![What does the notation $\mathbb R[x]$ mean?](https://ly.shilpakalanarail.gov.bd/uploads/what-does-the-notation-mathbb-r-x-mean_720.jpg)
updates
What does the notation $\mathbb R[x]$ mean?
What does the notation $\mathbb R[x]$ mean? I thought it was just the set $\mathbb R^n$ but then I read somewhere that my lecturer wrote $\mathbb R[x] = $...
Read Journal Category
Updates
updates
Joint Probability function in expected value of sum of 2 random variable and product of 2 random variable
I realized that same joint probability $f_{xy}(x,y)$ is used in calculation of expected value for sum $E[X+Y]$ and product of 2 random variables $E[XY]$. ...
Read Journal
updates
A triangular grid of side $n$ is formed from $n^2$ equilateral triangles with sides of length $1$. Determine the number of parallellograms.
So here is Question :- A triangular grid of side $n$ is formed from $n^2$ equilateral triangles with sides of length $1$.Determine the number of parallell...
Read Journal
updates
Solve the upper bound of the integral for arccosine
The function arccosine can defined as $$\arccos(x) = \int_{1}^{x} -\frac{1}{\sqrt{1 - t^2}} \, \mathrm{d}t$$ Let $\theta$ be a known angle such that $$\th...
Read Journal
updates
Approximating $\pi$ using the sine function
If we have some approximation $x$ for $\pi$, it is possible to improve that approximation by calculating $\sin(x) + x$ if $x$ is sufficiently close to $\p...
Read Journal
updates
Complexity/Operation count for the forward and backward substitution in the LU decomposition?
If I have a linear system of equations $Ax=b$ where $A \in \mathbb{R} ^{n\times n}, x \in \mathbb{R} ^{n}, b \in \mathbb{R} ^{n} $ this system can be solv...
Read Journal
updates
Motivation of Lebesgue differentiation theorem
Fundamental theorem of calculus states that the derivative of the integral is the original function, meaning that $$ f(x)=\frac{d}{dx}\int_{a}^{x}f(y)dy.\...
Read Journal
updates
How to find formula for recursive sequence sum?
I have the following sequence: $$a(1) = 1$$ $$a(n) = a(n-1) + n$$ For example: $$a(1) = 1$$ $$a(2) =3$$ $$a(3) =6$$ $$a(4) =10$$ $$a(5) =15$$ $$a(6) = 21$...
Read Journal
updates
Would a $\infty$ sided regular polygon describe a circle?
Help us settle this argument. Consider a circle. What would best describe a circle? A zero sided regular polygon? The other person thinks this because it ...
Read Journal
updates
How to derive a tight linear upper bound of $x \rightarrow \frac{1 - \exp(-Cx)}{1 - \exp(-C)}$?
let $C > 0$, I'm interested in finding tight linear upper bounds for the following function : $x \rightarrow \frac{1 - \exp(-Cx)}{1 - \exp(-C)}$. ...
Read Journal