Fx 0. Show that =-- dx Fy dy 8. Suppose y is a function of z, F(x, y) = 0, and F,メO. Show that d...
The figure shows the region of integration for the integral. fx, y, z dy dz dx 0 Jo Rewrite this integral as an equivalent iterated integral in the five other orders. (Assume yx) 6x and z(x)-36-) x. f(x, y, 2) dy dx dz x, , z) dz dx dy f(x, y, z) dz dy dx f(x, y, z) dx dy dz fx, y, z) dx dy dz J0 Jo Jo f(x, y, z) dz dx dy 0 0 f(x, y,...
f(x, y, z) dz dy da as an iterated integral in the 4. (6 points) Rewrite the integral order dx dy dz.
score: 0 of 1 pt X 15.1.6 Evaluate the iterated integral. || (x?y-9xy) dy dx S S (x+y=9xy) dy dx= [(Type an integer or a simplified fraction.) Homework: Section 15.1 Matt Score: 0 of 1 pt X 15.1.9 Evaluate the iterated integral. In 2 In 5 3x + 24 dy dx 0 1 In 2 In 5 3x + 2y dy dx = (Type an exact answer.) ints Homework: Section Score: 0 of 1 pt X 15.1.10 Evaluate the iterated...
Question 6 6 pts Suppose that f(x, y, z) is a scalar-valued function and F(x, y, z) = (P(x, y, z), Q(2,y,z), R(x, y, z)) is a vector field. If P, Q, R, and f all have continuous partial derivatives, then which of the following equations is invalid? O curl (aF) N21 = a curl F for any positive integer Q. REC o div (fF) = fdiv F+FVF Odiv curl F = 0 O grad div f = div grad...
work. 1(a). Find fa, fy and fx for the function f(x, y, z) = xpez
Write an iterated integral for SSS fex,y,z) av. S = {(x, y, z): 0 sxs8,0 sy s5,0<zs (5 - 6x - 2y)} 5 S 5-6x - 2y f(x, y, z) dz dy dx 5 8 5 f(x, y, z) dz dy dx s 8 5 5 - 6x - 2y f(x, y, z) dz dy dx 5 666 8 5 5 - 6x - 2y f(x, y, z) dx dy dz
4. (a Let (sin( x cos( ) dr + (x cos(x + y) - 2) dy. dz= Show that dz is an exact differential and determine the corresponding function f(x,y) Hence solve the differential equation = z sin( Cos( y) 2 x cos( y) dy 10] (b) Find the solution of the differential equation d2y dy 2 y e dx dæ2 initial conditions th that satisfi 1 (0) [15] and y(0) 0 4. (a Let (sin( x cos( ) dr...
2. Suppose X and Y are independent continuous random variables. Show that P(Y < X) = | Fy(x) · fx (x) dx -oo where Fy is the CDF of Y and fx is the PDF of X [hint: P[Y E A] = S.P(Y E A|X = x) · fx(x) dx]. Rewrite the above equation as an expectation of a function of X, i.e. P(Y < X) = Ex[•]. Use the above relation to compute P[Y < X] if X~Exp (2)...
For metric spaces (X, dx) and (Y, dy) consider their Cartesian product Z-X (p18). Show that the following constructions both give metris on the product (a) Define di : Z × c, d))-dr(a, c) + dy(b, d) for (a, b), (c, d) e X x Y (b) Define (lo : Z × Z → R by writing do ((a, b), (c, d))-maux {dx (a, c), dy(b, d)) for (a, b), (c, d) E X × Y Answer the following: (c)...
5. (4 points) Calculate integral $.264 + z sin y)dx + (x? cos y − 3yjº)dy along triangle with vertices (0,0), (1,0) and (1,1), oriented counterclockwise, using Green's theorem.