For each problem, calculate the directional derivative in the given direction and the gradient vector: 64 a) The temperature T of a circular disk at one of its points (x, y) is given by T = the center of the disc. Find, at point (1,2), the variation of T' in the direction 0 = π/3 x²+y²+2' the origin being b) The electric potential V at a point (x, y) is given by V = In √√x² + y². Find the variation of V at point (3,4) in the direction to point (2,6). Given the Surface z = 8 - 4x² - 2y², find the direction of the maximum slope at point P (1,1,2) and c) the direction of the tangent to the level curve z = constant. Note that both directions are perpendicular.
For each problem, calculate the directional derivative in the given direction and the gradient vector: 64 a) The temperature T of a circular disk at one of its points (x, y) is given by T = the center of the disc. Find, at point (1,2), the variation of T' in the direction 0 = π/3 x²+y²+2' the origin being b) The electric potential V at a point (x, y) is given by V = In √√x² + y². Find the variation of V at point (3,4) in the direction to point (2,6). Given the Surface z = 8 - 4x² - 2y², find the direction of the maximum slope at point P (1,1,2) and c) the direction of the tangent to the level curve z = constant. Note that both directions are perpendicular.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
Related questions
Question
show full and complete procedure HANDWRITTEN only
Transcribed Image Text:For each problem, calculate the directional derivative in the given direction and the gradient vector:
=
a)
The temperature T of a circular disk at one of its points (x, y) is given by T
the center of the disc. Find, at point (1,2), the variation of T' in the direction
64
x²+y²+2'
0 = π/3
the origin being
b)
The electric potential V at a point (x, y) is given by V = ln √√x² + y². Find the variation of V at point
(3,4) in the direction to point (2,6).
Given the Surface z = 8 - 4x² – 2y², find the direction of the maximum slope at point P (1,1,2) and
c) the direction of the tangent to the level curve z = constant. Note that both directions are
perpendicular.
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps with 8 images
Recommended textbooks for you
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Advanced Engineering Mathematics
Advanced Math
ISBN:
9780470458365
Author:
Erwin Kreyszig
Publisher:
Wiley, John & Sons, Incorporated
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…
Advanced Math
ISBN:
9781118141809
Author:
Nathan Klingbeil
Publisher:
WILEY
Mathematics For Machine Technology
Advanced Math
ISBN:
9781337798310
Author:
Peterson, John.
Publisher:
Cengage Learning,
