how to calculate index of lexicographical order
As far as my knowledge, this has something to do with the combinatorial number system and lexicographical order, but I can't tell exactly what it is....
22 Apr 2026 1 READS
Archive: General
Calculate definite integral using the definition (Riemann Sum)
I would like to know how to use the Riemann Sum (With Unequal width) to calculate $\displaystyle f(x) = \sqrt{x}$ from $[1,2]$ I know how to calculate it ...
22 Apr 2026 1 READS
How to solve integration with Dirac Delta function?
I am struggling to solve several problems in my 'Signals and Systems' textbook. However, I just met a confused problem. Q) $\displaystyle\int_{-...
22 Apr 2026 1 READS
How to find solutions of linear Diophantine ax + by = c?
I want to find a set of integer solutions of Diophantine equation: $ax + by = c$, and apparently $\gcd(a,b)|c$. Then by what formula can I use to find $x$...
22 Apr 2026 1 READS
![Find the vector equation for the line passing through two points [closed]](https://edu.smbbmcl.edu.pk/uploads/find-the-vector-equation-for-the-line-passing-through-two-points-closed_720.jpg)
Find the vector equation for the line passing through two points [closed]
The question is find the vector equation for the line passing through two points P1 = (6,2,4) and P2 = (12,0,3) But the formatting of the answer is throwi...
22 Apr 2026 1 READS
How to write the index number in the Wolfram Alpha search engine
I am trying to see some results for my sequence in Wolfram Alpha, but I don't know how to enter the "n" letter as an index. My sequence is a_(n+1) = ...
22 Apr 2026 1 READS
What is the meaning of equilibrium solution?
What are the equilibrium solutions for the differential equation $\dfrac{\mathrm{d}y}{\mathrm{d}t} = 0.2\left(y-3\right)\left(y+2\right)$ My Question: Wha...
22 Apr 2026 1 READS
What is the Domain of Gamma Function?
The gamma function is defined as $\Gamma(s)=\int_0^\infty t^{s-1}e^{-t}dt$ for s>0. But then it says that "The gamma function is defined for all complex n...
22 Apr 2026 1 READS
![The average radius of an ellipse [closed]](https://edu.smbbmcl.edu.pk/uploads/the-average-radius-of-an-ellipse-closed_720.jpg)
The average radius of an ellipse [closed]
I have recently been studying the 3rd Kepler´s law which uses the average radius of an orbit. I would love to know how to find the geometric average radiu...
22 Apr 2026 1 READS
![Find the Area of an Ellipse Given Shortest Distance and Longest Distance from a certain Focus to Circumference? [closed]](https://edu.smbbmcl.edu.pk/uploads/find-the-area-of-an-ellipse-given-shortest-distance-and-longest-distance-from-a-certain-focus-to-circumference-closed_720.jpg)
Find the Area of an Ellipse Given Shortest Distance and Longest Distance from a certain Focus to Circumference? [closed]
In an ellipse, I am given that the shortest distance from one focus to the circumference is $1.5$. Then the longest distance from that focus to the circum...
22 Apr 2026 1 READS
