User philmcole

8 votes

5 answers

4k views

Difference between polynomial and power series

asked Dec 14, 2017 at 21:23

7 votes

4 answers

268 views

Show that $e^{1-n} \leq \frac {n!}{n^n}$

real-analysis inequality binomial-theorem

asked Jan 6, 2018 at 22:34

6 votes

1 answer

196 views

For which $a$ is $y^2= x^3 + a$ a submanifold?

differential-geometry

asked May 22, 2018 at 9:45

5 votes

1 answer

584 views

Show the equivalence of arc length definitions

real-analysis differential-geometry curves arc-length

asked Jan 25, 2018 at 11:16

5 votes

1 answer

158 views

Best strategy to solve absolut value inequality

algebra-precalculus inequality absolute-value

asked Jul 2, 2017 at 19:17

4 votes

1 answer

1k views

Show every real number is the supremum of a set of rational numbers

real-analysis proof-verification supremum-and-infimum

asked Dec 8, 2017 at 21:42

4 votes

2 answers

795 views

Prove that nested interval theorem doesn't hold for $\mathbb{Q}$

real-analysis rational-numbers

asked Dec 14, 2017 at 0:38

4 votes

2 answers

3k views

Proof of convergence of newton method for convex function

real-analysis algorithms roots newton-raphson

asked Jan 22, 2018 at 18:12

4 votes

3 answers

121 views

Compute $\lim_{x \to \infty} \frac{e^x}{x^a}$

real-analysis limits limits-without-lhopital

asked Jan 5, 2018 at 13:21

3 votes

3 answers

3k views

Set of functions from empty set to $\{0,1\}$

functions elementary-set-theory

asked Dec 11, 2017 at 9:59

3 votes

1 answer

438 views

Why do we need $x_0$ to be a cluster point if we take take the limit $\lim_{x \to x_0} f(x)$?

real-analysis limits

asked Jan 4, 2018 at 19:42

3 votes

0 answers

522 views

Geometric interpretation of rank-$1$ matrices

linear-algebra matrices linear-transformations

asked Mar 28, 2018 at 19:33

3 votes

4 answers

2k views

Double summation identity

summation

asked Dec 28, 2017 at 9:13

2 votes

4 answers

142 views

Show that $f(x) = x^7 + x^5 + x^3 + x$ is bijective

real-analysis functions polynomials

asked Dec 28, 2017 at 14:34

2 votes

1 answer

118 views

Conflicting notation of the term random variable

probability notation random-variables

asked Dec 17, 2017 at 11:54

2 votes

4 answers

1k views

Prove there are exactly $\binom{n}{k}$ subsets of $\{1,\ldots,n\}$ with $k$ elements

combinatorics induction binomial-coefficients

asked Dec 26, 2017 at 12:30

2 votes

1 answer

699 views

Dirichlet approximation theorem proof

real-analysis elementary-number-theory proof-verification diophantine-approximation

asked Dec 9, 2017 at 0:18

2 votes

2 answers

552 views

Why is the probability the same when drawing two marbles in different order

probability

asked Oct 1, 2017 at 19:15

2 votes

2 answers

84 views

Proof that $(-x)^{-1} = -(x^{-1})$

real-analysis axioms

asked Oct 12, 2017 at 9:14

2 votes

1 answer

85 views

Evaluating $\sum_{k=nq}^{np-1}$...

real-analysis sequences-and-series limits

asked Nov 22, 2017 at 11:45

2 votes

1 answer

1k views

Matrix with only real eigenvalues is similar to upper triangular matrix

linear-algebra matrices

asked Apr 12, 2018 at 16:45

2 votes

1 answer

791 views

Restriction of diagonalizable transformation to invariant subspace is diagonalizable

linear-algebra proof-verification eigenvalues-eigenvectors linear-transformations diagonalization

asked Apr 13, 2018 at 15:42

2 votes

0 answers

2k views

Symmetric linear transformation has symmetric matrix

linear-algebra linear-transformations symmetric-matrices

asked Apr 19, 2018 at 8:57

2 votes

3 answers

859 views

Show that $g \circ f$ is n times differentiable

real-analysis derivatives chain-rule

asked Jan 16, 2018 at 12:47

2 votes

2 answers

77 views

Compute $\lim_{x \to \infty} \frac{\log(x)}{x^a}$

real-analysis limits limits-without-lhopital

asked Jan 5, 2018 at 16:48

1 vote

1 answer

94 views

Cluster point of set $\{a_n \,|\, n \in \mathbb N\}$ is limit point of sequence $(a_n)_n$

real-analysis sequences-and-series

asked Jan 3, 2018 at 13:12

1 vote

3 answers

93 views

Behaviour of $\sum\limits_{n=1}^\infty \frac1{n^2}\left(\sqrt{n^2+n} - \sqrt{n^2+1}\right)^n x^n$ for $|x|=2$

real-analysis convergence-divergence power-series

asked Jan 9, 2018 at 15:19

1 vote

3 answers

44 views

Find a power series for a given radius of convergence

real-analysis convergence-divergence power-series

asked Jan 9, 2018 at 17:28

1 vote

1 answer

528 views

Smooth function with $f^{(n)}=0$ is polynomial

real-analysis derivatives polynomials

asked Jan 16, 2018 at 21:48

1 vote

1 answer

78 views

Divergence of power series at the edge [closed]

real-analysis limits power-series

asked Jan 13, 2018 at 20:25

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67 Questions

Difference between polynomial and power series

Show that $e^{1-n} \leq \frac {n!}{n^n}$

For which $a$ is $y^2= x^3 + a$ a submanifold?

Show the equivalence of arc length definitions

Best strategy to solve absolut value inequality

Show every real number is the supremum of a set of rational numbers

Prove that nested interval theorem doesn't hold for $\mathbb{Q}$

Proof of convergence of newton method for convex function

Compute $\lim_{x \to \infty} \frac{e^x}{x^a}$

Set of functions from empty set to $\{0,1\}$

Why do we need $x_0$ to be a cluster point if we take take the limit $\lim_{x \to x_0} f(x)$?

Geometric interpretation of rank-$1$ matrices

Double summation identity

Show that $f(x) = x^7 + x^5 + x^3 + x$ is bijective

Conflicting notation of the term random variable

Prove there are exactly $\binom{n}{k}$ subsets of $\{1,\ldots,n\}$ with $k$ elements

Dirichlet approximation theorem proof

Why is the probability the same when drawing two marbles in different order

Proof that $(-x)^{-1} = -(x^{-1})$

Evaluating $\sum_{k=nq}^{np-1}$...

Matrix with only real eigenvalues is similar to upper triangular matrix

Restriction of diagonalizable transformation to invariant subspace is diagonalizable

Symmetric linear transformation has symmetric matrix

Show that $g \circ f$ is n times differentiable

Compute $\lim_{x \to \infty} \frac{\log(x)}{x^a}$

Cluster point of set $\{a_n \,|\, n \in \mathbb N\}$ is limit point of sequence $(a_n)_n$

Behaviour of $\sum\limits_{n=1}^\infty \frac1{n^2}\left(\sqrt{n^2+n} - \sqrt{n^2+1}\right)^n x^n$ for $|x|=2$

Find a power series for a given radius of convergence

Smooth function with $f^{(n)}=0$ is polynomial

Divergence of power series at the edge [closed]