Thm. ①) [V₁ +V₂] 8 − [V₁]₂ + [V2]g ⑦ [av] 3 - α [V]₂ 2 3 V=O [v]8 ≤V=0 [V]₂ = 0

1d. 1e. 1f.

Q.3) Find the constants a, b, c, d, e if f(z) = (ax³ + bxy² + 3x² + cy² + x) + i(dx²y – 2y³ + exy+ y) is analytic.

2.-Find the following complex function u (x, y) and v (x, y)

EVALUATE Sx csc(2x) cot(2x) dx A. -zse (27) + la (ese (2) – cot (2-) + C B. z csc (2z) +In csc (2z) – cot (2x) +C C. -z cse (2r) - In (ese (2r) – cot (2) +C 1 D. rcsc (2z) -In (cse (2z) – cot (2r) + C

Evaluate J₁ (xy + yz + xz)dV B B = {(x, y, z) | 0 ≤ x ≤ 10,0 ≤ y ≤ 10,0 ≤ z <10}.

Find ff f(x, y) dA, where f(x, y) ) = x and R = [5, 10] × [−5, –4]. SSR f(x, y) da