Let
.
Then
= , and
in the direction of
is .


(7 pts.) Let f(x, y, z) = "y and let R be the region {(x, y, z) |2 < x < 4,0 Sy < 3,15 zse}. 2 Evaluate | $180,0,.2) av. R
1. Let F(x,y,z) =< 32, 5x, – 2y >. Use Stokes's Theorem to evaluate the integral Scurl F.ds, where S is the part of the paraboloid z = x² + y2 that lies below the plane z = 4 with upward- pointing normal vector.
Assess a subjective triangular probability distribution for the
random variable, X, where X is defined as the amount of snowfall
you think we will get in our next snowstorm in inches. Suppose that
you expect your commute to increase in minutes according to the
function . What is the expected increase in your
commute for the next snowstorm?
Estimate E[f(X)] by creating simple Monte Carlo
simulation in Excel.
Here are some equations for the triangular distribution that may
help you:...
Let F(x, y, z) = 4i – 3j + 5k and S be the surface defined by z = x2 + y2 and x2 + y2 < 4. Evaluate SJ, F.nds, where n is the upward unit normal vector.
-n ', S Let f(x,yZFz2_xy. Let v=<1,1,1>. Let point P=<2,1,3> a. Compute gradient of fx,y,z) b. If the contours are far apart, is the length of the gradient large or small? Answer: Explain! What MATLAB command is used to draw the gradient vectors? Answer: - c. Compute the directional derivative in the direction of v. d. Compute the equation of the tangent plane to f(x,y,z) at the point P. e. Use the chain rule to compute r if x t2,...
Let F(x,y,z) = <7x, 5y, 2z > be a vector field. Find the flux of F through surface S. Surface S is that portion of 3x + 5y + 72 = 9 in the first octant. Answer: Finish attempt
Consider the vector field F (x, y, z) = <y?, z2, x?>. Compute the curl (F). Use Stokes' Theorem to evaluate S. F. dr where C is the triangle (0,0,0), (1,0,0), and (0, 1, 1) oriented counter-clockwise when viewed from above.
Let F(x,y,z) = <7x, 5y, 2z> be a vector field. Find the flux of F through surface S. Surface S is that portion of 3x + 5y + 7z = 8 in the first octant. Answer:
How to solve it?
Let F =< -2, x, y2 >. Find S Ss curlF.nds, where S is the paraboloid z = x2 + y?, OSz54.
12. Let g(x), h(y) and p(z) be functions and define f(x, y, z) = g(x)h(y)p(2). Let R= = {(x, y, z) E R3: a < x <b,c sy <d, eszsf} where a, b, c, d, e and f are constants. Prove the following result SS1, 5100,2)AV = L*()dx ["Mwdy ['Plzdz.