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tenepolis
  • Member for 7 years, 10 months
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11 votes
1 answer
989 views

Prove or disprove: $\sum_{k=1}^{\infty}\frac{\sqrt{k+1}-\sqrt{k}}{k\sqrt{k}}$ is convergent

10 votes
5 answers
62k views

How to quickly check if vectors are an orthonormal basis of a vector space?

9 votes
2 answers
180 views

Analyze if the function is uniformly continuous: $f(x) = \frac{x}{1+x^{2}}$

6 votes
2 answers
7k views

Proving that the exponential function is continuous

5 votes
6 answers
2k views

Is there a way to prove continuity without using epsilon-delta?

5 votes
4 answers
203 views

Find 2 basis $M=\left\{v_1,v_2,v_3\right\}$ and $N=\left\{w_1,w_2,w_3\right\}$ such that $T_{MN(f)}$

4 votes
2 answers
719 views

Proofing that the exponential function is continuous in every $x_{0}$

4 votes
4 answers
3k views

Determine the eigenvector and eigenspace and the basis of the eigenspace

3 votes
0 answers
159 views

Determine the eigenspace and eigenvector of this matrix (just for one eigenvalue)

3 votes
4 answers
493 views

Calculate the limit: $\lim_{x\rightarrow \infty}\frac{\ln x}{x^{a}}$

3 votes
1 answer
22k views

Quick and easy way to show whether a matrix is injective / surjective?

2 votes
2 answers
6k views

Is this matrix injective/surjective?

2 votes
2 answers
248 views

What's the kernel of the matrix?

2 votes
1 answer
150 views

We have the scalar product $\left \langle \cdot, \cdot \right \rangle$. How is its belonging norm $\left \| \cdot \right \|$ defined?

2 votes
1 answer
90 views

Extract the equalities / inequalities from the text (linear programming, optimization)

2 votes
2 answers
198 views

How is this read correctly (problem with brackets)? 2^2048 - 2^1984 - 1 + 2^64 * { [2^1918 pi] + 124476 }

2 votes
3 answers
323 views

How many real solutions does this equation have: $x^{2}-2\sin x+2x=33$

2 votes
1 answer
1k views

Differentiate $f(x)=\tanh(x)$

2 votes
1 answer
937 views

Prove that $f(x) = 2x^{2}-3$ is continuous in all of $\mathbb{R}$

2 votes
3 answers
157 views

True/false: There are $4$ linearly independent vectors $v_1,v_2,v_3,v_4 \in \mathbb{R}^3$

1 vote
1 answer
33 views

Task: Give an example for a group $(B, \circ) $ and a subgroup $U \subsetneq B$

1 vote
1 answer
52 views

True/false? $v,w$ are vectors in $\mathbb{R}^2$. The vector $u=\left \langle v,w \right \rangle v -\left \| v \right \|^2w$ lies vertically on $v$

1 vote
3 answers
211 views

True/false: Let $v,w \in \mathbb{R}^2$. If $v \perp w$, then we have that $\left \| v+w \right \|= \left \| v \right \|+\left \| w \right \|$

1 vote
2 answers
164 views

Calculate the taylor polynom for $a(x)=\ln(\cos x)$

1 vote
1 answer
138 views

$\varepsilon$-$\delta$-proof: $s(z)=(z-3)\cdot t(z)$ is continuous at $z_{0}=3$

1 vote
2 answers
91 views

$\varepsilon$-$\delta$-proof: $f(x)=2x+1$ is continuous at $x_{0}=2$

1 vote
2 answers
412 views

Calculate the limit: $\lim_{x\rightarrow1^{+}}\left(\frac{\sqrt{x}-1}{\sqrt{x-1}} \right )$

1 vote
2 answers
364 views

Calculate the limit: $\lim_{x\rightarrow 0}\frac{a^{x}-b^{x}}{x}$

1 vote
0 answers
39 views

Almost found the limit points of this set

1 vote
1 answer
45 views

How can both these definitions be equivalent (duality)?