Toronto Math Forum
MAT3342018F => MAT334Lectures & Home Assignments => Topic started by: syee on December 09, 2018, 06:36:19 PM

We never did any examples of questions like this in class, does anyone know the procedure to solve this question?

$x^2+y^2\leq4, z^2=x^2+y^2\Rightarrowz^2\leq4\Rightarrowz\leq2$
so,$ze^z=\sqrt{x^2+y^2}e^x$since $x\geq0,y\geq0$
If go through xaxis then y=0 and f(z)=$2e^x(0\leq x\leq2)$
then, x=$r\cos t\Rightarrowf(z)=2e^{2\cos t},0\leq t\leq \frac{\pi}{2}$around of circle, and then $x=0, f(z)=y,0\leq y\leq2$
On the xaxis, the max of fis $2e^2$, on the circle is t=0$\Rightarrowf(z)=2e^2$, on the yaxis is 2
so, Max${(2e^2,2e^2,2)}=2e^2 $