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Apr
5
revised Show that a system of equations can be solved in terms of $x,y,z$ (Rudin, ex 9.19)
added 3 characters in body
Mar
25
revised Are $1/\sqrt{x}$ or $1/x$ Lebesgue integrable on $(0,1)$? If so, why?
deleted 37 characters in body
Mar
21
revised If $f,g: R^n \to R^3$, what is the derivative of the cross product $(f \times g)(\vec{a})$ where $\vec{a} \in R^n$?
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Mar
16
revised What is the limit of $f(a,b) = \frac{a^\beta}{a^2 + b^2}$ as $(a,b) \to (0,0)$?
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Mar
13
revised Does $\int_0^\infty f(x) dx = \lim_{n \to \infty} \int_0^n f(x) dx$ for $f \geq 0$ or $f$ not positive?
edited title
Mar
3
revised Prove that any bounded open set has an arbitrarily close closed subset
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Mar
2
revised Prove that if $E$ is measurable then $\forall \epsilon > 0$ $\exists F \subset E$ closed such that $m(E \setminus F) < \epsilon$.
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Feb
28
revised Prove $m_*( \bigcup_{i=1}^\infty I_i ) = \sum_{i=1}^\infty \ell ( I_i )$ if $I_i \cap I_j = \emptyset \forall i,j$.
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Feb
17
revised Show that every measurable set $A$ can be written $A=B \cup C$
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Feb
15
revised Prove $(\overline{A \cap B}) \subseteq \overline{A} \cap \overline{B}$.
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Feb
14
revised Show that $\,f(x) = \sum_{n=0}^\infty a_nx^n$, for $x \in [0,1]$, is of bounded variation
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Feb
11
revised When writing the integral sign $\int$, how does one know what integral is being discussed?
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Dec
24
revised Prove that every nonempty open subset $G$ of $\mathbb{R}^n$ can be expressed as a countable union of nonoverlapping closed rectangles.
added 285 characters in body
Dec
12
revised What is the angle at critical point $z=1$ of $\left|z-\frac{i-1}{2}\right|=\frac{\sqrt{5}}{\sqrt{2}}$ under the Joukowski transform?
added attempted solution
Dec
2
revised $\{f_n\} \in \mathcal{R}[a,b]$, converges pointwise to $f\in \mathcal{R}[a,b]$. Prove $\lim_{n\to\infty}\int_a^b f_n \, dx = \int_a^b f \, dx$.
[Edit removed during grace period]
Nov
26
revised Sequence of $f_n \in R[0, 1]$ that converges pointwise to $f \in R[0, 1]$ such that $\lim_{n \to \infty} \int_0^1 f_n dx \neq \int_0^1 f dx$.
added 32 characters in body; edited tags
Nov
20
revised For what values $q,r$ does the improper integral $\int_0^1 x^q (1-x^2)^r dx$ converge?
deleted 29 characters in body
Nov
20
revised For what values $q,r$ does the improper integral $\int_0^1 x^q (1-x^2)^r dx$ converge?
edited body
Nov
20
revised For what values $q,r$ does the improper integral $\int_0^1 x^q (1-x^2)^r dx$ converge?
edited tags
Nov
15
revised Compute $\sum_{n=0}^\infty \frac{(-1)^n}{(2n+1)^3} = \frac{\pi^3}{32}$ using residue theory.
added 144 characters in body