1. If it's given that A: R2 -> R is defined by A(x, y)={1, if xy greater than or equal to 0.

and 0, if xy < 0.

(a) how do i show that the partial derivatives Ax(0) and Ay(0) exist? (Note that Ax and Ay doesn't mean A*x and A*y. I just mean the first order derivatives.)

(b) How do I prove that A is not continuous at 0?

2. If A(x, y, z) = xzsin2y + ye^z

(a) How do I find all the mixed partial derivatives of A and verify Clairant's Theorem holds?

(b) Will Ayxz = Ayzx? Will I know this without actually calculating?

(c) Will Axyy=Ayzx?

(d) Will Ayzy=Azyy?