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# CalculusofSeveralVariablesII MAT215

CSU Pomona

GPA 3.53

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This 2 page Class Notes was uploaded by Dr. Elody Harris on Saturday October 3, 2015. The Class Notes belongs to MAT215 at California State Polytechnic University taught by MichaelNasab in Fall. Since its upload, it has received 38 views. For similar materials see /class/218200/mat215-california-state-polytechnic-university in Mathematics (M) at California State Polytechnic University.

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Date Created: 10/03/15

Name Moth 215 Cale of Several Variables II Review Problems for MidTerm 2 Review problems for MidTerm 2 The midterm will cover sections 158 through 165 Please showyour work on your scratch papers No e This is by no means a practice exam You should not expect the problems on the midterm to be exactly like these Also just because a particular kind of problem isn39t here that doesn39t mean that it won39t be on the midterm 1 N 5 0 O M Given xy z 8quot sin y e y sin z 8 2 sinx Find a Curl I Using the triple integral In spherical coordinates find the volume ofa solid that is enclosed between the surfaces 62 y2 Z2 18 and 3 z x2 y2 Include a diagram in 3D Evaluate jfjjsewpz sin dp d d0 0 3 Evaluate J x2 y2 zzdzdxcb2 by changing it to spherical coordinates 0 vauae x C W ere COnSISO epara oa x rom O an en e Elt 3 ydx dy h c 39tfth bly 2f 00t11 dth th C line segment from 11 to 01 Include a diagram ofthe curve C Determine whether x y lt 1 2x y In x x2 gt is conservative If it is find a potential function xy for it NO short cuts Referring to the problem 5 evaluate Jl2xyln x abcx2 dy where C is any path from 1 0 to 91 C x Use Green s theorem to evaluategSlna y dXS l y where C is the triangle with vertices 0 0 2 0 and 0 4 V C y 4x Using the change of variables u y 4x and v y 4x evaluateJ d4 where R is the region enclosed R y 4x by the lines y 4 x y 4 x 2 y 2 4 x and y 5 4 x Include a diagram of the regions R and 8 Using the line integrals find the mass of a thin wire in the form ofthe curve x 8 cost y e Sint where 0 S t S1 if the density function is px y le y2 Use the Green s theorem to find the work done by a force 15x y lt EAE gt on a particle that moves 3 counterclockwise one time around the closed curve formed by y 0 x 2 and y x7 Use a line integral to find the area of the region in the rst quadrant enclosed by the graphs of 1 y x y and y Include a diagram of the region x bdiv 4 945 7 FSoluhuMS MAizyM g IJS 35 w 6 l Krv i011 quot hk Q 3 gt 3 C1 o b Xi quot xxwk L 39 39 C i hl x L C s x a El quot f um I C 2 5 09 701 3 K Max 3 L 2 2 SS 3713 wv M Ma 9 a fo V 1 W1 e 4 S 0cm s 13 Hx lb lira 3 H n 3 1 x k k a 2 on F re 9 a r Ax 59 a z Vbdmr 1 1 C Sub Z 42 L Sunk y a 7g 3 AHIF Lgmaj C sl l 4 77 h P PL5M 0 AG 3 15 sum 1 ultlv quot

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