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true or false is zero. F 9. The plane tangent to the surface za the point (0,0, 3) is given by the equation 2x - 12y -z+3-0. 10. If f is a differentiable function and zf(x -y), then z +. T 11. If...
5 and 6 please 5) Given the surface f(x, y, z) = 0 or z =...
5 and 6 please
5) Given the surface f(x, y, z) = 0 or z = f(x,y), find the tangent plane at P. a) z2 – 2x2 – 2y2 = 12 @ P=(1,-1,4) b) f(x,y) = 2x - 3xy3 @ 12,-1) c) f(x,y) = sin(x) @ (3,5) 6) Find an equation of the tangent plane and the equation of the normal line to surface f(x..zb=0 @P x2 + y2 + z2 = 9 P = (2,2,1)
b) Consider the surface in R3 described by f(x,y,z) = 2x²y3 + z + ye*2 =...
b) Consider the surface in R3 described by f(x,y,z) = 2x²y3 + z + ye*2 = 9 (i) Find Vf(x,y,z). [3 marks] (ii) Verify that (2,1,0) is a point on this surface. Find the cartesian equation of the tangent plane to this surface at the point (2.1,0). [5 marks]
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)...
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...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent p...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks]
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
Find an equation of the tangent plane to the surface at the given point. x2 +...
Find an equation of the tangent plane to the surface at the given point. x2 + 2z2ev - * = 22, P= (2, 3, te) Use the Chain Rule to calculate f(x, y) = x - 4xy, r(t) = (cos(5t), sin(3t)), t = 0 force) = +-/1 points RogaCalcET3 14.5.015. Use the Chain Rule to calculate f(x, y) = 5x - 3xy, r(t) = (t?, t2 - 5t), t = 5 merce) = + -/1 points RogaCalcET3 14.5.018. Use the...
Given is the surface enclosed by the x-axis, the y-axis, the function f(x)=2x-2 and its tangent...
Given is the surface enclosed by the x-axis, the y-axis, the function f(x)=2x-2 and its tangent line at x = 3. (5a) Determine the equation of the tangent line. (5b) Make a sketch of this surface. (50) Calculate the volume of revolution for rotation of the surface about the y-axis. (If you were not able to determine the tangent line, you're allowed to use the line y = 2 instead)
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...
Exercise 1. Tangent plane (15 pts) Let (S) be the surface given by the following equation....
Exercise 1. Tangent plane (15 pts) Let (S) be the surface given by the following equation. x+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 d. Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy...
Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the point (2...
Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the point (2.2,6) b) The parametric equations of the normal line at the point (2, 2, 6) c) The outward unit normal vector to the surface at the point (2, 2,6) d) Sketch the surface and the outward unit normal vector at the point (2, 2,6). 1.
Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the...
5 and 6 please
5) Given the surface f(x, y, z) = 0 or z = f(x,y), find the tangent plane at P. a) z2 – 2x2 – 2y2 = 12 @ P=(1,-1,4) b) f(x,y) = 2x - 3xy3 @ 12,-1) c) f(x,y) = sin(x) @ (3,5) 6) Find an equation of the tangent plane and the equation of the normal line to surface f(x..zb=0 @P x2 + y2 + z2 = 9 P = (2,2,1)
b) Consider the surface in R3 described by f(x,y,z) = 2x²y3 + z + ye*2 = 9 (i) Find Vf(x,y,z). [3 marks] (ii) Verify that (2,1,0) is a point on this surface. Find the cartesian equation of the tangent plane to this surface at the point (2.1,0). [5 marks]
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)...
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or skew. If they intersect, find the point of intersection Given SI: x2-2y2 = 4z2-252 &s2: (0 Show that the tangent planes to the two surfaces at P(2,0,-8) are perpendicular. whether the lines parallel, 2-z & 12 Marks] 4x2 +9y2-24. (B) Find the points on Si at which the tangent plane is parallel to the plane x+y+32-5 3 Marks]
Question (2): (5 Marks) x-1-3-y x-1-6-y:+2 are (A) Determine intersecting or...
Find an equation of the tangent plane to the surface at the given point. x2 + 2z2ev - * = 22, P= (2, 3, te) Use the Chain Rule to calculate f(x, y) = x - 4xy, r(t) = (cos(5t), sin(3t)), t = 0 force) = +-/1 points RogaCalcET3 14.5.015. Use the Chain Rule to calculate f(x, y) = 5x - 3xy, r(t) = (t?, t2 - 5t), t = 5 merce) = + -/1 points RogaCalcET3 14.5.018. Use the...
Given is the surface enclosed by the x-axis, the y-axis, the function f(x)=2x-2 and its tangent line at x = 3. (5a) Determine the equation of the tangent line. (5b) Make a sketch of this surface. (50) Calculate the volume of revolution for rotation of the surface about the y-axis. (If you were not able to determine the tangent line, you're allowed to use the line y = 2 instead)
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...
Exercise 1. Tangent plane (15 pts) Let (S) be the surface given by the following equation. x+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 d. Exercise 3. Chain rule (15 pts) Let f(x,y,z) = xy...
Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the point (2.2,6) b) The parametric equations of the normal line at the point (2, 2, 6) c) The outward unit normal vector to the surface at the point (2, 2,6) d) Sketch the surface and the outward unit normal vector at the point (2, 2,6). 1.
Given f(x, y): 10-2x2-y, find a) The equation of the tangent plane to the surface at the...
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