Which of the following sets has oo in its interior: (a) {z = « + iy, x² < y} (b) {z € C, zz > 0} (c) {z = x + yi, |z +1| > 1, x < 0} (d) {z € C, z³ – 2z² + 5z – 4 = 0} %3D
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- Prove that the limit of xy[(x^2 - y^2)/(x^2 + y^2)] is zero as (x, y) goes to (0,0)There's a connection between the Existence and Uniqueness Theorem for constant-coefficient, linear, homogeneous IVP's and linear algebra.1. Consider the following boundary value problem: uxy(x,y) = sin(x), x >0, y >0,u(x,0) =f(x), x≥0,u(0,y) =g(y), y≥0.(a) What consistency conditions should f and g satisfy? Solve the equation (assuming the consistency condition of the previous step).