44. Compute , where γ is the unit circle, oriented counterclockwise. More generally, show that for...
In problems 3-5 evaluate ∫?⃗∙??⃗? using Stokes’ theorem. In each
case ? is oriented counterclockwise when viewed from
above.
4. F(x, y, z) = (z)i + (x2)j + (y – sin(z))k; c is the boundary of the helicoid given by Õ(r,0) =< rcos(6), rsin(0),>; Osrs 1, osos
1. Consider the unit circle: (x,y) : x2 y2 = 1. T. Let f R2 ->R be defined by f(x,y) = x2-y, and let F : R2 -> R be defined by F(x, y) Compute the integral of f and F around the unit circle. For the integral of F, proceed in the standard (anticlockwise) direction
please show steps
5) Given the following circuit determine the voltage across the 192 resistor for all time >0. 10(--mA 19 w 250 ml
(2) Suppose V F = (ex: -2yre?",0). Compute SS (V F). ds, where is the upper unit hemisphere r? + y + z2 = 1, 2 > 0. (Hint: Can you use result of 1 and a more convenient surface over which to integrate?)
Given the logistic map Xn+1 = run(1 – Xn) with r > 0. Show the 2-cycle is stable for 3 <r <1+V6.
Consider scatering by a repulsive δ-shell potential. V(r) = 2-5(r-R), (γ > 0) (a) Set up an equation that determines the s-wave phase shift dg as a function of k (E-h2k2/2m). (b) Assume that γ is very large, γ 》 R-1, k. If tan kR is close e resonance behavior is scattering. Determine approximately the positions of the resonances, keeping terms of order of 1/y. Also obtain an ance width Γ defined ation expression for the r as 1.
Compute limn >oo A" for 1 1/2
where 7 is the region defined by >0, y >0, >0, r+y+z<3.
PROBLEM 2 Consider the family of circles P = {C, TER>0}, where Cr = {(x, y) R2 | x2 + y2 = p2} is a circle of radius r > 0. Prove that P is a partition of R2. State an equivalence relation induced by this partition. Hint: What is a property that is True for all points in a fixed circle?
(1 point) Find the inverse Laplace transform of 2s + 9 $2 + 23 S> 0 y(t) =