Sumários
Aula TP36
13 Maio 2021, 13:00 • Rita Sousa
Multiplicadores de Lagrange. Exercícios 1 e 2 da PUC (semana 12).
Summary of optimization problems
13 Maio 2021, 11:00 • Rita Sousa
In this class we summarized different approaches to solve different optimization problems. We revisited exercise 6 from PUC Week 11 - (shortest distance of plane from a point) before solved with Lagrange multipliers.
Now we showed that it can be solved also simply by replacement of one variable z as a function of x and y, and finding the roots of f_x=0 and f_y=0, where
f= distance^2=(x-x0)^2+(y-y0)^2+(z-z0)^2
Other exercises solved in this class were
- an example of application of Lagrange multiplers for a function of 3 variables f(x,y,z)=ln(x^2+1) + ln(y^2+1) + ln(z^2+1), subject to g(x,y,z)=x^2+y^2+z^2=12.
- f(x,y)=xy subject to 4x^2+y^2=8
We also did an additional example for how to find the equation of the tangent plane to a surface at a given point and the normal line at the point, - this was to reinforce earlier theoretical material, requested by the students.
Finally, we revisited also minima and maxima of functions involving trigonometric functions, namely the optima of the function f(x,y)=y^2-2y cos(x) when x in[-1,7].
Capítulo II - Funções de mais de uma variável - Aula 36
13 Maio 2021, 08:00 • Rita Sousa
Resolução de exercícios de preparação para a prova escrita.