User Joe

4 votes

5 answers

7k views

The difference between ∈ and ⊂

elementary-set-theory notation

asked Oct 7, 2017 at 18:13

3 votes

4 answers

708 views

Show that the series converges and find its sum [duplicate]

asked Sep 8, 2018 at 10:48

3 votes

1 answer

314 views

Prove that $(I+A^{-1})^{-1}=A(A+I)^{-1}.$

linear-algebra matrices

asked Oct 6, 2018 at 11:11

2 votes

1 answer

2k views

Reverse Triangle Inequality in vector space

vector-analysis

asked Sep 9, 2018 at 10:31

2 votes

0 answers

45 views

Find the partial derivatives of the function $f(x)=\|x\|^{\alpha}$ outside of $(0,0)$

derivatives partial-derivative vector-analysis

asked Oct 4, 2018 at 9:46

2 votes

0 answers

44 views

Prove that $xy^2+y^3z^4+z^5x^6=1$ has a solution in an open neighborhood about the point $x_0=(0,1,-1)$

calculus multivariable-calculus vector-analysis implicit-function-theorem

asked Dec 29, 2018 at 9:13

2 votes

2 answers

4k views

Show that the Mean Value Theorem does not apply to $f(x)=x^{-2}$ on $(-1,1)$

calculus

asked Dec 9, 2017 at 11:59

2 votes

3 answers

1k views

Use the Mean Value Theorem to prove that if a continuous and differentiable function $f$ has two roots, then $f'$ has at least one root

calculus

asked Dec 11, 2017 at 8:29

2 votes

1 answer

120 views

Prove events are independent if and only if $p=\frac{1}{2}$

probability combinatorics

asked Jan 31, 2018 at 13:47

2 votes

1 answer

2k views

Prove that if $v$ and $w$ are eigenvectors associated with the eigenvalue $\lambda,$ so is the vector $2v-w$.

linear-algebra eigenvalues-eigenvectors vectors

asked Oct 13, 2017 at 11:17

2 votes

2 answers

135 views

Solve $ \lim_{x\to ∞}\frac{x+\sin(x)}{2x+\cos(x)} $

calculus limits trigonometry fractions limits-without-lhopital

asked Oct 21, 2017 at 9:42

2 votes

2 answers

238 views

Quantile function of log-normal distribution

normal-distribution inverse-function quantile

asked Dec 15, 2019 at 11:14

1 vote

1 answer

3k views

Posterior distribution of uniform likelihood and Pareto prior

statistics probability-distributions statistical-inference bayesian

asked Feb 17, 2020 at 13:01

1 vote

3 answers

56 views

Show $\sum^{\infty}_0q^k$ converges with integral test

calculus sequences-and-series convergence-divergence definite-integrals

asked Mar 24, 2020 at 16:45

1 vote

1 answer

110 views

Show if the series $\sum^{\infty}_1\sin\frac{1}{n}$ converges using the integral test

calculus sequences-and-series convergence-divergence definite-integrals

asked Mar 25, 2020 at 17:07

1 vote

3 answers

93 views

Assume $f$ and $g$ are continuous at $x=a$. Prove $h=\max\{f,g\}$ is continuous at $x=a$.

calculus proof-verification continuity

asked Nov 6, 2019 at 17:00

1 vote

1 answer

823 views

Expected value of truncated distribution

integration probability-distributions random-variables expected-value

asked Dec 4, 2019 at 12:20

1 vote

4 answers

68 views

Let $\sum^\infty_{n=1}x_n$ where all the terms are positive. Prove that if this series is convergent, so is $\sum^\infty_{n=1}x_n^2.$

calculus sequences-and-series convergence-divergence

asked Apr 29, 2020 at 17:26

1 vote

1 answer

42 views

What is the linear regression model of this situation?

statistics normal-distribution statistical-inference hypothesis-testing linear-regression

asked May 6, 2020 at 10:20

1 vote

1 answer

30 views

What is the prior and sampling distribution of this situation?

probability statistics probability-distributions bayesian

asked May 13, 2020 at 18:00

1 vote

1 answer

208 views

Show that the series $\sum^\infty_{k=1}kx^k$ converges uniformly

sequences-and-series convergence-divergence uniform-convergence

asked Apr 8, 2020 at 11:26

1 vote

2 answers

135 views

How to choose the expression to substitute?

