Find the increment and differential of each of the following functions for the given values of the variables and their increments. 15. xIn y + y In x; x = y = 1, Ax = 0.01, Ay = 0.02 16. y tan- xy; x = 2, y = 0.5, Ax = -0.05, Ay = 0.01 17. Find, approximately, the amount of metal in a closed tin can 3 inches in diameter and 5 inches high, if the metal is 1/32 inches thick.

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Question
Find the increment and differential of each of the following functions for the given values of the
variables and their increments.
15. x In y + y In x; x = y = 1, Ax = 0.01, Ay = 0.02
16. y tan-1 xy; x = 2, y = 0.5, Ax = –0.05, Ay = 0.01
17. Find, approximately, the amount of metal in a closed tin can 3 inches in diameter and 5 inches
high, if the metal is 1/32 inches thick.
18. Find by use of differentials the approximate total area of a right circular cone whose base radius
and height are 5.03 inches and 11.89 inches, respectively.
Transcribed Image Text:Find the increment and differential of each of the following functions for the given values of the variables and their increments. 15. x In y + y In x; x = y = 1, Ax = 0.01, Ay = 0.02 16. y tan-1 xy; x = 2, y = 0.5, Ax = –0.05, Ay = 0.01 17. Find, approximately, the amount of metal in a closed tin can 3 inches in diameter and 5 inches high, if the metal is 1/32 inches thick. 18. Find by use of differentials the approximate total area of a right circular cone whose base radius and height are 5.03 inches and 11.89 inches, respectively.
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