x+\Delta x)+1-(x^2+2x+1)}{\Delta x} \right)
\]

Answer 10

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 \(x\to 0\).

Answer 11

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

Answer 12

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

Answer 13

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

Answer 14

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

Answer 15

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

Answer 16

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

Answer 17

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

Answer 18

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.

Answer 19

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.

Answer 20

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.

Answer 21

can you post the picture?

Answer 22

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

Answer 23

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!

Answer 24

you're welcome