S1=(x, y, z) belongs to R^3,x^2+y2 =1 and s2=(x, y, z) belongs to R^3 and y=x find parametrization of intersection s1and s2
S1=(x, y, z) belongs to R^3,x^2+y2 =1 and s2=(x, y, z) belongs to R^3 and y=x...
8 pts Question 3 Consider the function f(x,y, 2)(x 1)3(y2)3 ( 1)2(y2)2(z 3)2 (a) Compute the increment Af if (r,y, z) changes from (1,2,3 (b) Compute the differential df for the corresponding change in position. What does (2,3,4) to this say about the point (1, 2,3)? ( 13y2)3 ( 1)2(y 2)2(z 3)2 with C (c) Consider the contour C = a constant. Use implicit differentiation to compute dz/Ox. Your answer should be a function of z. (d) Find the unit...
Let S be the part of the sphere x^2 + y^2 + z^2 = 4 that lies between the cones z = √x^2 + y^2 and z = √3x^2 + 3y^2. (1) Let S be the part of the sphere x2 + y2 + Z2-4 that lies between the cones X +y and z a) Find a differentiable parametrization of S b) Find the area of S c) Find 22 dS. (1) Let S be the part of the sphere...
Let S1 be the part of the paraboloid z = 1 − x ^2 − y ^2 that lies above the plane z = 0. Let S2 be the part of the cone z = √ x ^2 + y ^2 + 2(sqrt till y^2) that lies inside of the cylinder x ^2 + y^ 2 = 1. Let S3 be the part of the cylinder x ^2 + y ^2 = 1 that lies between these surfaces. If S...
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 =...
Questions. Please show all work. 1. Consider the vector field F(x, y, z) (-y, x-z, 3x + z)and the surface S, which is the part of the sphere x2 + y2 + z2 = 25 above the plane z = 3. Let C be the boundary of S with counterclockwise orientation when looking down from the z-axis. Verify Stokes' Theorem as follows. (a) (i) Sketch the surface S and the curve C. Indicate the orientation of C (ii) Use the...
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...
Given f : R → R4, f(x, y, z) = (x2 + y2, 2, x + 2, y2 + x3) (Hint: f is not linear) (a) (1 point) Find the kernel of f. (b) (1 point) Find the range of f. (c) (1 point) Is f is 1-1? Is f onto? Justify your answers.
8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29 8. Find the area of the surface given by z - f(x, y) over the region R. f(x,y)- 42-x2-y2, R = {(x,y): x2 +y2 29
1 Use Stokes' theorem to evaluate the integrals: F(x, y, z) dr a) where F(r, y,z)(3yz,e, 22) and C is the boundary of the triangle i the plane y2 with vertices b) where F(x, y,z (-2,2,5xz) and C is in the plane 12- y and is the boundary of the region that lies above the square with vertices (3,5, 0), (3,7,0),(4,5,0), (4,7,0) c) where F(x, y,z(7ry, -z, 3ryz) and C is in the plane y d) where intersected with z...
5. (7 points) Let f: R3 → R be the function f(x,y,z) = x2 + y2 +3(2-1)2 Let EC R3 be the closed half-ball E = {(x, y, z) e R$: x² + y2 +< 9 and 2 >0}. Find all the points (x, y, z) at which f attains its global maximum and minimum on E.