User Nicholas Roberts

7 votes

4 answers

202 views

Is my method for computing $\lim_{x \to 0^+} \left( \dfrac{\sin x}{x} \right)^{1/x^2} = e^{-1/6}$ valid?

calculus limits

asked Jun 18, 2021 at 15:39

4 votes

3 answers

829 views

Show that $\text{Res}_{z = \infty}\left(f(z)\log\left(\frac{z-a}{z-b}\right)\right) = - \int_{a}^{b}f(z)\,dz$

complex-analysis residue-calculus

asked Apr 1, 2019 at 22:56

4 votes

0 answers

613 views

Munkres Exercise 70.1

proof-verification algebraic-topology homotopy-theory fundamental-groups

asked Dec 2, 2017 at 2:49

4 votes

0 answers

123 views

On the proof that a distribution with $\{0\}$ as support can be written as a sum of point masses

real-analysis distribution-theory

asked Jan 7, 2019 at 6:01

3 votes

1 answer

832 views

Fundamental group of circle union a line

proof-verification algebraic-topology

asked Dec 18, 2017 at 5:08

2 votes

1 answer

87 views

Does ${\frac{f(n)}{g(n)}} \rightarrow l$ imply ${\frac{f(n)}{g(n+1)}} \rightarrow l$?

sequences-and-series

asked Nov 3, 2017 at 16:35

2 votes

1 answer

460 views

Show that $\mathbb{C} \otimes_\mathbb{R} \mathbb{C}$ is not an integral domain

tensor-products

asked Nov 15, 2017 at 1:19

2 votes

2 answers

2k views

Annual Inflation Rate Problem

algebra-precalculus

asked May 17, 2016 at 18:30

2 votes

0 answers

215 views

Prove that a subset of $\mathbb{R}$ with positive outer measure contains almost a whole interval

real-analysis measure-theory proof-verification outer-measure

asked Jun 18, 2018 at 20:18

2 votes

3 answers

526 views

Losing Solutions to a Rational Equation

algebra-precalculus rational-functions

asked Oct 31, 2020 at 17:33

1 vote

2 answers

43 views

Show uniqueness of constants such that this limit is zero

calculus

asked Dec 17, 2020 at 19:14

1 vote

1 answer

231 views

Showing a linear map is continuous

real-analysis proof-verification vector-spaces normed-spaces

asked Aug 22, 2019 at 3:03

1 vote

0 answers

76 views

$f \in L^+$ with $\int f = k < \infty$ then $\{x : f(x) = \infty\}$ has measure zero proof verification

real-analysis integration measure-theory

asked Jan 6, 2020 at 0:39

1 vote

2 answers

86 views

Why does this sequence exist?

real-analysis hilbert-spaces supremum-and-infimum

asked Aug 27, 2020 at 16:07

1 vote

1 answer

467 views

Let $f$ be uniformly continuous and (Lebesgue) integrable on $\mathbb{R}$. Show that $\lim_{x \to \infty} f = 0$ proof verification

real-analysis proof-verification lebesgue-integral

asked Jul 7, 2018 at 4:01

1 vote

2 answers

402 views

Diff. Eq. solution by inspection

ordinary-differential-equations

asked May 6, 2016 at 20:22

1 vote

0 answers

247 views

Prove that $ze^{\lambda - z} - 1$ has a real root in the unit disk

calculus complex-analysis rouches-theorem

asked Mar 29, 2019 at 0:59

1 vote

1 answer

72 views

Expand $\frac{1}{z^2}$ as a series on $|z - 2| < 2$

proof-verification power-series

asked Apr 8, 2019 at 20:29

1 vote

2 answers

439 views

Show $\cosh(z) - \cos(z) = z^2\prod_{n = 1}^{\infty}\left(1 + \frac{z^4}{4\pi^4n^4} \right)$

complex-analysis infinite-product weierstrass-factorization

asked Apr 12, 2019 at 17:57

1 vote

2 answers

1k views

Combinations of $8$ digit binary strings

combinatorics combinations

asked Mar 17, 2016 at 1:40

1 vote

1 answer

701 views

Showing commutative semisimple ring with unity is direct sum of fields

proof-verification ring-theory modules semi-simple-rings

asked Mar 3, 2018 at 2:59

1 vote

1 answer

141 views

Showing a subset of tempered distributions equals the space of complex Radon measures

