A thin metal plate, located in the xy-plane, has temperature T(x, y) at the point (x, y). Sketch some level curves (isothermals) if the temperature function is given by T(x, y)= 100/1+x^2+2y^2

Step-by-step explanation:

Given that:

This implies that the level curves of a function(f) of two variables relates with the curves with equation f(x,y) = c

here c is the constant.

By cross multiply

From (2); let assume that the values of c > 0 likewise c < 100, then the interval can be expressed as 0 < c <100.

Now,

This is the equation for the  family of the eclipses centred at (0,0) is :

Therefore; the level of the curves are all the eclipses with the major axis:

 and a minor axis  which satisfies the values for which 0< c < 100.

The sketch of the level curves can be see in the attached image below.