![Surface Area In Exercises 23-42, compute the surface area of the surface S parametrized by r :D → R3, with D = [a, b] > [c, d](http://img.homeworklib.com/questions/30f0bc60-04ee-11eb-9f08-0fec74bc867e.png?x-oss-process=image/resize,w_560)
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17) r= ( 2 cosht cos 0,3 cosht sin o, sinht) (hyperboloid) 18....
1L COS v 21) Let H denote the surface parametrized by r(u, )sin, where 7 0S11 land 0 < u < 2T. (a...
1L COS v 21) Let H denote the surface parametrized by r(u, )sin, where 7 0S11 land 0 < u < 2T. (a) Compute Tu, Tu, and Tu X T, (b) Compute
1L COS v 21) Let H denote the surface parametrized by r(u, )sin, where 7 0S11 land 0
The tangent plane at a point Po(f(uo.VO) 9 (uo.vo) h(uo,VO)) on a parametrized surface r(u,v) =...
The tangent plane at a point Po(f(uo.VO) 9 (uo.vo) h(uo,VO)) on a parametrized surface r(u,v) = f(u,v) i + g(u,v) j+h(u, v) k is the plane through P, normal to the vector ru (uo.VO) XIV(40.VO) the cross product of the tangent vectors ru (uo. Vo) and rv (uo.VO) at Pg. Find an equation for the plane tangent to the surface at Po. Then find a Cartesian equation for the surface and sketch the surface and tangent plane together. (573 15...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos u) cos v, (2 + cos u) sin v), 0<u<27, 050521 parametrizes a torus T, which is depicted below. (a) Calculate ||ru x rull. (b) Show that T is smooth. (c) Find the equation of the tangent plane to T at (0,). (d) Find the surface area of T (e) Earlier in the semester, we observed that a torus can be built out of...
Find the flux integral SSs curl(Ē).d5, where F(x, y, z) = [2 cos(ny)+22 +22, 22 cos(z7/2)...
Find the flux integral SSs curl(Ē).d5, where F(x, y, z) = [2 cos(ny)+22 +22, 22 cos(z7/2) – sin(ny)e24, 222]T and S is the surface parametrized by F(s, t) = [(1 – 51/3) cos(t) – 4s, (1 – 51/3) sin(t), 5s]T with 0 <t< 27,0 < s < 1 and oriented so that the normal vectors point to the outside of the thorn.
10. Consider the surface S parameterized by w r= (cos y, sin v, u + sin...
10. Consider the surface S parameterized by w r= (cos y, sin v, u + sin v), -3 <u <3, 050 < 27 *** (a) Write a linear equation for the tangent plane to the surface at (0,1,1) (b) Compute the surface area of S.
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ &l...
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ < T* 2 marks (a) Describe this region. an appropriate integration, determine the volume of this shape [4 marks (b) Using 3 (Continued) 3 marks (c) Parametrise the surface of this shape. 3 marks (d) Find a normal to the surface [4 marks (e) What is the surface area of...
Hi need help for these Questions: a. Given f = yi + xzk and g = xyz2, determine (∇ x f ) . ∇g at the point (1,0,3) b. Point A lies on the curve r(t) = 2 cos t i + 2 sin t j + t k for the range 0 ≤ t...
Hi need help for these Questions:
a. Given f = yi + xzk and g =
xyz2, determine (∇ x f ) .
∇g at the point (1,0,3)
b. Point A lies on the curve r(t) = 2 cos t i +
2 sin t j + t k for the range 0 ≤
t ≤ 2π . At point A, the tangent vector is T = -
21/2i +
21/2j + k. Determine
the co-ordinates of point A and...
2. Consider the circular helix r(t)- (a cos t, a sin t, bt) where a > 0,b > 0. Let P(0, a, T) be ...
please answer all the 4 parts
of this question
2. Consider the circular helix r(t)- (a cos t, a sin t, bt) where a > 0,b > 0. Let P(0, a, T) be a point on the helix (a) Find the Frenet frame (T, N, B) at the point P (b) Find equations for the tangent and normal line at P (c) Find equations for the normal plane and the osculating plane at P (d) What is the curvature at...
