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1. Relationship between Riemann Sum and the Integral

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...
2. A question about the derivative

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}...
4. Integral of a constant function with/without endpoint

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...
5. What physics background needed for quantum mechanics?

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...
6. Basic question, integral at a specific point

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...
7. Why does cancellation in limits work like this?

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...