calculus integration substitution

asked Dec 4, 2017 at 15:40

1 vote

1 answer

38 views

Sampling without replacement with the sample size being chosen radomly

probability

asked Jan 31, 2018 at 14:59

1 vote

3 answers

215 views

A man forgets his umbrella to a store with a probability of $\frac{1}{4}$. What is the probability for the umbrella being left in the store $i$ ?

probability bayes-theorem

asked Feb 26, 2018 at 12:01

1 vote

2 answers

27 views

$S_f(r)=\{x\in A: f(x)=r\}$ is a plane curve

vector-analysis

asked Sep 9, 2018 at 9:52

1 vote

1 answer

23 views

Prove weak formulation of linear system of equations

linear-algebra inner-products

asked Aug 29, 2019 at 16:08

1 vote

1 answer

3k views

Proof inverse Gaussian distribution belongs to the exponential family

parametrization general-linear-group

asked Oct 14, 2019 at 7:38

1 vote

1 answer

108 views

Range of a convergent sequence is bounded.

calculus sequences-and-series convergence-divergence proof-explanation

asked Oct 24, 2019 at 11:19

1 vote

3 answers

44 views

Let $S=\{\frac{\sqrt{x}}{x+1}:x>0\}$. Show that $\inf{S}=0$.

calculus supremum-and-infimum upper-lower-bounds

asked Oct 28, 2019 at 18:31

1 vote

1 answer

51 views

How to graph $\eta(t)=(t,|t|)$?

calculus vector-analysis graphing-functions

asked Dec 13, 2018 at 21:20

Stack Exchange Network

current community

your communities

more stack exchange communities

56 Questions

The difference between ∈ and ⊂

Show that the series converges and find its sum [duplicate]

Prove that $(I+A^{-1})^{-1}=A(A+I)^{-1}.$

Reverse Triangle Inequality in vector space

Find the partial derivatives of the function $f(x)=\|x\|^{\alpha}$ outside of $(0,0)$

Prove that $xy^2+y^3z^4+z^5x^6=1$ has a solution in an open neighborhood about the point $x_0=(0,1,-1)$

Show that the Mean Value Theorem does not apply to $f(x)=x^{-2}$ on $(-1,1)$

Use the Mean Value Theorem to prove that if a continuous and differentiable function $f$ has two roots, then $f'$ has at least one root

Prove events are independent if and only if $p=\frac{1}{2}$

Prove that if $v$ and $w$ are eigenvectors associated with the eigenvalue $\lambda,$ so is the vector $2v-w$.

Solve $ \lim_{x\to ∞}\frac{x+\sin(x)}{2x+\cos(x)} $

Quantile function of log-normal distribution

Posterior distribution of uniform likelihood and Pareto prior

Show $\sum^{\infty}_0q^k$ converges with integral test

Show if the series $\sum^{\infty}_1\sin\frac{1}{n}$ converges using the integral test

Assume $f$ and $g$ are continuous at $x=a$. Prove $h=\max\{f,g\}$ is continuous at $x=a$.

Expected value of truncated distribution

Let $\sum^\infty_{n=1}x_n$ where all the terms are positive. Prove that if this series is convergent, so is $\sum^\infty_{n=1}x_n^2.$

What is the linear regression model of this situation?

What is the prior and sampling distribution of this situation?

Show that the series $\sum^\infty_{k=1}kx^k$ converges uniformly

How to choose the expression to substitute?

Sampling without replacement with the sample size being chosen radomly

A man forgets his umbrella to a store with a probability of $\frac{1}{4}$. What is the probability for the umbrella being left in the store $i$ ?

$S_f(r)=\{x\in A: f(x)=r\}$ is a plane curve

Prove weak formulation of linear system of equations

Proof inverse Gaussian distribution belongs to the exponential family

Range of a convergent sequence is bounded.

Let $S=\{\frac{\sqrt{x}}{x+1}:x>0\}$. Show that $\inf{S}=0$.

How to graph $\eta(t)=(t,|t|)$?