(a) To Draw: The parametrized form of the given curve.

Question

Want to see the full answer?

Answer 1

Question

Chapter 17.5, Problem 37E

To determine

(a)

To Draw:

The parametrized form of the given curve.

To determine

(b)

To Prove:

That the intersection of the surface S with the xy-plane is the unit circle given by $G (u, 0) = (\cos u, \sin u, 0)$

And verify that the normal vector along this circle is given by $N (u, 0) = (\cos u \sin \frac{u}{2}, \sin u \sin \frac{u}{2}, - \cos \frac{u}{2})$ parametrized form of the given curve.

To determine

(c)

To Show:

As u varies from 0 to 2p, the point $G (u, 0) = (\cos u, \sin u, 0)$ moves once around the unit circle, beginning and ending at $G (0, 0) = G (2 π, 0) = (1, 0, 0)$ .

That $N (u, 0) = (\cos u \sin \frac{u}{2}, \sin u \sin \frac{u}{2}, - \cos \frac{u}{2})$ is a unit vector that varies continuously but that $N (2 π, 0) = - N (0, 0)$ which shows that S is not orientable.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Students have asked these similar questions

On from the equation: 2 u = C₁ + C₂ Y + Czy + Cu y³ Find C₁, C₂, C3 and Cy Using these following Cases : (a) 4=0 at y=0 (b) U = U∞ at y = 8 du (c) at Y = S ду --y. ди = 0 at y = 0 буг

Tips S ps L 50. lim x2 - 4 x-2x+2 51. lim 22 - X 52. 53. x 0 Answer lim x 0 lim 2-5 X 2x2 2 x² Answer -> 54. lim T - 3x - - 25 +5 b+1 b3b+3 55. lim X x-1 x 1 Answer 56. lim x+2 x 2 x 2 57. lim x²-x-6 x-2 x²+x-2 Answer-> 23-8 58. lim 2-22-2

S 36. lim 5x+2 x-2 37. lim √√2x4 + x² x-3 Answer-> 2x3 +4 38. lim x12 √ x² + 1 √√x² + 8 39. lim x-1 2x+4 Answer 40. lim x3 2x x√x² + 7 √√2x+3

Answer 2

Question

Chapter 17.5, Problem 37E

To determine

(a)

To Draw:

The parametrized form of the given curve.

To determine

(b)

To Prove:

That the intersection of the surface S with the xy-plane is the unit circle given by $G (u, 0) = (\cos u, \sin u, 0)$

And verify that the normal vector along this circle is given by $N (u, 0) = (\cos u \sin \frac{u}{2}, \sin u \sin \frac{u}{2}, - \cos \frac{u}{2})$ parametrized form of the given curve.

To determine

(c)

To Show:

As u varies from 0 to 2p, the point $G (u, 0) = (\cos u, \sin u, 0)$ moves once around the unit circle, beginning and ending at $G (0, 0) = G (2 π, 0) = (1, 0, 0)$ .

That $N (u, 0) = (\cos u \sin \frac{u}{2}, \sin u \sin \frac{u}{2}, - \cos \frac{u}{2})$ is a unit vector that varies continuously but that $N (2 π, 0) = - N (0, 0)$ which shows that S is not orientable.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 3

Question

Chapter 17.5, Problem 37E

To determine

(a)

To Draw:

The parametrized form of the given curve.

To determine

(b)

To Prove:

That the intersection of the surface S with the xy-plane is the unit circle given by $G (u, 0) = (\cos u, \sin u, 0)$

And verify that the normal vector along this circle is given by $N (u, 0) = (\cos u \sin \frac{u}{2}, \sin u \sin \frac{u}{2}, - \cos \frac{u}{2})$ parametrized form of the given curve.

To determine

(c)

To Show:

As u varies from 0 to 2p, the point $G (u, 0) = (\cos u, \sin u, 0)$ moves once around the unit circle, beginning and ending at $G (0, 0) = G (2 π, 0) = (1, 0, 0)$ .

That $N (u, 0) = (\cos u \sin \frac{u}{2}, \sin u \sin \frac{u}{2}, - \cos \frac{u}{2})$ is a unit vector that varies continuously but that $N (2 π, 0) = - N (0, 0)$ which shows that S is not orientable.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 4

Question

Chapter 17.5, Problem 37E

To determine

(a)

To Draw:

The parametrized form of the given curve.

To determine

(b)

To Prove:

That the intersection of the surface S with the xy-plane is the unit circle given by $G (u, 0) = (\cos u, \sin u, 0)$

And verify that the normal vector along this circle is given by $N (u, 0) = (\cos u \sin \frac{u}{2}, \sin u \sin \frac{u}{2}, - \cos \frac{u}{2})$ parametrized form of the given curve.

To determine

(c)

To Show:

As u varies from 0 to 2p, the point $G (u, 0) = (\cos u, \sin u, 0)$ moves once around the unit circle, beginning and ending at $G (0, 0) = G (2 π, 0) = (1, 0, 0)$ .

