daSection: 1 of 1Question: 6 of 7Marks for this Question: 10 &Upload answer sheets(a) Find the gradient of (x, y, z)x'yz? at the point P(-2,0, 1). Hence find the%3Ddirectional derivative of y at P in the direction of A =i+2j+ 2k(b) Find the scalar potential of the conservative field:F = 2xy z²i+ 3x²?y'j+2x?y®zk.Once you upload files from your second device, click onS Sync to check your subOCamera

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Answered: (a) Find the gradient of V (x, y, z)…

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...

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7. Find the circulation of the field F(x, y) = xi+yj around the circle r(t) =(cost)i + ( sin t)j: 8. Find the flow of the velocity field F(x, y) = (x + y)i-(x2+y2)j alongeach of the following paths from (1, 0) to (-1, 0) in the xy-plane ne.a)The upper half of the circle x2+y2=1b) line segment from (1, 0) to (-1,0)
The inflationary slow-roll parameters ϵ(φ) and η(φ) are given by (found in image below) i) Calculate ϵ(φ) and η(φ) for the scalar field potential V =1/2m^2φ^2.ii) Inflation ends when ϵ(φ) = 1. Calculate the value of the field φ at the end of inflation.
For the vector field given by: F(x,y) = (2x+e-xcosy)i+(y2+e-xsiny)j a. Show that the vector field F is conservative. b. Find a potential function for F. c. Find the work done by the force field on an object moving along the curve C from the point (0,0) to the point (0,pi/2) along the curve y=sin(2x).
The vector field F = 2e^(y)i + (2xe^(y) + y)j is given. a-)Determine whether the vector field F is conservative. If it is conservative, find the potential function. b-)Calculate the curvilinear integral in the photograph, given that the curve C is given as the y=√x curve between the points (0,0) and (1,1).
The flow of a gas with a density of d = 0.001 kg/m2 over the closed curve r(t) = (-sin t)i + (cos t)j, 0<= t<=2pai, is given by the vector field F = dv, where v = xi + y2j is a velocity field measured in meters per second. Find the flux of F across the curve r(t).

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(a) Find the gradient of V (x, y, z) x'yz? at the point P(-2,0, 1). Hence find the directional derivative of y at P in the direction of A =i+2j+ 2k (h) Find th