Here the definition of positively homogeneous function $f$ is \begin{equation} f(\lambda x) = \lambda f(x), \quad \lambda \ge 0, \end{equation} and $f$ is...

The natural numbers are said to be a subset of the real numbers but how is this possible since in the set of natural numbers division is not allowed.

I don't understand what I should calculate if is said: "find the unique x", e.g. in the following exercise: "Find the unique x in the interval [0,pi]...

For $x,y$ in G, prove that $x = y =e$ if $xy^2=y^3x $ and $yx^2=x^3y$ where $e$ is the identity element in G. I have filled pages trying to solve but unab...

In order to estimate the eigenvalues of a real symmetric $n\times n$ matrix, I intend to use the Gershgorin Circle Theorem. Unfortunately, the examples on...

Q) For a given function on a given interval, the difference between the left-hand sum and right-hand sum always gets smaller as the number of subdivisions...

For example, I have the problem: $$ \int_{-1}^1x^4\left(1-x^2\right)^2dx $$ I set $\,u=1-x^2\,$, which gives $\,x^2=1-u\,$, $\,x=\pm\sqrt{1-u}\,$ and $\,-...

I got a question about his ODE: $(D-3)^3(D^2+25)^2(D-2)y = 7x^2e^{3x} + x\sin (5x)+4x^3$. So, in the solutions of the homogeneous eq. appears a complex ro...

Let $X_1,..,X_n$ be independent, identically distributed (continuous) random variables. Let $$\bar{X} = \frac{1}{n} \cdot \left(X_1+...+X_n\right)$$ Deter...

The equation for the volume of a cone is $\frac{1}{3}\pi r^2h$ starting from the base. However, I wanna calculate the height of the cone for a particular ...