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(1 point) Suppose COS u and sin u is negative. Here are some small variations on...
(1 point) Simplify the expression as much as possible. (cos(u)-1)/(sin(u)) - (sin(u))/(cos(u)+1)
(1 point) Simplify the expression as much as possible. (cos(u)-1)/(sin(u)) - (sin(u))/(cos(u)+1)
22 Suppose sin v = 3. Evaluate (a) cos u (c) tan u (b) sin u...
22 Suppose sin v = 3. Evaluate (a) cos u (c) tan u (b) sin u (d) cos v (e) tan v.
n-1 4. Solve u(1,0) cos(0)+sin(20). 5. Solve n-1 4. Solve u(1,0) cos(0)+sin(20). 5. Solve
n-1 4. Solve u(1,0) cos(0)+sin(20). 5. Solve
n-1 4. Solve u(1,0) cos(0)+sin(20). 5. Solve
(5) The image of the parametrization Φ(u, u) = (a . sin(u) . cos(u), b . sin(u) . sin(e), c . cos...
(5) The image of the parametrization Φ(u, u) = (a . sin(u) . cos(u), b . sin(u) . sin(e), c . cos(u)) sin(u sin() cosu with b < a, 0 r, 0 2π parametrizes an ellipsoid. u u a) Show that all the points in the image of Φ satisfy the Cartesian equation of an ellipsoid E b) Show that the image surface is regular at all points. c Write out the integral for its surface area A(E). (Do not...
16 Suppose COS U = (a) sin u (b) tanu Ž. Evaluate (c) cos v (d)...
16 Suppose COS U = (a) sin u (b) tanu Ž. Evaluate (c) cos v (d) sin v (e) tan v.
(1 point) Suppose that sin A < 0, and cos A > 0. In which quadrant...
(1 point) Suppose that sin A < 0, and cos A > 0. In which quadrant does the terminal side of ∠A locate?
(1 point) 5x2 — 5у, v %3D 4х + Зу, f(u, U) sin u cos v,u...
(1 point) 5x2 — 5у, v %3D 4х + Зу, f(u, U) sin u cos v,u = Let z = = and put g(x, y) = (u(x, y), v(x, y). The derivative matrix D(f ° g)(x, y) (Leaving your answer in terms of u, v, x, y ) (1 point) Evaluate d r(g(t)) using the Chain Rule: r() %3D (ё. e*, -9), g(0) 3t 6 = rg() = dt g(u, v, w) and u(r, s), v(r, s), w(r, s). How...
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...
Establish the identity csc u sinu - cos?u= sin ? Write the left side term csc...
Establish the identity csc u sinu - cos?u= sin ? Write the left side term csc u in term of sin u. . sin u-cos? Simplify the expression from the previous step by canceling the common factor. |-cos²u The expression from the previous step is equivalent to sinu using what? A. Pythagorean Identity OB. Even-Odd Identity OC. Cancellation Property D. Quotient Identity E. Reciprocal Identity OO Click to select your answer(s). 3,576 MAY 28
Consider the following surface parametrization. x-5 cos(8) sin(φ), y-3 sin(θ) sin(p), z-cos(p) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for θ in [...
Consider the following surface parametrization. x-5 cos(8) sin(φ), y-3 sin(θ) sin(p), z-cos(p) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for θ in [0, 2T] and φ in [0, π] -3 cos(θ) sin(φ), 5 sin(θ) sin(φ),-15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 3 cos(9) sin(9),-5 sin(θ) sin(9), 15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 v 16 sin2(0) sin2@c 216 cos2@t9(3 cos(θ) sin(φ), 5 sin(θ) sin(φ) , 15 cos(q) 216 cos(φ)...
22 Suppose sin v = 3. Evaluate (a) cos u (c) tan u (b) sin u (d) cos v (e) tan v.
n-1 4. Solve u(1,0) cos(0)+sin(20). 5. Solve
n-1 4. Solve u(1,0) cos(0)+sin(20). 5. Solve
(5) The image of the parametrization Φ(u, u) = (a . sin(u) . cos(u), b . sin(u) . sin(e), c . cos(u)) sin(u sin() cosu with b < a, 0 r, 0 2π parametrizes an ellipsoid. u u a) Show that all the points in the image of Φ satisfy the Cartesian equation of an ellipsoid E b) Show that the image surface is regular at all points. c Write out the integral for its surface area A(E). (Do not...
16 Suppose COS U = (a) sin u (b) tanu Ž. Evaluate (c) cos v (d) sin v (e) tan v.
(1 point) 5x2 — 5у, v %3D 4х + Зу, f(u, U) sin u cos v,u = Let z = = and put g(x, y) = (u(x, y), v(x, y). The derivative matrix D(f ° g)(x, y) (Leaving your answer in terms of u, v, x, y ) (1 point) Evaluate d r(g(t)) using the Chain Rule: r() %3D (ё. e*, -9), g(0) 3t 6 = rg() = dt g(u, v, w) and u(r, s), v(r, s), w(r, s). How...
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...
Establish the identity csc u sinu - cos?u= sin ? Write the left side term csc u in term of sin u. . sin u-cos? Simplify the expression from the previous step by canceling the common factor. |-cos²u The expression from the previous step is equivalent to sinu using what? A. Pythagorean Identity OB. Even-Odd Identity OC. Cancellation Property D. Quotient Identity E. Reciprocal Identity OO Click to select your answer(s). 3,576 MAY 28
Consider the following surface parametrization. x-5 cos(8) sin(φ), y-3 sin(θ) sin(p), z-cos(p) Find an expression for a unit vector, n, normal to the surface at the image of a point (u, v) for θ in [0, 2T] and φ in [0, π] -3 cos(θ) sin(φ), 5 sin(θ) sin(φ),-15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 3 cos(9) sin(9),-5 sin(θ) sin(9), 15 cos(q) 16 sin2(0) sin2(p)216 cos2(p)9 v 16 sin2(0) sin2@c 216 cos2@t9(3 cos(θ) sin(φ), 5 sin(θ) sin(φ) , 15 cos(q) 216 cos(φ)...
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