All Questions
3
questions
0
votes
1
answer
46
views
How can I study the changes of $f_k(x)=\frac{e^{kx}-1}{2e^x}$
Let $f_k(x)$ be a function defined on $\mathbb{R}$ by
$$f_k(x)=\frac{e^{kx}-1}{2e^x}$$
Where $k$ is a real , How can I study according to the values of $k$ the changes of the changes of $f_k$
I ...
- 59
1
vote
1
answer
98
views
Functional square root of a function $F([a,b])=[1−br+a,1−br+a+b]$.
Suppose we have a function $F\colon \mathbb{R}^2 \to \mathbb{R}^2$ over a numeric pair (pair of real numbers) $[a, b]$ such that:
$$F([a,b]) = [1-br+a, 1-br+a+b]$$
for some $r\in\mathbb{R}$.
find a ...
- 67
0
votes
1
answer
26
views
Re-definition of scalar product $x \cdot y$ as $\log( 1 + a \, \, x \cdot y)$
Is it possible to set $c_1= c_1(a)$ and $c_2=c_2(a)$ such that for any $a>0$, for any two angles $\theta_i, \theta_j \in [0, 2\pi]$, we have that:
$$
\log( 1 + a \cos(\theta_i - \theta_j) ) = c_1 \...
- 200