3.1 Using the differential length dl, find the length of each of the following curves: (a) p = 3, T/4 < ¢ < «/2, z = constant (b) r = 1, 0 = 30°, 0 < ¢ < 60° (c) r = 4, 30° < 0 < 90°, 6 = constant

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
icon
Related questions
Question
3.1
Using the differential length dl, find the length of each of the following curves:
(a) p = 3, T/4 < ¢ < «/2, z = constant
(b) r = 1, 0 = 30°, 0 < ¢ < 60°
(c) r = 4, 30° < 0 < 90°, ¢ = constant
3.2
Calculate the areas of the following surfaces using the differential surface area dS:
(a) p = 2, 0 < z < 5, 7/3 < ¢ < T/2
(b) z = 1, 1 < p < 3,0 < ¢ < T/4
(c) r = 10, 7/4 < 0 < 2#/3, 0 < ¢ < 2™
(d) 0 < r < 4, 60° < 0 < 90°, ø = constant
Transcribed Image Text:3.1 Using the differential length dl, find the length of each of the following curves: (a) p = 3, T/4 < ¢ < «/2, z = constant (b) r = 1, 0 = 30°, 0 < ¢ < 60° (c) r = 4, 30° < 0 < 90°, ¢ = constant 3.2 Calculate the areas of the following surfaces using the differential surface area dS: (a) p = 2, 0 < z < 5, 7/3 < ¢ < T/2 (b) z = 1, 1 < p < 3,0 < ¢ < T/4 (c) r = 10, 7/4 < 0 < 2#/3, 0 < ¢ < 2™ (d) 0 < r < 4, 60° < 0 < 90°, ø = constant
2.10 Express the following vectors in rectangular coordinates:
(а) А
psin ф a, + р cos ф а,
2z az
-
(b) В — 4r cos ф а, + rao
Transcribed Image Text:2.10 Express the following vectors in rectangular coordinates: (а) А psin ф a, + р cos ф а, 2z az - (b) В — 4r cos ф а, + rao
Expert Solution
Step 1

Advanced Math homework question answer, step 1, image 1

trending now

Trending now

This is a popular solution!

steps

Step by step

Solved in 2 steps with 2 images

Blurred answer
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
Numerical Methods for Engineers
Numerical Methods for Engineers
Advanced Math
ISBN:
9780073397924
Author:
Steven C. Chapra Dr., Raymond P. Canale
Publisher:
McGraw-Hill Education
Introductory Mathematics for Engineering Applicat…
Introductory Mathematics for Engineering Applicat…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
Basic Technical Mathematics
Basic Technical Mathematics
Advanced Math
ISBN:
9780134437705
Author:
Washington
Publisher:
PEARSON
Topology
Topology
Advanced Math
ISBN:
9780134689517
Author:
Munkres, James R.
Publisher:
Pearson,