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xbh's user avatar
xbh's user avatar
xbh
  • Member for 6 years, 6 months
  • Last seen more than a week ago
46 votes
Accepted

How can I justify this without determining the determinant?

13 votes
Accepted

Value of $\lim_{n\to \infty} \frac{1}{2^n} \sum_{k=1}^{2^n} \{\log_{2}k\}$

11 votes
Accepted

Solve: $\log_3(5(2^2+3^2)(2^4+3^4)(2^8+3^8)(2^{16}+3^{16})(2^{32}+3^{32})+2^{64})=?$

10 votes
Accepted

$ \begin{vmatrix} f(a) & g(a) & h(a) \\ f(b) & g(b) & h(b) \\ f'(c) & g'(c) & h'(c) \\ \end{vmatrix} =0 $

9 votes
Accepted

find the value of $\int_{-a}^{a} \frac{f(x)} {1+e^x} dx $?

9 votes

Justify: if $x\gt 0$, $\;\lim_{n\to\infty} \sqrt{n}\cdot{\overbrace{\sin\sin\cdots\sin}^{n\space\text{sines}}(x)}=\sqrt{3}$

8 votes

Definite integral of $x\sin^n x$ from $0$ to $\pi/2$

8 votes
Accepted

How to simplify or upperbound this summation?

8 votes

Limit for $e$ and $\frac{1}{e}$

7 votes
Accepted

Evaluate $ \lim\limits_{x \to 0}\frac{\int_0^{x^2}f(t){\rm d}t}{x^2\int_0^x f(t){\rm d}t}.$

7 votes
Accepted

Proving inequality using double integral

7 votes

Prove $\forall x \in \mathbb{R}$: $[\sinh(x)+\cosh(x)]^n = \cosh(nx)+\sinh(nx)$ ; $ n\in \mathbb{Q}$

7 votes

Evaluate $\lim_{n \to \infty} ((15)^n +([(1+0.0001)^{10000}])^n)^{\frac{1}{n}}$

7 votes
Accepted

If $I$ an interval and $x_1,x_2,x_3\in I$, why $t_1x_1+t_2x_2+t_3x_3\in I$ when $t_1+t_2+t_3=1, t_i\in [0,1]$?

6 votes

Easy ways to calculate matrix exponential of a particular $4\times 4$ matrix

6 votes
Accepted

Does $\sum^{\infty}_{n=1}xe^{-nx}$ converge uniformly on $[0,\infty)$?

6 votes

What is the main difference between pointwise and uniform convergence as defined here?

6 votes

How do you integrate $\int_{0}^{\infty}\frac{a\cos{(cx)}}{a^2+x^2}dx$?

6 votes
Accepted

Solve the following equation: $\sqrt {\sin x - \sqrt {\cos x + \sin x} } = \cos x$

6 votes

Limit $ \lim_{n \rightarrow \infty}\sqrt{(1+\frac{1}{n}+\frac{1}{n^3})^{5n+1}} $

6 votes
Accepted

$\int_0^{\infty}\frac{\sin x}{(1+x)^2}\,dx$ converges absolutely

5 votes
Accepted

Help find the mistake in this problem of finding limit (using L'Hopital)

5 votes

Suppose $ \alpha, \beta>0 $. Compute: $ \int_{0}^{\infty}\frac{\cos (\alpha x)-\cos (\beta x)}{x}dx $

5 votes

Does $(1+\frac12-\frac13) + (\frac14+\frac15-\frac16)+(\frac17+\frac18-\frac19)+\cdots$ converge?

5 votes

Permute columns by pre-multiplying and rows by post-multiplying?

5 votes

Determinant of matrix $[a_{ij}]$ where $a_{ij}=ij$ if $i\ne j$ and $a_{ij}=1+ij$ if $i=j$

5 votes
Accepted

Does $\lim_{n\to\infty} \sum^{n^2}_{k=n}\frac{1}{k}$ exist?

5 votes
Accepted

Suppose $f(x)$ is differentiable on $[0,1]$, and $f(0)=0$, $f(x)\ne 0,\forall x\in(0,1)$

5 votes

need of eigenvalue for a nontrivial solution

5 votes
Accepted

$f$ is differentiable in $[0,1]$ ,$\sup_{x\in[0,1]}|f'(x)| \le M\lt+\infty $

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