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the surface given by the parametric representation
writing down the parametric equations..
Now,
Since,
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b)
The surface S represents an elliptical paraboloid.
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6. Consider the surface S described by r(u, ucos v,...
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.
10. The surface described by r(u, v) = cosu i + sinu cosv j + sinu...
10. The surface described by r(u, v) = cosu i + sinu cosv j + sinu sinv k where 0 <u<r and 0 < < 2n is a a. Cone b. Cylinder c. Sphere d. Upper half of an ellipsoid e. Upper half of a sphere f. None of these 11. The surface described by r(u, v) = 3cosu cosv i + 2sinu cosv j + 6siny k where 0 <u<2n and 0 <vn/2 is a a. Cone b. Cylinder...
3. (3 points) Let the surface S be parametrized by r(u, v) = (bcos u, sin...
3. (3 points) Let the surface S be parametrized by r(u, v) = (bcos u, sin u, v) for (u, v) E D where D = {(u, v) O SUST, SU <3}. Set up the iterated integral, but do not evaluate, the surface area JJsdS (I want the iterated integral for du du, and in that order. Do not even try to evaluate this integral!).
1. Who's that surface? Consider the function Flu, y) = (v cosu, v sin u, u),...
1. Who's that surface? Consider the function Flu, y) = (v cosu, v sin u, u), 0 Su<27, -2 SU <2. The goal of this problem is to figure out what surface this function parametrizes! (a) Find a parametrization of the coordinate curve with u held constant as u = u. Plot a couple of these curves in 3D to see what they look like. (b) Find a parametrization of the coordinate curve with v held constant as v =...
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...
Consider the elliptic paraboloid which is given by (1) = {r(u, v) = (5u cos(u), 5u...
Consider the elliptic paraboloid which is given by (1) = {r(u, v) = (5u cos(u), 5u sin(u), u?)? | >0, v € (-,7]} . Below, we work in the chart (U,r) obtained by taking U = RX0 X (-,7), where the map r:U + R3 is defined in (1). 0 Question 2 (1 mark). Show that the second fundamental form II is given by 10 10 14u2 + 25 ( 0 u =
Give a parametric description of the form r(u, v) = (x(u,v),y(u,v),z(u,v)) for the following surface. The...
Give a parametric description of the form r(u, v) = (x(u,v),y(u,v),z(u,v)) for the following surface. The cap of the sphere x² + y2 + z = 36, for 3/3 sz56 Select the correct choice below and fill in the answer boxes to complete your choice. (Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than 21. Type exact answers in terms of ..) A. Fu.v) = (6 sin u cos V,6 sin...
(2) Let S be the surface parametrized by r(u, v) = (u? – 12)i + (u...
(2) Let S be the surface parametrized by r(u, v) = (u? – 12)i + (u + v)j + (u? + 3v)k. (a) Find a normal vector to S at the point (3,1,1). (b) Find an equation of the tangent plane to S at (3, 1, 1).
Consider the surface S, given by the parameterization: And consider the claims: S is smooth in...
Consider the surface S, given by the parameterization:
And consider the claims:
S is smooth in all its points.
S matches the graph of the equation
Select one:
a. Only (2) is true.
b. Both are false.
c. They are both true.
d. Only (1) is true.
r(u, v) = (u, v, u? + v2), donde Su<lyo Susi z2 = 2² + y para z>0yz² + y² <1.
6. (a) Consider the line integral (2) dx+2y dy, where C is part of the ellipse 9r26y144 from the ...
solve the proplem using Maple
6. (a) Consider the line integral (2) dx+2y dy, where C is part of the ellipse 9r26y144 from the point (0,3) to the point o.-3). Plot the curve C and evaluate the line integral. (b) Consider the surface integralVi++i where S is the surface of the helicoid r(mu) =< u cost, u sin v, u >, integral 0 u 1, 0 u 2r. Plot the surface S and evaluate the surface
6. (a) Consider the...
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.
10. The surface described by r(u, v) = cosu i + sinu cosv j + sinu sinv k where 0 <u<r and 0 < < 2n is a a. Cone b. Cylinder c. Sphere d. Upper half of an ellipsoid e. Upper half of a sphere f. None of these 11. The surface described by r(u, v) = 3cosu cosv i + 2sinu cosv j + 6siny k where 0 <u<2n and 0 <vn/2 is a a. Cone b. Cylinder...
3. (3 points) Let the surface S be parametrized by r(u, v) = (bcos u, sin u, v) for (u, v) E D where D = {(u, v) O SUST, SU <3}. Set up the iterated integral, but do not evaluate, the surface area JJsdS (I want the iterated integral for du du, and in that order. Do not even try to evaluate this integral!).
1. Who's that surface? Consider the function Flu, y) = (v cosu, v sin u, u), 0 Su<27, -2 SU <2. The goal of this problem is to figure out what surface this function parametrizes! (a) Find a parametrization of the coordinate curve with u held constant as u = u. Plot a couple of these curves in 3D to see what they look like. (b) Find a parametrization of the coordinate curve with v held constant as v =...
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...
Consider the elliptic paraboloid which is given by (1) = {r(u, v) = (5u cos(u), 5u sin(u), u?)? | >0, v € (-,7]} . Below, we work in the chart (U,r) obtained by taking U = RX0 X (-,7), where the map r:U + R3 is defined in (1). 0 Question 2 (1 mark). Show that the second fundamental form II is given by 10 10 14u2 + 25 ( 0 u =
Give a parametric description of the form r(u, v) = (x(u,v),y(u,v),z(u,v)) for the following surface. The cap of the sphere x² + y2 + z = 36, for 3/3 sz56 Select the correct choice below and fill in the answer boxes to complete your choice. (Type any angle measures in radians. Use angle measures greater than or equal to 0 and less than 21. Type exact answers in terms of ..) A. Fu.v) = (6 sin u cos V,6 sin...
(2) Let S be the surface parametrized by r(u, v) = (u? – 12)i + (u + v)j + (u? + 3v)k. (a) Find a normal vector to S at the point (3,1,1). (b) Find an equation of the tangent plane to S at (3, 1, 1).
Consider the surface S, given by the parameterization:
And consider the claims:
S is smooth in all its points.
S matches the graph of the equation
Select one:
a. Only (2) is true.
b. Both are false.
c. They are both true.
d. Only (1) is true.
r(u, v) = (u, v, u? + v2), donde Su<lyo Susi z2 = 2² + y para z>0yz² + y² <1.
solve the proplem using Maple
6. (a) Consider the line integral (2) dx+2y dy, where C is part of the ellipse 9r26y144 from the point (0,3) to the point o.-3). Plot the curve C and evaluate the line integral. (b) Consider the surface integralVi++i where S is the surface of the helicoid r(mu) =< u cost, u sin v, u >, integral 0 u 1, 0 u 2r. Plot the surface S and evaluate the surface
6. (a) Consider the...
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