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Find the derivative of f = myz at the point (1,3,2) in the direction of the...
Find an equation of the plane tangent to the following surface at the given point. yz...
Find an equation of the plane tangent to the following surface at the given point. yz e XZ - 21 = 0; (0,7,3) An equation of the tangent plane at (0,7,3) is = 0. Find the critical points of the following function. Use the Second Derivative Test to determine if possible whether each critical point corresponds to a local maximum local minimum, or saddle point. If the Second Derivative Test is inconclusive, determine the behavior of the function at the...
7. (20 pts) Consider the surface given by z wy - 4xy + 3x - 2y....
7. (20 pts) Consider the surface given by z wy - 4xy + 3x - 2y. (a) Find the equation of the tangent plane to this surface at the point where (x,y) - (1,3). (b) Find the gradient f at the point where (x,y) = (1,3). (c) Find the directional derivative DaS(1,3) where it is the unit vector in the direction of (1, -2). such that the directional derivative Daf(1.3) is a maximum (d) Find a unit vector in the...
a) Find and sketch the domain of f b) Find ) c) Find the directional derivative of f in the direction of 3i +4j at (2,3) d) Find an equation of the plane tangent to the surface-f(z, y) at (2,3,3)...
a) Find and sketch the domain of f b) Find ) c) Find the directional derivative of f in the direction of 3i +4j at (2,3) d) Find an equation of the plane tangent to the surface-f(z, y) at (2,3,3)
a) Find and sketch the domain of f b) Find ) c) Find the directional derivative of f in the direction of 3i +4j at (2,3) d) Find an equation of the plane tangent to the surface-f(z, y) at (2,3,3)
6) a (15 pts) Find the derivative of (x,y,z-xy, + x3yz + z3yx in the direction of v -2 -4k at the...
6) a (15 pts) Find the derivative of (x,y,z-xy, + x3yz + z3yx in the direction of v -2 -4k at the function fix.y z) at the point vo Can you find any direction(s) where the surface is neither increasing nor decreasing? e point vo (2, 1, -3). What is the rate of maximal increase to the b. (10 pts) Find a normal vector and the tangent plane to the following level surface x'y t yz+2 3 at (1, 1,...
TOTAL MARKS: 25 QUESTION 4 (a) Find a normal vector and an equation for the tangent plane to the ...
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]...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given ...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
Find a normal vector and an equation for the tangent plane to the surface: x3 - y2 - z2 - 2xyz + 6 =0 at the point P : (−2, 1, 3). Determine the equation of the line formed by the intersection of this...
Find a normal vector and an equation for the tangent plane to the surface: x3 - y2 - z2 - 2xyz + 6 =0 at the point P : (−2, 1, 3). Determine the equation of the line formed by the intersection of this plane with the plane x = 0. [10 marks] (b) Find the directional derivative of the function F(x, y, z) = 2x /zy2 , at the point P : (1, −1, −2) in the direction of...
12. (5 points) (a): Find the directional derivative of f(x, y) = y² In r at...
12. (5 points) (a): Find the directional derivative of f(x, y) = y² In r at P(1,4) in the direction of u = -3i + 3j. (b): Find the equation for the tangent plane and normal line to the surface cos(70) – z’y+e*2 + y2 = 4 at P(0,1,2).
(a): Find the directional derivative of
(5 points) (a): Find the directional derivative of \(f(x, y)=y^{2} \ln x\) at \(P(1,4)\) in the direction of \(\mathbf{u}=-3 \mathbf{i}+3 \mathbf{j}\)(b): Find the equation for the tangent plane and normal line to the surface \(\cos (\pi x)-x^{2} y+e^{x z}+y z=4\) at \(P(0,1,2)\)
Find the directional derivative of the function f(x,y,z) = z4−x3y2 at P(1,-1,1) in the direction of...
Find the directional derivative of the function f(x,y,z) = z4−x3y2 at P(1,-1,1) in the direction of the vector from P(1,-1,1) to the point Q(2,1,0). What is the maximum rate of change of f at the point P(1,-1,1) and in which direction
Find an equation of the plane tangent to the following surface at the given point. yz e XZ - 21 = 0; (0,7,3) An equation of the tangent plane at (0,7,3) is = 0. Find the critical points of the following function. Use the Second Derivative Test to determine if possible whether each critical point corresponds to a local maximum local minimum, or saddle point. If the Second Derivative Test is inconclusive, determine the behavior of the function at the...
7. (20 pts) Consider the surface given by z wy - 4xy + 3x - 2y. (a) Find the equation of the tangent plane to this surface at the point where (x,y) - (1,3). (b) Find the gradient f at the point where (x,y) = (1,3). (c) Find the directional derivative DaS(1,3) where it is the unit vector in the direction of (1, -2). such that the directional derivative Daf(1.3) is a maximum (d) Find a unit vector in the...
a) Find and sketch the domain of f b) Find ) c) Find the directional derivative of f in the direction of 3i +4j at (2,3) d) Find an equation of the plane tangent to the surface-f(z, y) at (2,3,3)
a) Find and sketch the domain of f b) Find ) c) Find the directional derivative of f in the direction of 3i +4j at (2,3) d) Find an equation of the plane tangent to the surface-f(z, y) at (2,3,3)
6) a (15 pts) Find the derivative of (x,y,z-xy, + x3yz + z3yx in the direction of v -2 -4k at the function fix.y z) at the point vo Can you find any direction(s) where the surface is neither increasing nor decreasing? e point vo (2, 1, -3). What is the rate of maximal increase to the b. (10 pts) Find a normal vector and the tangent plane to the following level surface x'y t yz+2 3 at (1, 1,...
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]...
Problem 1: Let F(, y,) be a function given by F(, y, z) (r2+y)e. Let S be the surface in R given by the equation Fr, y, 2) 2. (a) Find an equation of the tangent plane to the surface S at the point p(-1,1,0) (b)Find the directional derivative -1,1,0) of F(,y,2) in the direction of the unit vector u = (ui, t», t's) at the point p(-1,1,0) - In what direction is this derivative maximal? In what direction is...
12. (5 points) (a): Find the directional derivative of f(x, y) = y² In r at P(1,4) in the direction of u = -3i + 3j. (b): Find the equation for the tangent plane and normal line to the surface cos(70) – z’y+e*2 + y2 = 4 at P(0,1,2).
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