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Physor
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8 votes
Accepted

Why is $\lim_{x \to \infty} x \log(1+\frac{1}{x}) = \lim_{y \to 0} \frac{\log(1+y)}{y}$?

8 votes
Accepted

If whenever $|x-a|<\delta$, $|y-a|<\delta$ then $|f(x)-f(y)|<\epsilon$, is this equiv. to $f$ cont. at $c$ then $f$ cont. on some interval around $c$?

5 votes
Accepted

Large Vector Notation

4 votes
Accepted

Baby Rudin 10.11 and 10.12

4 votes

Is the set of strictly monotonic functions closed or open?

4 votes
Accepted

How to prove that this limit is equal to $0$?

4 votes
Accepted

Calculate $\int_{\mathbb R^n}\frac{1}{(1+\|x\|_2^n)^2}dx$

4 votes
Accepted

Alternating tensor definition

4 votes

Solve $y’ = \frac{2-xy^3}{3x^2y^2}$ using Bernoulli form

4 votes
Accepted

Applying Picard–Lindelöf theorem for a second order ODE

3 votes

Quotient space if $X=\mathbb{R}$ and $x \sim y$ iff $y=x +2\pi k$ for $k\in \mathbb{Z}$.

3 votes
Accepted

Method of spherical means/average

3 votes
Accepted

In an inner product space that is not complete, is there a closed orthonormal system that is also complete?

3 votes
Accepted

Solve $y''(x)^2= (1+y'(x)^2)^n$ where $n \in \mathbb N$

3 votes

Evaluate : $\displaystyle\int\limits_{\gamma }\frac{\log (1+z)}{1+z}dz$

3 votes
Accepted

Equivalence of Norms on Finite-Dimensional Spaces: Questions

3 votes

Find the explicit solution of the ODE

3 votes
Accepted

Tell me hint, $\sum ^{\infty }_{n=1}\dfrac{i}{\left( n+1\right) \left( n+2\right) }$

3 votes

Logic Translating into Symbols

2 votes

Proving the differentiablity of a function at the point (0,0)

2 votes

Propositional Logic (equivalence exercise)

2 votes

Finding the solution to $x^2y''+xy'-y=0$

2 votes
Accepted

Show that $(\forall x)\alpha(x) \lor (\forall x)\beta(x)\rightarrow (\forall x)(\alpha(x)\lor \beta(x)) $

2 votes
Accepted

How to solve this limit $\lim_{n\to \infty}(\frac{2^n}{n^k})$?

2 votes

$\lim_{(x,y,z)\rightarrow(0,0,0)}((\frac{xyz}{x^2+y^2+z^2})^{(x+y)})$

2 votes
Accepted

When does a rectangular matrix A $\in$ $\mathbb C^{𝑚\times 𝑛}$ have the property such that $\|Ax\|_2=\|x\|_2$, where $x \in \mathbb C^𝑛 $

2 votes

Prove: $T \in L(Y,\ell^\infty(\mathbb K))$ is bounded $\implies$ $\forall n \in \mathbb N:g_n \in L(Y,\mathbb K)$ is bounded

2 votes
Accepted

Is $g \circ f$ map $\mathbb{R}^2 \to \mathbb{R}^3$? yes/no

2 votes
Accepted

Difference between cartesian/ cylindric parametrisation of helix

2 votes
Accepted

Significance of the determinant of a pure rotation matrix

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