User Jay Wang

9 votes

2 answers

38k views

How to prove polynomials with degree $n$ does not form a vector space?

asked Sep 18, 2016 at 20:03

4 votes

6 answers

2k views

Does $\sum_{k=1}^{\infty}\frac{k!}{k^k}$ converge?

asked Jan 20, 2016 at 13:11

3 votes

3 answers

285 views

How to evaluate the following integral, $\int\frac{x \, dx}{x^2+2x+17}$?

asked Jan 2, 2016 at 20:59

3 votes

1 answer

148 views

Would the order of Taylor Polynomial change after substitution?

asked Jan 12, 2016 at 1:40

2 votes

4 answers

363 views

How to show $\int_{1}^{\infty} \frac{\sin^2(x)}{x^2}dx$ is finite?

asked Jan 12, 2016 at 0:53

2 votes

2 answers

79 views

Why $\|x\|^2\cdot \|y\|^2-(x\cdot y)^2=\sum_{1\leq i<j\leq n}(x_i y_j-x_j y_i)^2$?

asked Oct 2, 2017 at 14:56

2 votes

1 answer

538 views

Renewal Reward Process Problem

asked Nov 30, 2017 at 15:06

1 vote

1 answer

162 views

Is $R_2 =\max\{n \geq 0 : X_n = 2\}$ a stopping time?

asked Sep 20, 2017 at 14:24

1 vote

1 answer

3k views

Probability of picking balls with same color with replacement and without replacement

asked Jun 15, 2016 at 12:17

1 vote

2 answers

79 views

Suppose $f$ is continuous and verifies $f(x) = o(x)$. Does it follow that $\int_{0}^xf(y)\,dy = o(x^2)$?

asked Jan 12, 2016 at 1:15

1 vote

0 answers

61 views

Compute the limit of the error term of Taylor polynomial of $f(x)=e^{3x}-1$

asked Jan 9, 2016 at 22:08

0 votes

0 answers

54 views

What is the difference between $o(x)$ and $o(x^{2})$?

asked Jan 9, 2016 at 22:33

0 votes

3 answers

58 views

How to test whether $e^{3x^{2}} + \frac {1}{1+3x^2} - 2\cos(x^2)$ is $o(x^3)$?

asked Jan 11, 2016 at 1:41

0 votes

0 answers

41 views

How to find the value of $x$ that $T_{\infty} f(x)$ convert to $f(x)$?

asked Jan 16, 2016 at 16:48

0 votes

1 answer

29 views

Why $T_{\infty}\sin(x^2)$ could be written as $x^2+o(x^4)$?

asked Jan 20, 2016 at 12:45

0 votes

0 answers

68 views

How to solve recurrence $T(n) = T(\lceil{\frac{2n}{3}}\rceil)$?

asked Oct 19, 2016 at 21:48

0 votes

1 answer

93 views

How to diagonalize a transformation from a $2\times 2$ matrix to a $2 \times 2$ matrix?

asked Nov 18, 2016 at 13:29

0 votes

1 answer

1k views

How to show all states from this renewal chain are recurrent?

asked Oct 20, 2017 at 19:09

0 votes

0 answers

65 views

How to understand $\limsup\limits_{x\rightarrow \infty} = -\infty$?

asked Nov 16, 2017 at 23:20

Stack Exchange Network

19 Questions

How to prove polynomials with degree $n$ does not form a vector space?

Does $\sum_{k=1}^{\infty}\frac{k!}{k^k}$ converge?

How to evaluate the following integral, $\int\frac{x \, dx}{x^2+2x+17}$?

Would the order of Taylor Polynomial change after substitution?

How to show $\int_{1}^{\infty} \frac{\sin^2(x)}{x^2}dx$ is finite?

Why $\|x\|^2\cdot \|y\|^2-(x\cdot y)^2=\sum_{1\leq i<j\leq n}(x_i y_j-x_j y_i)^2$?

Renewal Reward Process Problem

Is $R_2 =\max\{n \geq 0 : X_n = 2\}$ a stopping time?

Probability of picking balls with same color with replacement and without replacement

Suppose $f$ is continuous and verifies $f(x) = o(x)$. Does it follow that $\int_{0}^xf(y)\,dy = o(x^2)$?

Compute the limit of the error term of Taylor polynomial of $f(x)=e^{3x}-1$

What is the difference between $o(x)$ and $o(x^{2})$?

How to test whether $e^{3x^{2}} + \frac {1}{1+3x^2} - 2\cos(x^2)$ is $o(x^3)$?

How to find the value of $x$ that $T_{\infty} f(x)$ convert to $f(x)$?

Why $T_{\infty}\sin(x^2)$ could be written as $x^2+o(x^4)$?

How to solve recurrence $T(n) = T(\lceil{\frac{2n}{3}}\rceil)$?

How to diagonalize a transformation from a $2\times 2$ matrix to a $2 \times 2$ matrix?

How to show all states from this renewal chain are recurrent?

How to understand $\limsup\limits_{x\rightarrow \infty} = -\infty$?