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1. Calculation method

You've misunderstood the whole thing! Definition: A fixed point of a function g(x) is a number p such that p = g(p). Caution. A fixed point is not a root of the equation 0 = g(x), it is a solution of the equation x = g(x). Geometrically, the fixed points of a function g(x) are the...
2. Quick Limit question

Stirling's formula/approximation works fine too.
3. Help with triple integration problem

No, since: \int_{\frac{\pi}{6}}^{\frac{\pi}{4}} sin\phi d\phi = [-cos\phi]_{\frac{\pi}{6}}^{\frac{\pi}{4}} = -cos(\frac{\pi}{4}) - (-cos(\frac{\pi}{6})) = cos(\frac{\pi}{6}) - cos(\frac{\pi}{4})
4. Limits and L'Hopital

"Calculations" of this kind possess no conclusive power. For example: \lim_{x\rightarrow0}\frac{e^x-1}{x} Differentiating the numerator and the denominator gives: \lim_{x\rightarrow0}\frac{e^x}{1}=1 But to know that D(e^x) = e^x we must master \lim_{x\rightarrow0}\frac{e^x-1}{x}
5. Limits and L'Hopital

"prove it" might not be the correct choice of words..
6. Symbolic Methodology

You can write D^{-2}f(x) and/or D^{-2}(x^n).
7. Infinite Series/Calculus III

Have you tried the case for which x=1? f(1) = 1 + 1 + (1^2)/2 + (1^3)/6 + (1^4)/24 + (1^5)/120 + (1^6)/720 = ?
8. 3rd Derivative Theorem?

Take a look at Leibniz Identity.
9. Can you do this?

It takes Ronald McDonald 1 minute to cross, the Hambugular 2 minutes to cross, ther French Fry Guy 5 minutes to cross, and Grimace 10 minutes to cross. (->) Ronald McDonald and Hambugular: 2min. (<-) Ronald McDonald: 1min. (->) French Fry Guy and Grimace: 10min (<-) Hambugular: 2min...