FINDING A POINT ON THE SURFACE GIVEN AN EQUATION....
FIND THE POINT ON THE SURFACEZ = 3X2 - Y2 AT WHICH THE TANGENT PLANE IS PARALLEL TO THE PLANE 6X +4Y - Z = 5
Homework Answers
The plane 6x + 4y - z = 5 has normal (6, 4, -1).
The normal to the surface 3x2 - y2 - z = 0 is (6x, -2y, -1) (The gradient!) Setting (6x, -2y, -1) = (6, 4, -1) we seethat x = 1, y = -2.
Remark: The normal to the level set of a function is given by the gradient, so rewriting the original surface as the zero level set of thefunction F(x, y, z) = 3x2 - y2 - z allows us to easily find the normal, and parallel planes in 3-d have the same normals.
Show steps please Find the point on the surface 6x = y2 + z2 so that...
Show steps please
Find the point on the surface 6x = y2 + z2 so that its tangent plane is parallel to 3x + 2y - 2z = 1.
Find the equation of the tangent plane to the surface at the given point a. z...
Find the equation of the tangent plane to the surface at the given point a. z = x2 + y2 + 2 (1,3,12)
Find an equation of the plane tangent to the following surface at the given point. 4xy...
Find an equation of the plane tangent to the following surface at the given point. 4xy + yz + 3x2 - 32 = 0; (2,2,2) The equation of the tangent plane at (2,2,2) is = 0.
(1 point) Find the points on the surface 3x2 + 4y2 3z2 -1 at which the tangent plane is parallel ...
(1 point) Find the points on the surface 3x2 + 4y2 3z2 -1 at which the tangent plane is parallel to the plane ) and We were unable to transcribe this imageWe were unable to transcribe this image(1 point) Consider the surface xuz48 A. Find the unit normal vector to the surface at the point (3, 4,4) with positive first coordinate. B. Find the equation of the tangent plane to the surface at the given point. Express your answer in...
= 1 at which the tangent plane (1 point) Find the points on the surface 5x2...
= 1 at which the tangent plane (1 point) Find the points on the surface 5x2 + 1y2 + 4z2 is parallel to the plane – 1x + 4y + 3z = -1. ( ) and (
(1 point) Find the equation of the tangent plane to the surface z = y In(x)...
(1 point) Find the equation of the tangent plane to the surface z = y In(x) at the point (1. -9,0). Z- Note: Your answer should be an expression of x and y, e.g. 3x - 4y + 6.
Exercise 1. Tangent plane (15 pts) Let (5) be the surface given by the following equation....
Exercise 1. Tangent plane (15 pts) Let (5) be the surface given by the following equation. x2+y2 = 1+z2 An equation of the tangent plane to (S) at A(1,2,2) is: a. 2x + 4y – 4z = 1 b. x + y - z=0 c. x + 2y – 2z = 1 d. x + y - z = 2 e. None of the above a. b. C. O d. e.
The equation of a surface is f(x, y) = 4xy + x2 - y2 +9. Which...
The equation of a surface is f(x, y) = 4xy + x2 - y2 +9. Which is an equation of the plane that is tangent to the surface at the point(4,2,49)? 34x –19y –20 b) z =-18x-12y +20 c) z = 5x-3y +27 d)z=16x+4y-23 e) z =-12x-18y+20
Exercise 1. Tangent plane (15 pts) Let (5) be the surface given by the following equation....
Exercise 1. Tangent plane (15 pts) Let (5) be the surface given by the following equation. x2+y2 = 1+z2 An equation of the tangent plane to (S) at A(1,2,2) is: a. 2x + 4y – 4z = 1 b. x + y - z=0 c. x + 2y – 2z = 1 d. x + y - z = 2 e. None of the above a. b. C. O d. e. Exercise 2. Directional derivative (6 pts + 9 pts)...
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone ...
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area (1 point) Find the surface area of the part of the plane 2a 4y+z 1 that lies inside the cylinder 2y21. Surface Area2pi
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area
(1 point) Find...
Show steps please
Find the point on the surface 6x = y2 + z2 so that its tangent plane is parallel to 3x + 2y - 2z = 1.
Find the equation of the tangent plane to the surface at the given point a. z = x2 + y2 + 2 (1,3,12)
Find an equation of the plane tangent to the following surface at the given point. 4xy + yz + 3x2 - 32 = 0; (2,2,2) The equation of the tangent plane at (2,2,2) is = 0.
(1 point) Find the points on the surface 3x2 + 4y2 3z2 -1 at which the tangent plane is parallel to the plane ) and We were unable to transcribe this imageWe were unable to transcribe this image(1 point) Consider the surface xuz48 A. Find the unit normal vector to the surface at the point (3, 4,4) with positive first coordinate. B. Find the equation of the tangent plane to the surface at the given point. Express your answer in...
= 1 at which the tangent plane (1 point) Find the points on the surface 5x2 + 1y2 + 4z2 is parallel to the plane – 1x + 4y + 3z = -1. ( ) and (
(1 point) Find the equation of the tangent plane to the surface z = y In(x) at the point (1. -9,0). Z- Note: Your answer should be an expression of x and y, e.g. 3x - 4y + 6.
Exercise 1. Tangent plane (15 pts) Let (5) be the surface given by the following equation. x2+y2 = 1+z2 An equation of the tangent plane to (S) at A(1,2,2) is: a. 2x + 4y – 4z = 1 b. x + y - z=0 c. x + 2y – 2z = 1 d. x + y - z = 2 e. None of the above a. b. C. O d. e.
The equation of a surface is f(x, y) = 4xy + x2 - y2 +9. Which is an equation of the plane that is tangent to the surface at the point(4,2,49)? 34x –19y –20 b) z =-18x-12y +20 c) z = 5x-3y +27 d)z=16x+4y-23 e) z =-12x-18y+20
Exercise 1. Tangent plane (15 pts) Let (5) be the surface given by the following equation. x2+y2 = 1+z2 An equation of the tangent plane to (S) at A(1,2,2) is: a. 2x + 4y – 4z = 1 b. x + y - z=0 c. x + 2y – 2z = 1 d. x + y - z = 2 e. None of the above a. b. C. O d. e. Exercise 2. Directional derivative (6 pts + 9 pts)...
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area (1 point) Find the surface area of the part of the plane 2a 4y+z 1 that lies inside the cylinder 2y21. Surface Area2pi
1 point) Find the surface area of the part of the sphere x2 + y2 + z2-1 that lies above the cone z = x2+y2 Surface Area
(1 point) Find...
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