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1 3. (10 points) Let S be the quadratic surface given by 22-2-y (a) Classify S...
Can someone help me understand part c, I'm not quire how to do it. The answer is (0,0, plus/minus root(10)) and I d...
Can someone help me understand part c, I'm not quire how to do
it. The answer is (0,0, plus/minus root(10)) and I don't know how
to get there.
3. (9 points) Let S be the quadratic surface given by 2y22 (a) Classify S 10 elliptic paraboloid (B) S is a hyperboloid of one sheet (A) S is an (C) S is a hyperboloid of two Answer (Letter): (D) S is an elliptic cone sheets (E) S is an ellipsoid (b)...
Consider the surface whose equation is z = -2(y+1)^2 + (x+1)^2 - 1 i) determine a...
Consider the surface whose equation is z = -2(y+1)^2 + (x+1)^2 - 1 i) determine a surface of the form (*) whose graph you can translate, rotate, or reflect to obtain the graph of the given surface. Provide the steps one would follow to manipulate the graph of your surface to get the graph of the given surface. Form could be Ellipsoid, Cone, Elliptic Paraboloid, Hyperboloid of One sheet, Hyperbolic paraboloid, and Hyperboloid of two sheets.
1) Let (S): x² + (z – 1)2 = 1. Then (S) can be represented by:...
1) Let (S): x² + (z – 1)2 = 1. Then (S) can be represented by: a Ob None of the above 2) Let (S) be the surface given by: y = 4–3x2 – 5z2. Then (S) is: a. an elliptic cone around y-axis b. a circular cone around y-axis c. an elliptic paraboloid around y-axis d. a circular paraboloid around y-axis e. an ellipsoid O a. O b. O c. O d. O e.
1) Assume you are given the surface S with equation 2 1- (a) Find the equation of the tangent plane to S at the p...
1) Assume you are given the surface S with equation 2 1- (a) Find the equation of the tangent plane to S at the point (V6, 1) (b) Find a point on the surface S so that the tangent plane to S at that point contains the point (3,0, 0). (c) Give an equation for and geometrically describe the set of points on S so that the tangent plane to S at those points contains the point (3, 0,0).
1)...
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...
Question 3 (a) Consider the bowl-shaped paraboloid, for s,. E R 0 If you are locasied on the paraboboid st ti (20th?). 2 4 direction should you move in order to ascend on the surface at the maximum r...
Question 3 (a) Consider the bowl-shaped paraboloid, for s,. E R 0 If you are locasied on the paraboboid st ti (20th?). 2 4 direction should you move in order to ascend on the surface at the maximum rate? (4 marks) (2 marks) (iü) What is the rate of change in this direction? (b) Given the ellipsoid with equation 9 25 At what points on the ellipsoid is the tangent plane horiaontal? (6 marks)
Question 3 (a) Consider the bowl-shaped...
Let P = (0,0, 2)and let S be the unit sphere with equation x2 + y2...
Let P = (0,0, 2)and let S be the unit sphere with equation x2 + y2 + z2 = 1.The collection of points on the sphere where the tangent plane of the sphere contains the point Pforms a curve. Parametrize this curve.
A surface S described as circular paraboloid x2 + y2-z bounded by plane z-3. a) Find a parametrization for S. b) Find plane tangent to S at (1, 1, 2) A surface S described as circular paraboloid...
A surface S described as circular paraboloid x2 + y2-z bounded by plane z-3. a) Find a parametrization for S. b) Find plane tangent to S at (1, 1, 2)
A surface S described as circular paraboloid x2 + y2-z bounded by plane z-3. a) Find a parametrization for S. b) Find plane tangent to S at (1, 1, 2)
13. (1 point) Let S be the part of the paraboloid 1 222y that lies above the plane 4 2y -z1. Find the surface area of S. 13. (1 point) Let S be the part of the paraboloid 1 222y that lies above...
13. (1 point) Let S be the part of the paraboloid 1 222y that lies above the plane 4 2y -z1. Find the surface area of S.
13. (1 point) Let S be the part of the paraboloid 1 222y that lies above the plane 4 2y -z1. Find the surface area of S.
Example A.3 Surface normal vector. Let S be a surface that is represented by f(x, y, z) -c, where...
Example A.3 Surface normal vector. Let S be a surface that is represented by f(x, y, z) -c, where f is defined and differentiable in a space. Then, let C be a curve on S through a point P-Go, yo,Zo) on S, where C is represented by rt)[x(t), y(t), z(t)] with r(to) -[xo. Vo, zol. Since C lies on S, r(t) must satisfy f(x, y. z)-c, or f(x(t), y(t), z(t))-c. Show that vf is orthogonal to any tangent vector r'(t)...
Can someone help me understand part c, I'm not quire how to do
it. The answer is (0,0, plus/minus root(10)) and I don't know how
to get there.
3. (9 points) Let S be the quadratic surface given by 2y22 (a) Classify S 10 elliptic paraboloid (B) S is a hyperboloid of one sheet (A) S is an (C) S is a hyperboloid of two Answer (Letter): (D) S is an elliptic cone sheets (E) S is an ellipsoid (b)...
1) Let (S): x² + (z – 1)2 = 1. Then (S) can be represented by: a Ob None of the above 2) Let (S) be the surface given by: y = 4–3x2 – 5z2. Then (S) is: a. an elliptic cone around y-axis b. a circular cone around y-axis c. an elliptic paraboloid around y-axis d. a circular paraboloid around y-axis e. an ellipsoid O a. O b. O c. O d. O e.
1) Assume you are given the surface S with equation 2 1- (a) Find the equation of the tangent plane to S at the point (V6, 1) (b) Find a point on the surface S so that the tangent plane to S at that point contains the point (3,0, 0). (c) Give an equation for and geometrically describe the set of points on S so that the tangent plane to S at those points contains the point (3, 0,0).
1)...
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...
Question 3 (a) Consider the bowl-shaped paraboloid, for s,. E R 0 If you are locasied on the paraboboid st ti (20th?). 2 4 direction should you move in order to ascend on the surface at the maximum rate? (4 marks) (2 marks) (iü) What is the rate of change in this direction? (b) Given the ellipsoid with equation 9 25 At what points on the ellipsoid is the tangent plane horiaontal? (6 marks)
Question 3 (a) Consider the bowl-shaped...
Let P = (0,0, 2)and let S be the unit sphere with equation x2 + y2 + z2 = 1.The collection of points on the sphere where the tangent plane of the sphere contains the point Pforms a curve. Parametrize this curve.
A surface S described as circular paraboloid x2 + y2-z bounded by plane z-3. a) Find a parametrization for S. b) Find plane tangent to S at (1, 1, 2)
A surface S described as circular paraboloid x2 + y2-z bounded by plane z-3. a) Find a parametrization for S. b) Find plane tangent to S at (1, 1, 2)
13. (1 point) Let S be the part of the paraboloid 1 222y that lies above the plane 4 2y -z1. Find the surface area of S.
13. (1 point) Let S be the part of the paraboloid 1 222y that lies above the plane 4 2y -z1. Find the surface area of S.
Example A.3 Surface normal vector. Let S be a surface that is represented by f(x, y, z) -c, where f is defined and differentiable in a space. Then, let C be a curve on S through a point P-Go, yo,Zo) on S, where C is represented by rt)[x(t), y(t), z(t)] with r(to) -[xo. Vo, zol. Since C lies on S, r(t) must satisfy f(x, y. z)-c, or f(x(t), y(t), z(t))-c. Show that vf is orthogonal to any tangent vector r'(t)...
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