Find a vector function P(1) that parameterizes the curve of intersection of the cyinder X*+ ---...
X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the graph of y = sin | 2x | in the xy-plane.) An equation for the circle of curvature is (Type an equation. Type an exact answer, using π as needed.)
X) 13.4.21 Find an equation for the circle of curvature of the curve r(t)-21 + sin(t) j at the point (z,1). (The curve parameterizes the...
Find a vector function that represents the curve of intersection of the two surfaces: The cone z=sqrt(x^2 + y^2) and the plane z =1 + y.
a) Find the length of the curve traced by the given vector function on the indicated interval: r(t)e' costie' sin tj+e'k 0<t<In2 b) Find the gradient of the scalar function f 6xyz + 2x+ xz at (1, 1, -1) c) Find the curl of the given vector field: F(x, y,z) 4xyi + (2x2 +2yz)j+(3z2+y2)k
Question 3 3 pts Find a vector function, r(t), that represents the curve of intersection of the two surfaces. The cone z = V x2 + y2 and the plane z =6+y 12 1 12 a. r= 1 (61,42 – 36,42 +36) b. 1) = 1 (12t,t2 + 36,42 +36) +(12t,– 12,42 +12) ${12t,t2 – 36,2 +36) P(8) = 1 / 2 C. d. (6) 2 1
Find a normal vector and an equation for the tangent plane to the surface: x3 - y2 - z2 - 2xyz + 6 =0 at the point P : (−2, 1, 3). Determine the equation of the line formed by the intersection of this plane with the plane x = 0. [10 marks] (b) Find the directional derivative of the function F(x, y, z) = 2x /zy2 , at the point P : (1, −1, −2) in the direction of...
7. Find (a) the curl and (b) the divergence of the vector field F(x, y, z)= e' sin yi+e' cos yj+zk F.de where is the curve of intersection of the plane : = 5 - x and the cylinder rº + y2 = 9. 8. Use Stokes Theorem to evaluate F(x, y, - ) = xyi +2=j+3yk
Consider the surface z = f(x, y) = sin(x) + cos(y) and the curve C in the xy plane defined parametrically as x(t) = 2cos(t), y(t) = sin(t) a. Find z'(t). Imagine you are walking directly above the curve C in the direction of increasing t. Find the values of t for which you are walking uphill. Hint:Graph z'(t). Graph f(x, y) for -7 < x < 7 and -7 < y < 7. (You will have to find software...
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Which vector function represents the curve of intersection of the surfaces x = y2 and y² + x2 25 ? = Find a vector that is parallel to both of the planes 2 – y + 2z = 2 and x + y + 3z = 13.
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...
Problem 13 15pts Carefully sketch the vector field vf(z, y) using at least 25 points if Problem 14 Demonstrate that the vector field is or is not con.servative. Problem 15 25pts Find a vector field n(u, v) of unit normals to r(u,)(2cos(u)sin(), 3sin(u)sin(v), cos(v)
Problem 13 15pts Carefully sketch the vector field vf(z, y) using at least 25 points if Problem 14 Demonstrate that the vector field is or is not con.servative. Problem 15 25pts Find a vector field n(u,...