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Section 2.5-Constant-Coordinate Surfaces 2.31 Describe the intersection of the following surfaces: (a) * =...
Q4. Describe the intersection of the following surfaces a) p = 3, and 3, and the...
Q4. Describe the intersection of the following surfaces a) p = 3, and 3, and the surface 90° SO = 135°, 90° 5o = 180°, r = 5. b) y = 1 and the surface, r = 3. c) -2 5 x,y s 2,2 = 2 and the surface, 0 = 90°. d) 0 = 45° and the surface , Q = 270º.
MINl Review Problems for CH. 1, 2 and 3 Q) Describe the following surfaces with a...
MINl Review Problems for CH. 1, 2 and 3 Q) Describe the following surfaces with a drawing and determine the type of the coordinate system used: a) x5 b) p 3 c) D 3/2 d)r 2 e) 0 60° Q2) Describe the intersection of surfaces (1) and (2) Surface Surface 2 D 45 z 5 X-2 z 3 D-45 0-60 p-5 r-1 e-60° D-45 p-5 z-5 r 3 D45 Q3) Verify that A (Ax B) 0 B (Ax B) A...
Find an equation for the family of level surfaces corresponding to f. Describe the level surfaces....
Find an equation for the family of level surfaces corresponding to f. Describe the level surfaces. 6 f(x,y,z) =- x + y +Z Write an equation for the family of level surfaces where C is constant. Find an equation for the family of level surfaces corresponding to f. Describe the level surfaces. f(x,y,z) = Vy2 + 1022 Write an equation for the family of level surfaces where C is constant.
Parameterize the following surfaces in R3. Describe if the surface is open or closed. If the surf...
Parameterize the following surfaces in R3. Describe
if the surface is open or closed. If the surface is open, give a
parameterization of its boundary,
6. Parametrize the following surfaces in R3. Describe if the surface is open or closed. If the surface is open, give a parametrization of its boundary (positively oriented). (a) The part of the plane z - 2y 3 inside the cylinder 2 y16 (b) The sphere of radiuscentered at the origin. (c) The part of...
6. (a) Newton's method for approximating a root of an equation f(x) 0 (see Section 3.8) can be ad...
6. (a) Newton's method for approximating a root of an equation f(x) 0 (see Section 3.8) can be adapted to approximating a solution of a system of equations f(x, y) 0 and gx, y) 0. The surfaces z f(x, y) and z g(x, y) intersect in a curve that intersects the xy-plane at the point (r, s), which is the solution of the system. If an initial approxi- mation (xi, yı) is close to this point, then the tangent planes...
15. (1 point) Let C be the intersection curve of the surfaces z = 3x +...
15. (1 point) Let C be the intersection curve of the surfaces z = 3x + 5 and x2 + 2y2-1, oriented clockwise as seen from the origin. Let F(x, y, 2) (2z - 1)i +2xj+(-1)k. Compute F.dr (a) directly as a line integral AND (b) as a double integral by using Stokes' Theorem
Consider the following. z = x2 + y2, z = 36 − y, (6, -1, 37) (a) Find symmetric equations of the tangent line to the curve of intersection of the surfaces at the given point. x − 6 12 = y + 1 −2 = z −...
Consider the following. z = x2
+ y2, z = 36 − y, (6, -1, 37) (a) Find symmetric equations of the
tangent line to the curve of intersection of the surfaces at the
given point. x − 6 12 = y + 1 −2 = z − 37 −1 x − 6 1 = y + 1 12 = z
− 37 −12 x − 6 = y + 1 = z − 37 x − 6 12 =...
question #6 1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1...
question #6
1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...
Chapter 13, Section 13.7, Question 017 (a) Find all points of intersection of the line x...
