general
If a part of the series diverges, does the whole diverge?
I couldn't find an easy to way to check for the convergence of the series. The sum is supposed to be from 2 to infinity and there is a little mistake...
Apr 22, 2026
Archive: General
general
Multivariate Normal Difference Distribution
Since the distribution of a difference of two normally distributed variates X and Y with means and variances $(\mu_x,\sigma_x^2)$ and $(\mu_y,\sigma_y^2)$...
Apr 22, 2026
general
Left & Right Cosets of $A_{4}$ in $S_{4}$
So I'm looking through solutions for a practice problem in my modern algebra textbook that has me completely stumped. Let $S_{4}$ be the group of per...
Apr 22, 2026
general
solve an implicit function
I have seen that an example of implicit function that can be solved only numerically is (solving for x knowing y): $$ \sin(x) = y\cdot x $$ I was wonderin...
Apr 22, 2026
general
Is the graph of a continuous function homeomorphic to its domain?
Let $f:\mathbb{R}^n\rightarrow\mathbb{R}$ be a continuous real function and we consider its graph identified by the subset: $$\mathcal{G}(f)=\{(x,f(x))\in...
Apr 22, 2026
general
sum of this series: $\sum_{n=1}^{\infty}\frac{1}{4n^2-1}$
I am trying to calculate the sum of this infinite series after having read the series chapter of my textbook: $$\sum_{n=1}^{\infty}\frac{1}{4n^2-1}$$ my s...
Apr 21, 2026
general
How to calculate the range of this function without the use of graphs?
I would like to know how you can find the range of this function $f(x)=x+\frac{1}{x}$ through for example algebra I know it is possible to calculate the a...
Apr 21, 2026
general
Why is the range of inverse trigonometric functions defined in this way?
My question is really simple, why is the range of the $\sin^{-1}(x)$, $\cos^{-1}(x)$ and $\tan^{-1}(x)$ defined as $[-\pi/2,\pi/2]$, $[0,\pi]$ and $[-\pi/...
Apr 21, 2026
general
Function is surjective (onto) or not
I am trying to find if this function is surjective (onto) or not: $f: \mathbb{Z}\to \mathbb{Z}$ given by the rule $3n + 1$. I know that $3n-1$ is not surj...
Apr 21, 2026
general
Expanding the integrand
Can anyone help me find the solution to this integral: $$\int\limits{(t-4)(t-2)^{4/5}}dt?$$ I think I need to expand the integrand but I do not know how. ...
Apr 21, 2026
