4 marks] Find a unit vector in the direction in which J(x,y) - V marks Find a unit vector in the ...
(b) (i) Given the function f(x,y)= xe' + 3x, find two unit vectors who are orthogonal to the gradient of f at the point P(3,0). (7 Marks) (ii) In which direction does f(x,y)= xey + 3x increase most rapidly at the point P(3,0)? What is the maximum rate of change at that point? (3 Marks)
TOTAL MARKS: 25 QUESTION 4 (a) Find a normal vector and an equation for the tangent plane to the surface at the point P: (-2,1,3). Determine the equation of the line formed by the intersection of this plane with the plane z = 0. 10 marks (b) Find the directional derivative of the function F(r, y, z)at the point P: (1,-1,-2) in the direction of the vector Give a brief interpretation of what your result means. 2y -3 [9 marks]...
(1 point) Suppose f (r,y)= P = (1, -2) and v=3i - 3j. A. Find the gradient of 1 Uf = 1 it -x/y^2 Note: Your answers should be expressions of x and y, eg "3x - 4y" j j B. Find the gradient off at the point P. (VA)(P) = 1 i+ -2 Note: Your answers should be numbers C. Find the directional derivative off at P in the direction of v. Duf = 9 Note: Your answer should...
1. Let f(x,y) = (2-7-% and g(x,y) = v f(x,y). J(1)(4 points) Find the maximum value of g(y). |(272 points) At which point(s) (x,y) and in the direction of which unit vector(s) ů does the maximum value for the directional derivative Dif(x,y) occur?
5. [0/4 Points] DETAILS PREVIOUS ANSWERS SCALCCC4 11.6.031. Suppose that over a certain region of space the electrical potential V is given by the following equation. V(x, y, z) = 8x2 - 5xy + xyz (a) Find the rate of change of the potential at P(4, 4, 6) in the direction of the vector v = i + j - k. (b) In which direction does V change most rapidly at P? <68, (c) What is the maximum rate of...
Homework 4: Problem 3 Previous Problem Problem List Next Problem (6 points) Consider the function f(x, y) - (e - x) sin(y). Suppose S is the surface z- f(x, y) (a) Find a vector which is perpendicular to the level curve of f through the point (5,5) in the direction irn which f decreases most rapidly. vector (b) Suppose u = 31 + 3/4 ak is a vector in 3-space which is tangent to the surface S at the point...
Suppose that over a certain region of space the electrical potential V is given by V(xyz) = 5x -3xy + xyz (a) Find the rate of change of the potential at P(3,4,5) in the direction of the vector V i+j-k (b) In which direction does V change most rapidly at P? (c) What is the maximum rate of change at P? Suppose that over a certain region of space the electrical potential V is given by V(xyz) = 5x -3xy...
(1 point) Consider the function f (x, y) = 3x2 + 4y2. f at the point (-4,1) in the direction given by Find the the directional derivative of the angle 0 Find the vector which describes the direction in which f is increasing most rapidly at (-4, 1) (1 point) Consider the function f (x, y) = 3x2 + 4y2. f at the point (-4,1) in the direction given by Find the the directional derivative of the angle 0 Find...
please circle the answer! (1 point) Suppose f (x, y) = , P = (1, 3) and v 3i - 2j A. Find the gradient of f Vf = i+ j Note: Your answers should be expressions of x and y; e.g. "3x - 4y" B. Find the gradient of f at the point P. (Vf) (P) it j Note: Your answers should be numbers C. Find the directional derivative of f at P in the direction of v. Duf...
Previous Problem Problem List Next Problem f(x, y) (1 point) Consider the function f(x, y) = (e* - 5x) sin(y). Suppose S is the surface z (a) Find a vector which is perpendicular to the level curve of f through the point (5,4) in the direction in which f decreases most rapidly. vector -(eA5-5)sin(4)i+-(e^5-5(5)cos(4)j (b) Suppose above (5,4). What is a? 2i 8jak is a vector in 3-space which is tangent to the surface S at the point P lying...