Chapter 13, Section 13.7, Question 017 (a) Find all points of intersection of the line x = -2+1, y = 3 +t, z = 2t +21 and the surface z= x2 + y2 (b) At each point of intersection, find the cosine of the acute angle between the given line and the line normal to the surface. Enter your answers in order of ascending x-coordinate value. (a) (b) (x1,91,21) = (003 Edit cos 01 = ? Edit (x2, Y2, 22)...
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...
Q4. Describe the intersection of the following surfaces a) p = 3, and 3, and the surface 90° SO = 135°, 90° 5o = 180°, r = 5. b) y = 1 and the surface, r = 3. c) -2 5 x,y s 2,2 = 2 and the surface, 0 = 90°. d) 0 = 45° and the surface , Q = 270º.
MINl Review Problems for CH. 1, 2 and 3 Q) Describe the following surfaces with a drawing and determine the type of the coordinate system used: a) x5 b) p 3 c) D 3/2 d)r 2 e) 0 60° Q2) Describe the intersection of surfaces (1) and (2) Surface Surface 2 D 45 z 5 X-2 z 3 D-45 0-60 p-5 r-1 e-60° D-45 p-5 z-5 r 3 D45 Q3) Verify that A (Ax B) 0 B (Ax B) A...
Find an equation for the family of level surfaces corresponding to f. Describe the level surfaces. 6 f(x,y,z) =- x + y +Z Write an equation for the family of level surfaces where C is constant. Find an equation for the family of level surfaces corresponding to f. Describe the level surfaces. f(x,y,z) = Vy2 + 1022 Write an equation for the family of level surfaces where C is constant.
Parameterize the following surfaces in R3. Describe
if the surface is open or closed. If the surface is open, give a
parameterization of its boundary,
6. Parametrize the following surfaces in R3. Describe if the surface is open or closed. If the surface is open, give a parametrization of its boundary (positively oriented). (a) The part of the plane z - 2y 3 inside the cylinder 2 y16 (b) The sphere of radiuscentered at the origin. (c) The part of...
6. (a) Newton's method for approximating a root of an equation f(x) 0 (see Section 3.8) can be adapted to approximating a solution of a system of equations f(x, y) 0 and gx, y) 0. The surfaces z f(x, y) and z g(x, y) intersect in a curve that intersects the xy-plane at the point (r, s), which is the solution of the system. If an initial approxi- mation (xi, yı) is close to this point, then the tangent planes...
15. (1 point) Let C be the intersection curve of the surfaces z = 3x + 5 and x2 + 2y2-1, oriented clockwise as seen from the origin. Let F(x, y, 2) (2z - 1)i +2xj+(-1)k. Compute F.dr (a) directly as a line integral AND (b) as a double integral by using Stokes' Theorem
Consider the following. z = x2
+ y2, z = 36 − y, (6, -1, 37) (a) Find symmetric equations of the
tangent line to the curve of intersection of the surfaces at the
given point. x − 6 12 = y + 1 −2 = z − 37 −1 x − 6 1 = y + 1 12 = z
− 37 −12 x − 6 = y + 1 = z − 37 x − 6 12 =...
question #6
1. Sketch the following surfaces: (a) z-+y2/9 (b) a2 =y2 +22 (c) 2/4+(y-1)2+(z+1)/9 1 (d) r2+y-22+1 0 (e) -y2+-1 0. 2. Find an equation for the surface consisting of all points that are- point (1,-3, 5) and the plane r = 3. 3. Sketch the curve F(t)<t cos(t), t sin (t), t > 4. Find a vector equation that represents the curve of the intersec r2y =9 and the plane y + z = 2. 5. Find a...
Chapter 13, Section 13.7, Question 017 (a) Find all points of intersection of the line x = -2+1, y = 3 +t, z = 2t +21 and the surface z= x2 + y2 (b) At each point of intersection, find the cosine of the acute angle between the given line and the line normal to the surface. Enter your answers in order of ascending x-coordinate value. (a) (b) (x1,91,21) = (003 Edit cos 01 = ? Edit (x2, Y2, 22)...
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...
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