Lagrange's rational function theorem states that if one has two rational functions in multiple variables $f(x_1,x_2,...x_n)$ and $g(x_1,x_2,...,x_n)$...

Find $x$ if $2^{16^x} = 16^{2^x}$. If $x = 0$ we have $2=16$. $8$ times or $(2^3)$ difference and if $x = 1$ we have $65536=256$. $256$ or $2^8$ differenc...

Today I studied about circle that it is a closed figure with $0$ edges. Then I thought about a wire with fixed length and tried to make closed polygons of...

As evident in the image, the function consists of linear segments and one curved segment (DE). I thought maybe I can find the equation for the function bu...

It is safe to say that every mathematician, at some point in their career, has had some form of exposure to analysis. Quite often, it appears first in the...

i am a programmer who interest in math , lately in palindromic numbers , so if it's stupid question i am sorry ! i was reading about palindromic numb...

I've the text below given in my notes: Derivative of linear function: Let $R:X\to Y$ be a linear function .Then $R':X\to L(X,Y)$ is a constant f...

The matrix is as follows: $$ \left[ \begin{array}{ccc|cc} a&0&b&2\\ a&a&4&4\\ 0&a&2&b \end{array} \right] $$ I need to...

I am using Stewart Calculus and trying to understand one of the formulas for the surface area of revolution generated by a curve about an axis on an inter...

Consider a seven-letter word formed by mixing up the letters in the word COMBINE. How many ways can you do this if no vowel is isolated between two conson...