Let f(z) - 5 | 4, if z ‡ 0, if z = 0 Prove the following: - 1. The function of is continuous at the point z₁ = 0). 2. The Cauchy-Riemann equations are satisfied at Zo = = 0. 3. The function f does not have a complex derivative at zo = 0.

This is a calculus 3 problem. Please explain each step clearly, no cursive writing.

Which of the following is a true statement? d (10) = 5 (104) da O The equation of the tangent line to the parabola y = x2 at (-2, 4) is y – 4 = 2x (x + 2). O The slope of the tangent line to y = 4x + 1 is never 0. O The nth derivative da" d" (5x3 + 2x + 5) equals O for every integern> 3. O If f is continuous at x = a, then f is differentiable at x = a.

Define harmonic function. Prove that the function u =! 3x?y+2x² – y' – 2 y² is harmonic. Find its harmonic conjugate v and express u+iv as an analytic function of z.