Homework Help is Here – Start Your Trial Now!
Math
Calculus
Given : 6 (x, y, z) Compute the gradient = 3 6y³ z³ - 5 ex at PA (2,2,1-5) of G (x, y, z)

Given : 6 (x, y, z) Compute the gradient = 3 6y³ z³ - 5 ex at PA (2,2,1-5) of G (x, y, z)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
See similar textbooks
icon
Related questions
Question
Given : 6 (x, y, z) Compute the gradient 3 6y²z³ - 5 ex at PA (2,2,1-5) of G (x, y, z)
Transcribed Image Text:Given : 6 (x, y, z) Compute the gradient 3 6y²z³ - 5 ex at PA (2,2,1-5) of G (x, y, z)
EXAMPLE PROBLEM पर५,८१- VG(x, y, z) = gradient field note: a gradient field is a vector field. there fore, 2 az VG (x,y,2) = (2 ax + 2 ay +3_9²) G(x,y, 2) z) 2y VG(x, y, z) = (2G(x, y, z) 2x org ау G=3x²y-422 = 6xy 2G 2Z 2G 2x 2G - 3x² 2 SUSISI Sample: Solve the gradient at P(2,3,1) of G(x, y, z) = 3x²y - 42². Solution: Let: G(x, y, z) = G = 3x²y - 4z² = scalar field function. Given: .ax + VG = = (2x ax + 2 Ay+ 22 9₂ ) G = ( 26 ax + 26 May +26 a₂) 2x 2y ау 2Z =-82 2 G(x, y, z). ay + 2y ×Ç(x,y,z) .az 22 VG=2G ax + -ax+ 26 ay + 26 a₂) જે 2G :) ау 2Z VG = 6xy ax + 3x² Ay - 8z Az 2x gradient field at P(2,3,1), VG = 6(2)(³) Ax +3 (2)²ay - 8 (1) Az VG = 36 Ax + 12 Ay - 8 Az |VG = 36.000 ax +12.000 Ay - 80.000X10²¹ az
Transcribed Image Text:EXAMPLE PROBLEM पर५,८१- VG(x, y, z) = gradient field note: a gradient field is a vector field. there fore, 2 az VG (x,y,2) = (2 ax + 2 ay +3_9²) G(x,y, 2) z) 2y VG(x, y, z) = (2G(x, y, z) 2x org ау G=3x²y-422 = 6xy 2G 2Z 2G 2x 2G - 3x² 2 SUSISI Sample: Solve the gradient at P(2,3,1) of G(x, y, z) = 3x²y - 42². Solution: Let: G(x, y, z) = G = 3x²y - 4z² = scalar field function. Given: .ax + VG = = (2x ax + 2 Ay+ 22 9₂ ) G = ( 26 ax + 26 May +26 a₂) 2x 2y ау 2Z =-82 2 G(x, y, z). ay + 2y ×Ç(x,y,z) .az 22 VG=2G ax + -ax+ 26 ay + 26 a₂) જે 2G :) ау 2Z VG = 6xy ax + 3x² Ay - 8z Az 2x gradient field at P(2,3,1), VG = 6(2)(³) Ax +3 (2)²ay - 8 (1) Az VG = 36 Ax + 12 Ay - 8 Az |VG = 36.000 ax +12.000 Ay - 80.000X10²¹ az
Expert Solution
steps

Step by step

Solved in 3 steps

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer
Recommended textbooks for you
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781285741550
Author:
James Stewart
Publisher:
Cengage Learning
Thomas' Calculus (14th Edition)
Thomas' Calculus (14th Edition)
Calculus
ISBN:
9780134438986
Author:
Joel R. Hass, Christopher E. Heil, Maurice D. Weir
Publisher:
PEARSON
Calculus: Early Transcendentals (3rd Edition)
Calculus: Early Transcendentals (3rd Edition)
Calculus
ISBN:
9780134763644
Author:
William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz
Publisher:
PEARSON
Calculus: Early Transcendentals
Calculus: Early Transcendentals
Calculus
ISBN:
9781319050740
Author:
Jon Rogawski, Colin Adams, Robert Franzosa
Publisher:
W. H. Freeman
Precalculus
Precalculus
Calculus
ISBN:
9780135189405
Author:
Michael Sullivan
Publisher:
PEARSON
Calculus: Early Transcendental Functions
Calculus: Early Transcendental Functions
Calculus
ISBN:
9781337552516
Author:
Ron Larson, Bruce H. Edwards
Publisher:
Cengage Learning
SEE MORE TEXTBOOKS