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1. (a) Given the scalar function g(x, y, z) = (1+x³) sin z+e cos y, calculate v = Vg and find V ·v. (b) In what direction from the point P(0, –T, 7/2) and at what rate does function g increase in the quickest way? (c) What is the rate of change of the above function in the direction of vector a = (1,2,2) at point P?

1. (a) Given the scalar function g(x, y, z) = (1+x³) sin z+e cos y, calculate v = Vg and find V ·v. (b) In what direction from the point P(0, –T, 7/2) and at what rate does function g increase in the quickest way? (c) What is the rate of change of the above function in the direction of vector a = (1,2,2) at point P?

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Please help with vector calculus questions, if possible please provide solutions to all questions. thank you

1. (a) Given the scalar function g(x,y, z) = (1+x³) sin z+e cos y, calculate v = Vg %3D and find V · V. (b) In what direction from the point P(0, –7, 1/2) and at what rate does function g increase in the quickest way? (c) What is the rate of change of the above function in the direction of vector a = (1,2, 2) at point P?
Transcribed Image Text:1. (a) Given the scalar function g(x,y, z) = (1+x³) sin z+e cos y, calculate v = Vg %3D and find V · V. (b) In what direction from the point P(0, –7, 1/2) and at what rate does function g increase in the quickest way? (c) What is the rate of change of the above function in the direction of vector a = (1,2, 2) at point P?
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