real-analysis distribution-theory

asked Jan 13, 2019 at 4:18

0 votes

1 answer

472 views

Show that $\cos(2\pi nx) \nrightarrow 0$ almost everywhere on $[0, 1]$

real-analysis sequences-and-series

asked Jan 21, 2019 at 18:16

0 votes

2 answers

151 views

Radius of convergence of $\sum_{n=1}^{\infty}\frac{(-1)^n}{n}z^{n(n+1)}$

complex-analysis power-series

asked Feb 6, 2019 at 2:12

0 votes

1 answer

127 views

Projecting a parametric curve to a plane

integration parametric

asked Apr 8, 2016 at 17:27

0 votes

0 answers

630 views

Global Extrema of Cosine

calculus trigonometry maxima-minima

asked Jan 15, 2017 at 18:12

0 votes

1 answer

43 views

Volume bounded between to multivariable functions

calculus integration multivariable-calculus

asked May 21, 2016 at 18:39

0 votes

1 answer

26 views

simplification question on Diff. Eq. Solution

algebra-precalculus ordinary-differential-equations

asked May 26, 2016 at 2:46

0 votes

2 answers

92 views

Sequence of holomorphic functions converging on compact sets with $f_n(D) \subset U$ implies $f(D) \subset U$ or $f(z) = c$ for $c \in \partial U$

complex-analysis

asked Apr 28, 2019 at 3:17

-1 votes

1 answer

6k views

dimension of span of vectors

linear-algebra vector-spaces

asked Jul 6, 2016 at 16:05

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31 Questions

Is my method for computing $\lim_{x \to 0^+} \left( \dfrac{\sin x}{x} \right)^{1/x^2} = e^{-1/6}$ valid?

Show that $\text{Res}_{z = \infty}\left(f(z)\log\left(\frac{z-a}{z-b}\right)\right) = - \int_{a}^{b}f(z)\,dz$

Munkres Exercise 70.1

On the proof that a distribution with $\{0\}$ as support can be written as a sum of point masses

Fundamental group of circle union a line

Does ${\frac{f(n)}{g(n)}} \rightarrow l$ imply ${\frac{f(n)}{g(n+1)}} \rightarrow l$?

Show that $\mathbb{C} \otimes_\mathbb{R} \mathbb{C}$ is not an integral domain

Annual Inflation Rate Problem

Prove that a subset of $\mathbb{R}$ with positive outer measure contains almost a whole interval

Losing Solutions to a Rational Equation

Show uniqueness of constants such that this limit is zero

Showing a linear map is continuous

$f \in L^+$ with $\int f = k < \infty$ then $\{x : f(x) = \infty\}$ has measure zero proof verification

Why does this sequence exist?

Let $f$ be uniformly continuous and (Lebesgue) integrable on $\mathbb{R}$. Show that $\lim_{x \to \infty} f = 0$ proof verification

Diff. Eq. solution by inspection

Prove that $ze^{\lambda - z} - 1$ has a real root in the unit disk

Expand $\frac{1}{z^2}$ as a series on $|z - 2| < 2$

Show $\cosh(z) - \cos(z) = z^2\prod_{n = 1}^{\infty}\left(1 + \frac{z^4}{4\pi^4n^4} \right)$

Combinations of $8$ digit binary strings

Showing commutative semisimple ring with unity is direct sum of fields

Showing a subset of tempered distributions equals the space of complex Radon measures

Show that $\cos(2\pi nx) \nrightarrow 0$ almost everywhere on $[0, 1]$

Radius of convergence of $\sum_{n=1}^{\infty}\frac{(-1)^n}{n}z^{n(n+1)}$

Projecting a parametric curve to a plane

Global Extrema of Cosine

Volume bounded between to multivariable functions

simplification question on Diff. Eq. Solution

Sequence of holomorphic functions converging on compact sets with $f_n(D) \subset U$ implies $f(D) \subset U$ or $f(z) = c$ for $c \in \partial U$

dimension of span of vectors