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Question 2: Consider the surface defined by the equation f(x, y, z) = -6/5. Show that P(1, 0, -2) lies on this surface, then find the tangent plane to the surface at the point P.

Question 2: Consider the surface defined by the equation f(x, y, z) = -6/5. Show that P(1, 0, -2) lies on this surface, then find the tangent plane to the surface at the 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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Q2&Q3 needed By Hand solution needed Needed to be solved both Q2&Q3 questions correctly in 1 hour and get the thumbs up please solve correctly in the order to get positive feedback I need accuracy for both question by hand please
4 The gradient Consider the function f(x, y, z): Question 1: Answer the following questions: 3xz x² + y² +2² Compute the gradient of f at any point (x, y, z). • Use the gradient to find the unit vector pointing in the direction of steepest ascent at the point P (1,0,-2). • Use the gradient to find the unit vectors pointing along a level curve at the point P(1, 0, -2). • What is the directional derivative of f in the direction of steepest descent, at the point P (1,0, -2)? Question 2: Consider the surface defined by the equation f(x, y, z) = -6/5. Show that P(1, 0, -2) lies on this surface, then find the tangent plane to the surface at the point P. Question 3: Transform the function f into spherical polar coordinates. What is the gradient when expressed in this new coordinate system?
Transcribed Image Text:4 The gradient Consider the function f(x, y, z): Question 1: Answer the following questions: 3xz x² + y² +2² Compute the gradient of f at any point (x, y, z). • Use the gradient to find the unit vector pointing in the direction of steepest ascent at the point P (1,0,-2). • Use the gradient to find the unit vectors pointing along a level curve at the point P(1, 0, -2). • What is the directional derivative of f in the direction of steepest descent, at the point P (1,0, -2)? Question 2: Consider the surface defined by the equation f(x, y, z) = -6/5. Show that P(1, 0, -2) lies on this surface, then find the tangent plane to the surface at the point P. Question 3: Transform the function f into spherical polar coordinates. What is the gradient when expressed in this new coordinate system?
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