1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the...
1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc length parameter with s = 0 corresponding to the point (0, 1.9) oriented counter-clockwise as seen from above Spring 2016) 1. (1 point) Find the arc-length parametrization of the curve that is the intersection of the elliptic cylr 1 and the plane z-2y = 7. Use s as the arc...
You need to find vector r(t) first. 1. Find the arc-length parametrization of the curve that is the intersection of the elliptic cylinder a21 and the plane z2. Use s as the arc-length parameter wih s 0 corresponds to the point (1,0,-1). Specify the limits for
Find the arc length parameter along the curve from the point where t=0 by evaluating the integral s | |vIdT. Then find the length of 0 the indicated portion of the curve. The arc length parameter is s(t) (Type an exact answer, using radicals as needed.) Find T, N, and k for the plane curve r(t) (2t+9) i+ (5-t2) j T(t)= (Type exact answers, using radicals as needed.) (Type exact answers, using radicals as needed.) Find the arc length parameter...
Consider the paraboloid z=x2+y2. The plane 2x−2y+z−7=0 cuts the paraboloid, its intersection being a curve. Find "the natural" parametrization of this curve. Hint: The curve which is cut lies above a circle in the xy-plane which you should parametrize as a function of the variable t so that the circle is traversed counterclockwise exactly once as t goes from 0 to 2*pi, and the paramterization starts at the point on the circle with largest x coordinate. Using that as your...
Find the length of the arc of the curve from point P to point Q. *2 = (y - 3)3, P(1,9), Q(8, 12)
ili Quot 12.3.14 Find the arc length parameter along the curve from the point where t = 0 by evaluating the integral s - Sivce)| dr. Then find the length of the indicated portion of the curve. -jwel de r(t)- (5 + 3)i + (4 +31)j + (2-7)k, - 1sts The arc length parameter is s(t)=0 (Type an exact answer, using radicals as needed.)
Suppose s(t) is the arc-length parametrization of a space-turd flying through space. What is the arc-length of the space-turd's path between time t = 1 and t = 70 ? Question 10 1 pts Suppose f(x, y, z) = xy cos z.Compute the partial derivative of f with respect to the variable y at the point (4,2, 7).
do the three with mark 1.31. Show that the union of two regions with nonempty intersection is itself a region. 1.32. Show that if ACB and B is closed, then dAC B. Similarly, if AC B and A is open, show that A is contained in the interior of B 1.33. Find a parametrization for each of the following paths: (a) the circle C[1+ i, 1], oriented counter-clockwise (b) the line segment from -1-to 2 (c) the top half of...
Help Entering Answers 1 point) Verify that Stokes' Theorem is true for the vector field F that lies above the plane z1, oriented upwards. 2yzi 3yj +xk and the surface S the part of the paraboloid z 5-x2-y To verify Stokes' Theorem we will compute the expression on each side. First computecurl F dS curl F0,3+2y,-2 Edy dx curl F dS- where x2 = curl F ds- Now compute F.dr The boundary curve C of the surface S can be...
the plane 7-1 with the cylinder Consider the vector field F(x, y, z) = (x²); + (x+y); + (4y2Z) K and the curve C defined by the intersection Counter clockwise as viewed from above. Evaluate the Work- SF. dr done by F along in the following ways (a) Directly, using parametrization of C (b) Using stakes theorem