Calculus in Higher Dimensions

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 +...

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MAT2615 EXAM PACK 2025 QUESTIONS WITH COMPLETE ANSWERS

(Sections 2.11,2.12) The parametric equations of two lines are given below: ℓ1 : (x, y, z) = (1, 0, 0) + t(1, 0, 1), t ∈ R ℓ2 : (x, y, z) = (1, 0,−1) + t(0, 1, 1), t ∈ R Calculate the equation of the plane containing these two lines. [5] 2. (Sections 2.11,2.12) MAT2601 Given the two planes 3x + 2y − z − 4 = 0 and −x − 2y + 2z = 0. Find a parametric equation for the intersection. [5] 3. (Sections 2.11,2.12) MAT2611 Find the point of intersection of the line ℓ : (x, y, z) = (5,...

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Calculus in Higher Dimensions - MAT2615 Assignment 4 2025 ;100 % TRUSTED workings, Expert Solved, Explanations and Solutions. For assistance call or W.h.a.t.s.a.p.p us on ...(.+.2.5.4.7.7.9.5.4.0.1.3.2)........... Problem Statement (Section 14.6, Chapter 17) Let VVV be a region in R3mathbb{R}^3R3 bounded above by the hemisphere z=1−x2−y2z = sqrt{1 - x^2 - y^2}z=1−x2−y2 and below by the cone z=x2+y2−1z = sqrt{x^2 + y^2 - 1}z=x2+y2−1. Let SSS be the surface of VVV (cons...

MAT2615 Assignment 4 2025 QUESTIONS WITH DETAILED ANSWERS

MAT2615 Assignment 3 (COMPLETE ANSWERS) 2025 - DUE 2025; 100% TRUSTED Complete, trusted solutions and explanations

MAT2615 Assignment 4 (COMPLETE ANSWERS) 2025 - DUE 2025; 100% TRUSTED Complete, trusted solutions and explanations.