# Having trouble understanding

by TheAntithesis
Tags: trouble
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,565 $$f(x,y)= \frac{1+ y^2sin(x)}{y(2cos(x)- 1)}$$ is continuous as long as the denominator is not 0- that is, as long as y is not 0 and 2cos(x)- 1 is not 0 which is same as saying cos(x) is not 1/2. $$f_y(x)= \frac{y^2 sin(x)}{y^2(2cos(x)- 1)}$$ is continuous as long as the denominator is not 0- that is, as long as y is not 0 and cos(x) is not 1/2- the same as the previous condition. Find the largest square, having (0, 1) as center, bounded by y= 0 and x= $\pi/3$ (where cos(x)= 1/2).