general
Conversion of trigonometric identity to hyperbolic version
I have been asked to convert a circular trigonometric identity into its corresponding hyperbolic version using Osborn’s rule. The identity is $\cos2x = 1-...
Apr 13, 2026
Archive: General
general
Derivative of $\sqrt{\sin (x^2)}$
I have problems calculating derivative of $f(x)=\sqrt{\sin (x^2)}$. I know that $f'(\sqrt{2k \pi + \pi})= - \infty$ and $f'(\sqrt{2k \pi})= + \i...
Apr 13, 2026
general
Proof variance of Geometric Distribution
I have a Geometric Distribution, where the stochastic variable $X$ represents the number of failures before the first success. The distribution function i...
Apr 13, 2026
general
Theorem 4.14 Rudin Functional analysis (a) $\Rightarrow$ (b)
Statement If $X$ and $Y$ are Banach Spaces ad if $T \in \mathcal{B}(X,Y)$, then each one of the following three conditions implies the other two: (a) $\ma...
Apr 13, 2026
general
How to quickly convert to the parametric form of equation of line?
I have a straight line given by: $$ \begin{cases} x - y - 4z + 12 = 0 \\ 2x + y -2z + 3 = 0 \end{cases}$$ I'm looking to convert it to the parametric...
Apr 13, 2026
general
Rudin functional analysis theorem 1.13 (f) and theorem 1.11.
Theorem 1.13 (f) states: Let $X$ a topological vector space. I $E$ is a bounded subset of $X$, so is $\bar{E}$. The proof relies on theorem 1.11, which st...
Apr 13, 2026
general
Fisher information of the Rayleigh distribution
Problem description: Find the Fisher information of the Rayleigh distribution. I was satisfied with my solution until I saw that it disagreed with the sol...
Apr 12, 2026
general
How the dot product of two vectors can be zero?
I am given, $\vec s$$=2\hat i+\hat j-3\hat k$ and $\vec r$$=4\hat i+\hat j+3\hat k$ Now I am asked to calculate the dot product $\vec s\cdot\vec r$ But I ...
Apr 12, 2026
general
Proving a subset is a subspace of a Vector Space
To prove a subset is a subspace of a vector space we have to prove that the same operations (closed under vector addition and closed under scalar multipli...
Apr 12, 2026
general
Interval Notation and Infinity- Closed or Open?
I was wondering whether I should use closed $[-\infty, \infty ]$ or open $(-\infty, \infty )$ notation when representing the infinity sign in interval not...
Apr 12, 2026
