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drawar
  • Member for 11 years, 6 months
  • Last seen more than 3 years ago
11 votes
5 answers
2k views

Prove that $ f(x) $ has at least two real roots in $ (0,\pi) $

8 votes
1 answer
1k views

Probability of at least one male and one female sharing the same birthday

8 votes
3 answers
1k views

Rolle's Theorem

7 votes
1 answer
22k views

How to tell if a limit of a multi-variable function exists?

6 votes
3 answers
474 views

Evaluate $\lim\limits_{x \to \infty } {\left( {\int_0^{\pi /6} {{{(\sin t)}^x}dt} } \right)^{1/x}}$

4 votes
5 answers
2k views

What is the probability that the first card is an ace given that the 15th card is an ace

4 votes
2 answers
576 views

Prove that there exists $x_n$ such that $0 \leq x_n \leq 1-\frac{1}{n}$ and $f(x_n)=f(x_n+\frac{1}{n})$. [duplicate]

3 votes
2 answers
97 views

Evaluate $\mathop {\lim }\limits_{n \to \infty } {\left( {\frac{{{a^n} + {a^{2n}}}}{{1 + a}}} \right)^{1/n}}$ where $0<a<1$

3 votes
2 answers
2k views

Approximation by Taylor polynomial

3 votes
1 answer
2k views

Find the smallest positive integer $k$ such that $A^k=0$ where $A$ is a nonzero matrix

3 votes
0 answers
2k views

Find the expectation and variance

3 votes
0 answers
76 views

Compute $E\left[\frac{W_{N(t)+1}}{N(t) + 1}\right]$ where $(N(t))$ is a homogenous Poisson process

2 votes
1 answer
655 views

Draw the composition of directed graphs?

2 votes
3 answers
123 views

Show that $f$ is differentiable on $(−1, 1)$.

2 votes
2 answers
445 views

Prove that $S$ is countably infinite

2 votes
2 answers
4k views

Prove that if $G$ is a tree with maximum degree of vertices $\Delta$, and $k$ $\leq \Delta$, then G has at least $k$ leaves

2 votes
1 answer
330 views

Joint probability density

2 votes
2 answers
78 views

Linear span proof

2 votes
0 answers
275 views

Post-optimality analysis: Change in one of the constraints

2 votes
1 answer
76 views

Jordan Canonical Form of $A^{-1}$

2 votes
1 answer
1k views

Positive definite matrix and self-adjoint invertible matrix

1 vote
1 answer
305 views

Construct an extrapolation table with optimal rate of convergence for cubic spline approximation

1 vote
2 answers
420 views

$\displaystyle\mathop {\lim }\limits_{(x,y,z) \to (0,0,0)} \frac{{x{y^2}z}}{{{x^2} + 4{y^4} + 9{z^6}}}$

1 vote
1 answer
258 views

Prove that there exists a number $ x_{0} \in (0,1) $ such that $ f''(x_{0})=0 $

1 vote
4 answers
298 views

$\mathop {\lim }\limits_{x \to {0^ + }} \left( {\frac{1}{x} - \frac{1}{{\sqrt x }}} \right)\;$?

1 vote
3 answers
206 views

If $A=(a_{ij})$ is positive semidefinite, prove that $a_{ij}^2 \leq a_{ii}a_{jj}$ for all $i \neq j$

1 vote
1 answer
107 views

Find an invertible matrix $B$ such that all eigenvectors of $B$ are scalar multiples of a given vector.

1 vote
1 answer
200 views

Let$(a,b,c)$ be a nonzero vector in the row space of a $3\times 3$ matrix $B$. Show that the nullspace of $B$ is a subset of the plane $ax+by+cz=0$

1 vote
1 answer
81 views

Evaluate the expectation of $\frac{1}{UV}$

0 votes
1 answer
39 views

Given $P : R^n → R^n$ is a linear transformation. Show that there is an integer $k$ such that $R(P^k)=R(P^{k+1})=R(P^{k+2})=...$