Finding the formula of a sequence.
I have a sequence $\{0,1,1,2,2,3,3,4,4,5,5,...\}$ and I am supposed to find a formula for the n-th term. I do not see a pattern between the terms except t...
20 Apr 2026 1 READS
Archive: News
Limit definition of the osculating circle
Let $I$ be an interval and $c:I \to \mathbb{R}^2$ a smooth curve with $c' \neq 0$ everywhere. I am currently trying to figure out how to define the o...
20 Apr 2026 1 READS
Relative Extrema
I did a question to find relative extrema for the following function: $f(x)=x^2$ on $[−2,2].$ The answer said that there is no relative maxima for this fu...
20 Apr 2026 1 READS
Show that a matrix has full column rank
Consider a matrix $A$ of size $T\times 2K$. Consider the collection of numbers $k_1,k_2,...,k_T$, where each $k_t\in \{1,...,K\}$. Each $t$-th row of the ...
20 Apr 2026 1 READS
How to parametrize the ellipse $4x^2+\frac{y^2}9+xy=36$?
I know how to parametrize an ellipse that looks like $4x^2+\dfrac{y^2}9=36$ by using polar coordinates:$$2x=6\cos t\Longrightarrow x=3\cos t\\\frac y3=6\s...
20 Apr 2026 1 READS
The relation between trace and determinant of a matrix
Let $M$ be a symmetric $n \times n$ matrix. Is there any equality or inequality that relates the trace and determinant of $M$?
20 Apr 2026 1 READS
What does non-zero integer mean?
The definition for the Rational Number is given as Numbers that can be expressed as a fraction of an integer and a non-zero integer. at http://en.wikipedi...
20 Apr 2026 1 READS
Find mean and variance using Moment generating function of the negative binomial.
I was asked to derive the mean and variance for the negative binomial using the moment generating function of the negative binomial. However i am not sure...
20 Apr 2026 1 READS
![Is it possible for two non parallel planes to not intersect with each other in 3d? [closed]](https://edu.smbbmcl.edu.pk/uploads/is-it-possible-for-two-non-parallel-planes-to-not-intersect-with-each-other-in-3d-closed_720.jpg)
Is it possible for two non parallel planes to not intersect with each other in 3d? [closed]
I read that two lines in 2d if they are not parallel they will always intersect but in 3d it is possible for two non parallel lines to not intersect but w...
20 Apr 2026 1 READS
Why is the area between these two graphs positive?
Why is the area between these two functions positive? \begin{align*} f(x) &= (x-1)^3\\ g(x) &= (x-1). \end{align*} The area between $f(x)$ and $g(...
20 Apr 2026 1 READS
