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## FreeTrader 4 years ago Factoring Advice: Goal is to eliminate the x's. [(x+y)^2 - x^2] / y

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1. fiddlearound

it's equal to 2x+y , eliminate the x's ?

2. fiddlearound

oh that's different than the first one

3. FreeTrader

I think there is a way to do it, but I am not sure how I can get them to all cancel out.

4. FreeTrader

$((x+y)2−y2)/y$ goal is to eliminate the x's and be left with only y's to deal with...

5. FreeTrader

Thoughts? I have tried the usual things I can think of, but unless I made an error I am not catching, I am stumped.

6. FreeTrader

BRB

7. fiddlearound

is this part of a LIM problem ?

8. FreeTrader

Yes, how on earth did you guess?

9. fiddlearound

I mean are you looking for: $\lim_{y \rightarrow 0} \frac{(x+y)^2-x^2}{y}$

10. FreeTrader

Uh, indeed I am...

11. FreeTrader

Can you help me get unstuck? I really want to learn how to do this...

12. FreeTrader

I have it down to y + 2x and I don't know if I can use x in my lim answer, I've never seen a variable in a lim.

13. fiddlearound

$\lim_{y \rightarrow 0} \frac{\cancel{x^2}+2xy+y^2-\cancel{x^2}}{y}=\lim_{y \rightarrow 0}2x+y=2x$

14. FreeTrader

Is it acceptable to have a variable in the lim solution?

15. fiddlearound

yes, coz it's basically the derivative: $(x^2)'=2x$

16. FreeTrader

Or is this DNE?!?

17. fiddlearound

the final answer is 2x which is the derivative of x^2

18. FreeTrader

I don't know enough to understand that in the context of this problem. I understand what a first derivative is, and how you showed that, but I do not understand it in relation to my first "evaluate lim's" homework assignment.

19. fiddlearound

how was the problem worded ?

20. FreeTrader

So the lim is really 2x?!?

21. FreeTrader

The lim stmt you wrote, preceded by the word "Evaluate:"

22. fiddlearound

yes, so the answer would be 2x

23. FreeTrader

We haven't covered derivatives yet - not until tomorrow. So this is kinda tricky!

24. fiddlearound

this is how they introduce you to derivatives

25. fiddlearound

you don't have to know what a derivative is to solve the LIM problem. But in effect, they will reveal that what you were doing was calculating the derivative.

26. FreeTrader

Have you seen Gilbert Strang's high school calculus course on MIT OCW, called "The Big Picture of Calculus?" THAT's how to teach calculus.

27. FreeTrader

Are you a student or faculty?

28. fiddlearound

that formula is basically calculating rise over run (where they make the run smaller and smaller)

29. FreeTrader

Ahhhh

30. fiddlearound

neither. I studied math about 20 years ago.

31. FreeTrader

What do you do now that allows you to stay fresh on it? I am 44, BTW.

32. fiddlearound

we are very close in age :) I just started solving problems on openstudy to keep the mind from rusting too much.

33. FreeTrader

Well, thank you for your help. I am now a fan.

34. fiddlearound

BTW, I started going over the MIT OCW single variable calculus - but then got sucked in over here in the math group.

35. FreeTrader

I want to build up a community on MIT OCW SCHOLAR SVC.

36. FreeTrader

I am trying to login there every night at 8 PM. I missed it tonight, the first time others were there, too.

37. FreeTrader

So, if you are around at 8PM ET, I will try to be there in the MIT OCW SVC (NOT the 18.01 - the SCHOLAR version. It is a new and improved course, totally self contained.

38. FreeTrader

Thanks. Over and out on this case. I had solved it and didn't realize I was done.

39. fiddlearound

My schedule in the evenings is not fixed, juggling around kids & work . And I didn't continue past the first OCW lecture - btw I didn't know they now have the new and improved course.

40. FreeTrader

It is wonderful. I hope you find time to give it a try during your "me time."

41. FreeTrader

I'm going to resume my homework. I have about a zillion more to go...

42. fiddlearound

OK :)

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