Limits are vital to mathematical analysis and calculus. They are also used to define derivatives, integrals, and continuity. Rules of Limits Here are some well-known rules/laws/properties of limits. Rules Expressions Sum/Difference Rule limx→b[f(x) ± h(x)] = limx→b[f(x)] ± limx...
And central to the idea of a limit is the idea of a sequence of rational numbers.A sequence of rational numbersWe encounter such a sequence in geometry when we determine a formula for the area of a circle. To do that, we inscribe in the circle a regular polygon of n sides. The area...
This also shows that \(G^\varepsilon _\alpha \) depends on the choice of \(\lambda ^\varepsilon \) only through \(\alpha \), and therefore, the definition is well posed. We also extend by continuity this definition to the case \(\alpha =\dot{\ell }^\varepsilon (t)=0\), by...
In many cases, the lateral extension of economically valuable mineral deposits is linked to fractures. Knowing the characteristics of these tectonic structures is crucial for determining the continuity of mineralization in the subsoil and, consequently,