MAT2615 Assignment 4 (DETAILED ANSWERS) 2025 - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED - DISTINCTION GUARANTEED Answers, guidelines, workings and references ,... 1. (Section 14.6, Chapter 17) Let V be a region in R3 bounded above by the hemisphere z = p1 − x2 − y2 and below by the cone z = px2 + y2 − 1. Let S be the surface of V (consisting of the hemisphere on top and the paraboloid below). (a) Compute the volume of V using spherical coordinates. (10) (b) Sketch S and the XY-projection of S. (3) (c) Use a surface integral to evaluate the area of S. (8) [21] 2. (Chapter 17,Section 19.1) Consider the intersection R between the two circles x2 + y2 = 2 and (x − 2)2 + y2 = 2. y R x (a) Find a 2-dimensional vector field F = (M(x, y),N(x, y)) such that @N @x − @M @y = 1. (3) (b) Using this F and Green’s theorem (Theorem 19.1.1), write the area integral Z ZR 1 dA as a line integral. [Hint: Any function y = f (x) can be parametrised by r (t ) =
Quality you can trust: written by students who passed their tests and reviewed by others who've used these notes.
No worries! You can instantly pick a different document that better fits what you're looking for.
No subscription, no commitments. Pay the way you're used to via credit card and download your PDF document instantly.
“Bought, downloaded, and aced it. It really can be that simple.”