5
votes
1answer
101 views

Prove that a mapping $f:[-1,1]^2\to\mathbb R^2$ with certain properties has the value $(0,0)$.

The mapping $f:[-1,1]^2\to\mathbb R^2$ is known to be continuous. Also the image of the upper edge of the rectangle is contained in the upper half-plane, the left edge's image is contained in the left ...
0
votes
3answers
87 views

What are the methods to find approximatly the 5th roots of an equations

By which method, can I find the nearest root of : $x^5−2x+1.1=0$ ? Thank you.
0
votes
1answer
80 views

Finding root between two points

The function $f:[0,1]\to \mathbb{R}$ is continuous, $f(0)<0$, $f(1)>0$ and there is one root in between. Using $f(0)$ and $f(1)$, the expression $\frac{1\cdot f(0)-0\cdot f(1)}{f(0)-f(1)}$ would ...
0
votes
0answers
90 views

Isolation of zeros in the case of univariate analytic functions expressed as a bivariate function.

We know that the zeros of an analytic non-constant function are always isolated. A proof is here. Let $L(v)$ be an analytic function in $v$, where $v\in\mathbb{R}$. Let us write $L(v) \equiv L(v,p)$ ...
1
vote
0answers
56 views

Lower-bounding the distance between zeros of a continuous function

Consider a continuous function of the form: $L(v) = \sum_{i = 0}^{m}[vA_{i} - B_{i}]p^{i}$ where $p$ is the root of the polynomial equation: $vf(p) - g(p) = 0$ with $f(p)$ and $g(p)$ being two ...