Homework Statement
The notation for a Riemann sum - Ʃ f(x*i)Δx - is very similar to the notation for the integral (the Ʃ becomes ∫, the f(x*i) becomes f(x) and the Δx becomes dx).
\int f(x)dx = \lim_{n \to \infty}\sum_{k=0}^{n} f(x_i) Δx
Is there a way to explicitly define the values on the...
Homework Statement
Generally the derivative has the limit x-- h applied to the whole thing like
$$\lim_{h\to 0} \frac{f(x+h)-f(x)}{h}$$
I'm guessing you can't express it as
$$\frac{\lim_{h\to 0} f(x+h)-f(x)}{\lim_{h\to 0} h}$$
because the quotient rule for limits doesn't hold when...
Homework Statement
I hope this is in the right forum, because this is a question on theory and not related to a specific problem.
I was reading onlne about the Fundamental Theorem of Calculus. On one site the author wrote:
F(x) = \int_{0}^{x} f(t) dt
Later, he wrote:
\int_{a}^{b}...
Homework Statement / The Attempt at a Solution
I know that given f(x)=c, the integral from a≤x≤b is c(b-a) (at least, I hope I know that! :D).
Is the integral the same value if you don't include an endpoint? That is, if you were evaluating f(x) from a≤x<b?
Intuitively I think it both...
A while back I read that, roughly speaking, these are the main topics that make up the backbone of a physicist's education: classical mechanics, electromagnetism, statistical mechanics/thermodynamics, special relativity, quantum mechanics, and general relativity.
(If that's incorrect, please...
Homework Statement
This isn't a specific problem ;)
Homework Equations
The Attempt at a Solution
My thought process, skip to the last paragraph if you want the question:
I was wondering how you compute an integral at a specific x value, lets say c. Based on the fact that the...
Homework Statement
There isn't a problem statement, I'm just confused about something.
Homework Equations
The Attempt at a Solution
Ok, for a while I didn't understand how cancelling in the following limit works:
(x+5)(x-5)
lim ----------
x--> 5...
Homework Statement
This isn't really a problem that was assigned to me, (I'm studying independently) I just have a question about the general concept behind some identities.
Homework Equations
sin(a+b) = sin(a)*cos(b) + cos(a)*sin(b)
sin(theta) = sin(180-theta)
The...