That $N (u, 0) = (\cos u \sin \frac{u}{2}, \sin u \sin \frac{u}{2}, - \cos \frac{u}{2})$ is a unit vector that varies continuously but that $N (2 π, 0) = - N (0, 0)$ which shows that S is not orientable.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 5

Chapter 17.5, Problem 37E

To determine

(a)

To Draw:

The parametrized form of the given curve.

To determine

(b)

To Prove:

That the intersection of the surface S with the xy-plane is the unit circle given by $G (u, 0) = (\cos u, \sin u, 0)$

And verify that the normal vector along this circle is given by $N (u, 0) = (\cos u \sin \frac{u}{2}, \sin u \sin \frac{u}{2}, - \cos \frac{u}{2})$ parametrized form of the given curve.

To determine

(c)

To Show:

As u varies from 0 to 2p, the point $G (u, 0) = (\cos u, \sin u, 0)$ moves once around the unit circle, beginning and ending at $G (0, 0) = G (2 π, 0) = (1, 0, 0)$ .

That $N (u, 0) = (\cos u \sin \frac{u}{2}, \sin u \sin \frac{u}{2}, - \cos \frac{u}{2})$ is a unit vector that varies continuously but that $N (2 π, 0) = - N (0, 0)$ which shows that S is not orientable.

Answer 6

Chapter 17.5, Problem 37E

To determine

(a)

To Draw:

The parametrized form of the given curve.

Answer 7

Chapter 17.5, Problem 37E

To determine

(a)

To Draw:

The parametrized form of the given curve.

Answer 8

To determine

(b)

To Prove:

That the intersection of the surface S with the xy-plane is the unit circle given by $G (u, 0) = (\cos u, \sin u, 0)$

And verify that the normal vector along this circle is given by $N (u, 0) = (\cos u \sin \frac{u}{2}, \sin u \sin \frac{u}{2}, - \cos \frac{u}{2})$ parametrized form of the given curve.

Answer 9

To determine

(b)

To Prove:

That the intersection of the surface S with the xy-plane is the unit circle given by $G (u, 0) = (\cos u, \sin u, 0)$

And verify that the normal vector along this circle is given by $N (u, 0) = (\cos u \sin \frac{u}{2}, \sin u \sin \frac{u}{2}, - \cos \frac{u}{2})$ parametrized form of the given curve.

Answer 10

To determine

(c)

To Show:

As u varies from 0 to 2p, the point $G (u, 0) = (\cos u, \sin u, 0)$ moves once around the unit circle, beginning and ending at $G (0, 0) = G (2 π, 0) = (1, 0, 0)$ .

That $N (u, 0) = (\cos u \sin \frac{u}{2}, \sin u \sin \frac{u}{2}, - \cos \frac{u}{2})$ is a unit vector that varies continuously but that $N (2 π, 0) = - N (0, 0)$ which shows that S is not orientable.

Answer 11

To determine

(c)

To Show:

As u varies from 0 to 2p, the point $G (u, 0) = (\cos u, \sin u, 0)$ moves once around the unit circle, beginning and ending at $G (0, 0) = G (2 π, 0) = (1, 0, 0)$ .

That $N (u, 0) = (\cos u \sin \frac{u}{2}, \sin u \sin \frac{u}{2}, - \cos \frac{u}{2})$ is a unit vector that varies continuously but that $N (2 π, 0) = - N (0, 0)$ which shows that S is not orientable.

Answer 12

Expert Solution & Answer

Answer 13

Expert Solution & Answer

Answer 14

Want to see the full answer?

Check out a sample textbook solution

See solution

Answer 15

Ch. 17.1 - Prob. 1PQ Ch. 17.1 - Prob. 2PQ Ch. 17.1 - Prob. 3PQ Ch. 17.1 - Prob. 4PQ Ch. 17.1 - Prob. 1E Ch. 17.1 - Prob. 2E Ch. 17.1 - Prob. 3E Ch. 17.1 - Prob. 4E Ch. 17.1 - Prob. 5E Ch. 17.1 - Prob. 6E

(a) To Draw: The parametrized form of the given curve.

Solution Summary: The author illustrates the parametrized form of the given curve by drawing the surface with parametrization G and verifying the normal vector along this circle.

Videos

(a)

To Draw:

The parametrized form of the given curve.

Want to see the full answer?

Chapter 17 Solutions

(a) To Draw: The parametrized form of the given curve.

Solution Summary: The author illustrates the parametrized form of the given curve by drawing the surface with parametrization G and verifying the normal vector along this circle.

Videos

(a) To Draw: The parametrized form of the given curve.

(b) To Prove: That the intersection of the surface S with the xy-plane is the unit circle given by G(u,0)=(cosu,sinu,0) And verify that the normal vector along this circle is given by N(u,0)=(cosusinu2,sinusinu2,−cosu2) parametrized form of the given curve.

Want to see the full answer?

Chapter 17 Solutions

(a)

To Draw:

The parametrized form of the given curve.