pls help (9) Determine the order of the pole z = 0 of sin(2) - f(2)...
Log(2+5) 1. Consider function f(z) sin 2 (a) Determine all singular point (s) of f enclosed in the circle C4(0) (b) Are they isolated singularities? If so, which kind of isolated singularity are they (remov- able, pole, essential)? (c) Compute the residue of f at each of these singularities (d) Evaluate the integral f f(2)dz where y is the circle Ca(0) oriented counterclockwise 1.0 0.5 -0.5 Answer key 1. (а) z0,-T, T (b) Yes. Each is a pole of order...
This is a complex variable question!!!!!!!!!!!!!! Let e2 f(z) = P1-2) This function has a pole at 0. What is the order of that pole, and what is the residue Res (f;0) of that pole?
pls help (6) Show that all singularities of f(2) and evaluate sin() are simple poles. Find the residues 22:-1 ffo where is the circle 2| = 3 in ced.
9. Suppose that f (z) has a simple pole at ao on a closed curve C, but is analytic elsewhere inside and on C except for poles at a finite number of interior points a1,a2,, (a) If the contour C is indented at ao by a circular arc with center at ao, show that the limiting form of the integral of f (x) around the indented contour is as the radius of the indentation tends to zero, regardless of whether...
Question 2 If F(x, y, z) = (ef sin y, e' sin z, é sin x), find a) Determine V.F b) Determine V x F [101
Find the all first-order partial derivatives 9. f(x, y, z) = 3x In(x?yz) + xhiz 2 10. f(x, y, z)= 7,21 02 +22 Sin 6. fls. 1) = sin(x – ») + x?tany 7. f(x, y) = ["sindi
Problem 5. (i) Prove that sin (5) if 0 < If z = 0 £1 f(z) = 1。 is Riemann integrable on 0, (ii) Prove that if z if z E {0, π, 2r) g(z) = 0 is Riemann integrable on [0,2
9. If f(x, y, z) = x sin yz. (a) (2 points) Find the gradient off (b) (3 points) Find the directional derivative off at (1, 3, 0) in the direction of v= i +2j – k.
(3) For the following velocity fields F on R3, find the flow along the given curve. r(t) = (t, t2, 1) F=(-4xy, 83, 2) with 0 2 t 1l F=(z-z, 0,2) r(t)-(cost, 0, sin t) with 0 t π F = (-y,2, 2) with r(t) = (-2 cost, 2 sin t, 2t) 0 < t < 2π (3) For the following velocity fields F on R3, find the flow along the given curve. r(t) = (t, t2, 1) F=(-4xy, 83,...
9. Find the Laurent series about 0 that represents the complex function f(z)22 sin in the domain 0 < Izl < 00 0o rn i+ Answer: 9. Find the Laurent series about 0 that represents the complex function f(z)22 sin in the domain 0