Thread: I want nothing more than to take calculus

I think we are arguing semantics here, but oh well.

In the problem, x isn't 'going' anywhere. Its a fixed value. So, the limit of the function as x goes to infinity happens to be a good approximation, but is still not exact at that point.

Sounds fun. Good luck with that.

I think the author of that book had his priorities backwards though... Clearly pizza should come first!

How far have you gone in this book?

Because the hardest stuff in calculus is most definately Series Error and the LaGrange Method is the only way to go.

Plus I also just finished AP Calculus and I've been waiting for a month on my test results.

My teacher worked our class like dogs and I thought Calc was equally hard as Physics *insert giant laugh*

>>> Because the hardest stuff in calculus is most definately Series Error and the LaGrange Method is the only way to go.

Wait until you get into some more calculus. Partial diff-eq's are quite "fun".

>>Wait until you get into some more calculus. Partial diff-eq's are quite "fun".

Partials can be a real pain in the ass. I mean there are even Partials that cant be solved... like we have this TI-92 and in school we always used to type in these very complex partials and then let the machine worj it out, and then see wich calculator took the longest.

What's so special about the number 'e'. How are base e logarithms useful. Isn't e an irrational number (like pi) that goes on forever? and isnt' it something like 2.71.....

EDIT: and they showed how to find the instantaneous velocity of a falling piece of pizza using derivaties. From what I read derivaties are just new functions that can represent slope when no time has passed (because otherwise it is an illegal divide by zero). I was confused because when they were creating the derivative they integrated functions or something and I didn't know what they were doing. But the books shows a shortcut for calculating the derivative:

F(x) = (x^n) is the original
F(x) = (nx^n-1) is the derivative

Were you all shown this?

Yes, that's called the power rule, and works only when n is a constant - not if it's variable. They weren't integrating, they were taking the limit of a difference quotient (slope) as h approached 0. I hope you read about limits before you started derivatives...

e is a special number. It is the only number k where k^x is its own derivative. (e^x)'=e^x (note the prime on the left side) There's a big long elaborate proof for getting e, but since you're just starting, you wouldn't understand it (it's probably in your book anyway) The slope of e^x at x=1 is e. The slope of e^x at x=2 is e^2, etc. If that reason doesn't make sense to you yet, think of it like this: it's easier to write ln(x) than log(x), so just do it and learn why later

e... 2.718281828459045 (off the top of my head)

Only two functions are the same as there derivatives:
f(x) = e^x
f(x) = 0

And there are other reasons why e is important (as you'll see when you get to the definition of ln). Plus, the definition of e, stated informally (rather poorly actually) is 1 to the infinite power.

More technically,

e = lim [x->0] (1 + x)^(1/x)