Docsity
Log inSign up
Docsity
Prepare for your exams
Prepare for your exams

Study with the several resources on Docsity

Earn points to download
Earn points to download

Earn points by helping other students or get them with a premium plan

Guidelines and tips
Guidelines and tips
Sell on Docsity
Sell on Docsity
Log inSign up

Prepare for your exams

Study with the several resources on Docsity

Find documents

Prepare for your exams with the study notes shared by other students like you on Docsity

Search Store documents

The best documents sold by students who completed their studies

Search through all study resources
Docsity AINEW

Summarize your documents, ask them questions, convert them into quizzes and concept maps

Explore questions

Clear up your doubts by reading the answers to questions asked by your fellow students

Earn points to download

Earn points by helping other students or get them with a premium plan

Share documents
download point icon20 Points

For each uploaded document

Answer questions
download point icon5 Points

For each given answer (max 1 per day)

All the ways to get free points
Get points immediately

Choose a premium plan with all the points you need

Study Opportunities

Choose your next study program

Get in touch with the best universities in the world. Search through thousands of universities and official partners

Community

Ask the community

Ask the community for help and clear up your study doubts

University Rankings

Discover the best universities in your country according to Docsity users

Free resources

Our save-the-student-ebooks!

Download our free guides on studying techniques, anxiety management strategies, and thesis advice from Docsity tutors

From our blog

Exams and Study
Go to the blog

Double Integral - Calculus III - Exam, Exams of Advanced Calculus

Symbiosis InternationalAdvanced Calculus

Double Integral, Evaluate Integral, Order of Integration, Use Differentials, Implicit Differentiation, Maximum Rate of Change, Coordinate Planes, Vertex in Plane, First Octant, Intersects Paraboloid. Above given points are from questions of this past exam paper. Its past exam paper of Calculus III.

Typology: Exams

2012/2013

Uploaded on 03/16/2013

avani
avani 🇮🇳

4.6

(5)

85 documents

1 / 5

Toggle sidebar

This page cannot be seen from the preview

Don't miss anything!

bg1
MA-227/6D: Calculus III
Test#2, March 14, 2012
Time available: 110 min.
Your name (print):
Your signature:
Please always explain your answer, at least by including your calcula-
tions. You should work on this sheet. A right answer without calculation
brings you no credit!
1. Evaluate the double integral
ZZD
(x+y)dA,
where Dis bounded by y=√2xand y=x2/2.
12 points
2. Evaluate the integral
Z4
0Z2
√ypx3+ 1dxdy
by reversing the order of integration.
12 points
pf3
pf4
pf5

Partial preview of the text

Download Double Integral - Calculus III - Exam and more Exams Advanced Calculus in PDF only on Docsity!

MA-227/6D: Calculus III Test#2, March 14, 2012

Time available: 110 min. Your name (print):

Your signature:

Please always explain your answer, at least by including your calcula- tions. You should work on this sheet. A right answer without calculation brings you no credit!

  1. Evaluate the double integral

∫ ∫

D

(x + y)dA,

where D is bounded by y =

2 x and y = x^2 /2. 12 points

  1. Evaluate the integral

∫ (^4)

0

√y

x^3 + 1dxdy

by reversing the order of integration.

  1. Find the limit, if exists, or show that the limit does not exist.

lim (x,y)→(0,0)

x^3 − 5 y^3 x^2 + y^2

12 points

  1. Find frrr and fsss for f (r, s, t) = ln(r^2 s^4 t^6 ).
  1. Let z = x^2 − 2 xy^3 , x = uv + w^3 , y = u + ew^. Find ∂z/∂u, ∂z/∂v, and ∂z/∂w when u = 2, v = −1, w = 0. 12 points
  2. Find the maximum rate of change of the function f (x, y, z) = sin(x − 4 y + 3z) at (1, 1 , 1) and the direction in which it occurs.
  1. Find the volume of the largest rectangular box in the first octant with three faces in the coordinate planes and one vertex in the plane 3x + 4y + 5z = 1. 12 points
  2. The plane x + y + z = 1 intersects the paraboloid z = 4x^2 + 4y^2 in an ellipse E. Find the points on E that are nearest to and farthest from the origin.