## anonymous one year ago I need help finding this limit.

1. anonymous

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

2. anonymous

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

3. anonymous

Yes, sorry for not inputting it correctly.

4. thomas5267

$$\Delta$$ can be inputed by typing \Delta

5. anonymous

Thank you!

6. thomas5267

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

7. anonymous

np. and is $$x$$ or $$\Delta x$$ approaching 0?

8. anonymous

just x is approaching 0, not \Delta

9. 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) $\lim_{x \to 0} \left( \frac{x+\Delta x^2-2(x+\Delta x)+1-(x^2+2x+1)}{\Delta x} \right)$

10. 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 $$x\to 0$$.

11. anonymous

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

12. anonymous

Oh, I'm sorry, it is $\Delta x$

13. anonymous

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

14. anonymous

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

15. anonymous

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

16. anonymous

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

17. anonymous

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

18. 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.

19. 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.

20. 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.

21. anonymous

can you post the picture?

22. anonymous

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

23. 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!

24. anonymous

you're welcome