ProblemSet9
.pdf
School
Johns Hopkins University**We aren't endorsed by this school
Course
AS.110 202
Subject
Mathematics
Date
Jan 15, 2025
Pages
1
Uploaded by SuperResolve15998
HOMEWORK PROBLEM SET 9DUE SUNDAY, OCTOBER 27, 2024, 11:59PM EDT:UTC-4AS.110.202.FA24 CALCULUS IIIPROFESSOR RICHARD BROWNThe following problem set is based onSections 5.1,5.2, and5.3of the text. Along withthe exercises below, please do the following:•WeBWorK:Complete Problem Set 9 on WeBWorK by Saturday, October 26, 2024,11:59pm EDT:UTC-4.•Reading for next week:ReadSection 5.4,5.5,6.1, and6.2.For practice (neither to be handed in nor graded), here is a set of selected textbook problems:•Section 5.1:3cd, 4d, 6, 9, 11, 13•Section 5.2:4, 10, 12•Section 5.3:3, 4f, 7, 8, 12, 13, 15The following exercises are to be handed in for grade in Gradescope on the due date above:Exercise 1.Letfbe a continuous function on the interval [a, b] andgcontinuous on [c, d].Do the following:(a)Show thatZZR[f(x)g(y)]dA=Zbaf(x)dxZdcg(y)dy,whereR= [a, b]×[c, d].(b)For the particular case thata=c= 0 andb=d= 1, calculatelimm,n→∞f(m, n) =ZZRxmyndx dy.(c)Calculatelimm,n→∞Zπ−πZπ−πcos(nx) sin(my)dx dy.(double integrals, the definite integral, rectangular regions, notation)Exercise 2.LetDbe the region given by the set of (x, y), where 1≤x2+y2≤2 andy≥0.IsDan elementary region? EvaluateRRDf(x, y)dA, wheref(x, y) = 1 +xy.(double integrals, the definite integral, elementary regions)1
