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Oct
20
revised Specific form of differential equation
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Oct
20
asked Specific form of differential equation
Oct
16
awarded  Popular Question
Oct
16
revised Quotient of two rational sequences and the nature of its limit
added 19 characters in body
Oct
16
accepted Quotient of two rational sequences and the nature of its limit
Oct
15
revised Quotient of two rational sequences and the nature of its limit
added 66 characters in body
Oct
15
revised Quotient of two rational sequences and the nature of its limit
edited tags
Oct
15
asked Quotient of two rational sequences and the nature of its limit
Oct
15
answered Let$\ x$ be a real number between$\ 0$ and$\ 1$. Is it possible to write$\ e^{x}$ as a function of$\ \Gamma \left(x+1\right)$?
Oct
13
comment How do I choose between $\lim_{x\to a} \frac {f(x) - f(a)}{x-a}\ $ and $\lim_{x\to a} \frac{f(a+h)-f(a)}{h}$?
To avoid the symbolic "overkill" you could always write the short hand notation for the binomial expansion, e.g. $$(x+h)^4=\sum_{k=0}^4{4\choose k}x^{4-k}h^k,$$ especially for large powers.
Oct
12
comment Find the limit of a Riemann Sum
$ f (X)=(1-X)(1+X) $.
Oct
9
accepted Are these functions identical?
Oct
8
asked Is it possible to abstract a Riemann integral into a “higher” integral with measure?
Oct
8
answered How to calculate $\sum\limits_{k=0}^{n}{k\dbinom{n}{k}}$
Oct
7
comment Calculating a complex definite improper integral: $I= \int_{0}^\infty x^{it}\,\mathrm{e}^{-ax}\, dx$
For a general treatment of these types of integrals, you may be interested in learning about the Bilateral Laplace Transform: en.wikipedia.org/wiki/…
Oct
3
comment how to calculuate $\int_0^ \pi \sqrt{1+x^2 \sin^2x}dx$
For what it's worth the integrand is symmetric, so we may write $$I = \frac{1}{2}\int_{-\pi}^\pi\sqrt{1+(x\sin x)^2}dx.$$
Oct
2
reviewed Approve Algebraic Integers and Irreducible Polynomials
Oct
2
comment Change of variable in complex integral
Your substitution should be $z=Re^{i\theta}$, so that $dz=Rie^{i\theta}d\theta$, and $0\leq \theta< \pi/4$. We make this substitution because the substitution describes the path $\Gamma$ which you give.
Oct
2
comment What is the relation between two integrals?
On the real line you would have $I_1\leq I_2$. But from your language it's unclear whether you're talking about integration over $\mathbb{R}$ or $\mathbb{C}$.
Oct
2
awarded  Nice Answer