8. Solve V?u=0, 2<r<4,0<O<21, (u(2,0) = sin 0, u(4,0) = cos 0,0 5 0 5 21.
8. Solve V?u=0, 2<r<4,0<O<21, (u(2,0) = sin 0, u(4,0) = cos 0,0 5 0 5 21.
2. Define g(r, y,z) = 22 sin(y - rz) 2y. Answer the following questions (a) Compute...
2. Define g(r, y,z) = 22 sin(y - rz) 2y. Answer the following questions (a) Compute the gradient of g at the point P (1,1,1) (b) The point P defined above is on the level surface g = C. What is the value of C? (c) Find an equation of the tangent plane to the level surface g C at the point P (d) Suppose we want to travel from the point P to the level surface g = C...
1L COS v 21) Let H denote the surface parametrized by r(u, )sin, where 7 0S11 land 0 < u < 2T. (a) Compute Tu, Tu, and Tu X T, (b) Compute
1L COS v 21) Let H denote the surface parametrized by r(u, )sin, where 7 0S11 land 0
The tangent plane at a point Po(f(uo.VO) 9 (uo.vo) h(uo,VO)) on a parametrized surface r(u,v) = f(u,v) i + g(u,v) j+h(u, v) k is the plane through P, normal to the vector ru (uo.VO) XIV(40.VO) the cross product of the tangent vectors ru (uo. Vo) and rv (uo.VO) at Pg. Find an equation for the plane tangent to the surface at Po. Then find a Cartesian equation for the surface and sketch the surface and tangent plane together. (573 15...
5. In class we saw that the function r(u, v) = (sin u, (2 + cos u) cos v, (2 + cos u) sin v), 0<u<27, 050521 parametrizes a torus T, which is depicted below. (a) Calculate ||ru x rull. (b) Show that T is smooth. (c) Find the equation of the tangent plane to T at (0,). (d) Find the surface area of T (e) Earlier in the semester, we observed that a torus can be built out of...
Find the flux integral SSs curl(Ē).d5, where F(x, y, z) = [2 cos(ny)+22 +22, 22 cos(z7/2) – sin(ny)e24, 222]T and S is the surface parametrized by F(s, t) = [(1 – 51/3) cos(t) – 4s, (1 – 51/3) sin(t), 5s]T with 0 <t< 27,0 < s < 1 and oriented so that the normal vectors point to the outside of the thorn.
10. Consider the surface S parameterized by w r= (cos y, sin v, u + sin v), -3 <u <3, 050 < 27 *** (a) Write a linear equation for the tangent plane to the surface at (0,1,1) (b) Compute the surface area of S.
3. A shape is defined as: (x, y, z) = (rcos 0 sin 0,r sin sin d, r cos ø) with 0r1, T/4 < 0< 7t/4 and 0 < ¢ < T* 2 marks (a) Describe this region. an appropriate integration, determine the volume of this shape [4 marks (b) Using 3 (Continued) 3 marks (c) Parametrise the surface of this shape. 3 marks (d) Find a normal to the surface [4 marks (e) What is the surface area of...
Hi need help for these Questions:
a. Given f = yi + xzk and g =
xyz2, determine (∇ x f ) .
∇g at the point (1,0,3)
b. Point A lies on the curve r(t) = 2 cos t i +
2 sin t j + t k for the range 0 ≤
t ≤ 2π . At point A, the tangent vector is T = -
21/2i +
21/2j + k. Determine
the co-ordinates of point A and...
please answer all the 4 parts
of this question
2. Consider the circular helix r(t)- (a cos t, a sin t, bt) where a > 0,b > 0. Let P(0, a, T) be a point on the helix (a) Find the Frenet frame (T, N, B) at the point P (b) Find equations for the tangent and normal line at P (c) Find equations for the normal plane and the osculating plane at P (d) What is the curvature at...
8. Solve V?u=0, 2<r<4,0<O<21, (u(2,0) = sin 0, u(4,0) = cos 0,0 5 0 5 21.
2. Define g(r, y,z) = 22 sin(y - rz) 2y. Answer the following questions (a) Compute the gradient of g at the point P (1,1,1) (b) The point P defined above is on the level surface g = C. What is the value of C? (c) Find an equation of the tangent plane to the level surface g C at the point P (d) Suppose we want to travel from the point P to the level surface g = C...
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