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2x+y+3z=4
8. At which point(s) on the ellipsoid x2 + 4y2 + 9z2 = 36 the...
For 18-20 graph the following equations. 18. [6] 2x-4y+3z = 12 19. [6] x2 +4y2 +9z2 =1 20. [6] z 2x2 + y7 For 18-2...
For 18-20 graph the following equations. 18. [6] 2x-4y+3z = 12 19. [6] x2 +4y2 +9z2 =1 20. [6] z 2x2 + y7
For 18-20 graph the following equations. 18. [6] 2x-4y+3z = 12 19. [6] x2 +4y2 +9z2 =1 20. [6] z 2x2 + y7
Find the point(s) on the sphere x2 + y2 + z2 = 1 where the tangent...
Find the point(s) on the sphere x2 + y2 + z2 = 1 where the tangent plane is parallel to the plane 2.C + V3y – 3z = 2. Then write the equation(s) of the tangent plane(s). (Explain how you found the point(s) and simplify the equation(s) of the tangent plane(s)).
(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...
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...
Use the given transformation to evaluate the integral. 21)--2x + y, v = 9x + y; 21) (y-2x)(9x + y...
21-23
Use the given transformation to evaluate the integral. 21)--2x + y, v = 9x + y; 21) (y-2x)(9x + y) dx dy where R is the parallelogram bounded by the lines y - 2x +6.y -2x+7.y 13 A) D) 1573 B) 1573 C) 22) // f (x2 + y2 +內0xdy dz. x2 y2 22 where R is the interior of the ellipsoid 1002361 D) 180: C) 240π B) 20От A) 120π 23) Solve the problem. 23) Evaluate x2- y...
Puestion 4 ot yet aswered Find the mass of the ellipsoid given by 4x2 + 4y2...
Puestion 4 ot yet aswered Find the mass of the ellipsoid given by 4x2 + 4y2 + z = 16 lying above the xy-plane and the density function is given by p(x,y,z) = z. arked out of 0 lag Select one: 16 a. 3 stion 8 b. TT 3 c. 167 d. 871 e. 4 bus page
Please write neatly! 22. Let S denote the plane 2x +y+ 3z = 6 in the...
Please write neatly!
22. Let S denote the plane 2x +y+ 3z = 6 in the first octant with the upward normal, and C denote its triangular boundary. Use Stokes' Theorem to evaluate the line integral F dr where F = <2z - x, x +y +z, 2y-x>.
22. Let S denote the plane 2x +y+ 3z = 6 in the first octant with the upward normal, and C denote its triangular boundary. Use Stokes' Theorem to evaluate the line...
Consider the real valued function of two variablesz-f(x,y), which satisfies Ar2 +4y2+ 224 (a) Des...
Consider the real valued function of two variablesz-f(x,y), which satisfies Ar2 +4y2+ 224 (a) Describe all points (ro. yo. f(ro. yo)), such that the tangent plane to f(x, y) at (o.yof(ro. yo)) the point (2,0,0). Include scription. (b) Describe all points (roo,f(o, yo)), such that the tangent plane to f(x, y) at (zo. yo. f(o. yo) passes through the point (2,0,27), where >0 is an arbitrary constant. With the aid of a computer or by hand, provide a sketch of...
Question 3 Let the function f be defined by f(x,y)--3y3 +4y2-15y +x2-8x. The set A consists of all points (x,y) in the...
Question 3 Let the function f be defined by f(x,y)--3y3 +4y2-15y +x2-8x. The set A consists of all points (x,y) in the xy-plane that satisfy 0sx S 10, 0sy s10 and x +y28.Find the global minimum value of f(x,y) over the set A. (Hint: see example 8 in lecture 7.) (6 marks)
Question 3 Let the function f be defined by f(x,y)--3y3 +4y2-15y +x2-8x. The set A consists of all points (x,y) in the xy-plane that satisfy 0sx S 10,...
14. (a) Determine all possible critical point(s) of f(, y) = x2 + xy + y2...
14. (a) Determine all possible critical point(s) of f(, y) = x2 + xy + y2 - 3.c - 6y. (b) without using the Second Order Partial Derivatives Test (SOPDT), de- termine the nature of the obtained C.P(s). (c) Check your answer in (b) through the (SOPDT). 15. Find a point on the hyperboloid 2z = x2 - y², where the tangent plane is parallel to the plane x - 3y - 2 = 1.
For 18-20 graph the following equations. 18. [6] 2x-4y+3z = 12 19. [6] x2 +4y2 +9z2 =1 20. [6] z 2x2 + y7
For 18-20 graph the following equations. 18. [6] 2x-4y+3z = 12 19. [6] x2 +4y2 +9z2 =1 20. [6] z 2x2 + y7
Find the point(s) on the sphere x2 + y2 + z2 = 1 where the tangent plane is parallel to the plane 2.C + V3y – 3z = 2. Then write the equation(s) of the tangent plane(s). (Explain how you found the point(s) and simplify the equation(s) of the tangent plane(s)).
(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...
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...
21-23
Use the given transformation to evaluate the integral. 21)--2x + y, v = 9x + y; 21) (y-2x)(9x + y) dx dy where R is the parallelogram bounded by the lines y - 2x +6.y -2x+7.y 13 A) D) 1573 B) 1573 C) 22) // f (x2 + y2 +內0xdy dz. x2 y2 22 where R is the interior of the ellipsoid 1002361 D) 180: C) 240π B) 20От A) 120π 23) Solve the problem. 23) Evaluate x2- y...
Puestion 4 ot yet aswered Find the mass of the ellipsoid given by 4x2 + 4y2 + z = 16 lying above the xy-plane and the density function is given by p(x,y,z) = z. arked out of 0 lag Select one: 16 a. 3 stion 8 b. TT 3 c. 167 d. 871 e. 4 bus page
Please write neatly!
22. Let S denote the plane 2x +y+ 3z = 6 in the first octant with the upward normal, and C denote its triangular boundary. Use Stokes' Theorem to evaluate the line integral F dr where F = <2z - x, x +y +z, 2y-x>.
22. Let S denote the plane 2x +y+ 3z = 6 in the first octant with the upward normal, and C denote its triangular boundary. Use Stokes' Theorem to evaluate the line...
Consider the real valued function of two variablesz-f(x,y), which satisfies Ar2 +4y2+ 224 (a) Describe all points (ro. yo. f(ro. yo)), such that the tangent plane to f(x, y) at (o.yof(ro. yo)) the point (2,0,0). Include scription. (b) Describe all points (roo,f(o, yo)), such that the tangent plane to f(x, y) at (zo. yo. f(o. yo) passes through the point (2,0,27), where >0 is an arbitrary constant. With the aid of a computer or by hand, provide a sketch of...
Question 3 Let the function f be defined by f(x,y)--3y3 +4y2-15y +x2-8x. The set A consists of all points (x,y) in the xy-plane that satisfy 0sx S 10, 0sy s10 and x +y28.Find the global minimum value of f(x,y) over the set A. (Hint: see example 8 in lecture 7.) (6 marks)
Question 3 Let the function f be defined by f(x,y)--3y3 +4y2-15y +x2-8x. The set A consists of all points (x,y) in the xy-plane that satisfy 0sx S 10,...
14. (a) Determine all possible critical point(s) of f(, y) = x2 + xy + y2 - 3.c - 6y. (b) without using the Second Order Partial Derivatives Test (SOPDT), de- termine the nature of the obtained C.P(s). (c) Check your answer in (b) through the (SOPDT). 15. Find a point on the hyperboloid 2z = x2 - y², where the tangent plane is parallel to the plane x - 3y - 2 = 1.
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