MATH 171- Final Exam Guide - Comprehensive Notes for the exam ( 28 pages long!)

Math 227 Exam 4- Page 7 of 8 Due: 12/01/2017 6. Evaluate ll. F . ids with F = (z-12 , 2zy , 2) and S: boundary of region enclosed on top by the plane z = 4 and below by the parabaloid z = z2+ Math 227 Exam 4-Page 8 of 8 Due: 12/01/2017 Bonus (no partial credit): It turns out that F-(-y , x , zy-vray satisfies ▽ × F*-x2 , 2ry , 2). (the field from problem 6) Use this fact, Stokes' Theorem, and properties of surface/line integrals to answer problem 6 without doing any computations.

Math 227 Due: 12/01/2017 Exam 4-Page 8 of 8 Bonus (no partial credit): It turns out that F = 《-v , z , zy- (the field from problem 6) Use this fact, Stokes' Theorem, and properties of surface/line integrals to yr* 》satisfies ▽ × F-6-2 , problem 6 without doing any computations.

Math 227 Exam 4 - Page 8 of 8 Due: 12/01/2017 Bonus (no partial credit): It turns out that F-(-y , x , zy-yz*) satisfies ▽ x F the field from problem 6) (z -22 , 2y , 2). Use this fact, Stokes' Theorem, and properties of surface/line integrals to answer problem 6 without doing any computations.