(ii) R= [0, 1] x [0, 1] C R2 olsun. f: RR fonksiyonu f(x,y) = 2-Y eğer (2, y) + (0,0) ise (x+y)3 0 eğer (x,y) = (0,0) ise şeklinde tanımlansın. f fonksiyonunun Rüzerinde integrallenebilir olup/olmadığını ispatlayıp, eğer integrallenebilir ise SR fdA integralini hesaplayınız. Prove whether the f function is integrable on R. if it can be integrated; calculate the integral SR fdA.
Consider z-f(x,y)-1-xy cos(xy) at (2,-1/2) variations in x and y respectively. and let ΔΧ and ây represent small a) (i) Compute ΔΖ, given that ΔΧ_ 0.028 and Δy_-0.039. 1 1 6DP Az 5DP ii) Write out an expression for dz in terms of x,y and d, dy. dz= 2 (iii) Compute dz assuming dr_Δι and dy_ây dz- 5DP b) Use the equation of the tangent plane to z at (2,-1/2) to approximate Approximate value = 1 5DP Consider z-f(x,y)-1-xy cos(xy)...
1. Suppose that E(X) E(Y) E(Z) 2 Y and Z are independent, Cov(X, Y) V(X) V(Z) 4, V(Y) = 3 Let U X 3Y +Z and W = 2X + Y + Z 1, and Cov(X, Z) = -1 Compute E(U) and V (U) b. Compute Cov(U, W). а.
Let F = <z, 0, y> and let S be the oriented surface parametrized by G(u, v) = (u2 − v, u, v2) for 0 ≤ u ≤ 6, −1 ≤ v ≤ 4. Calculate the normal component of F to the surface at P = (24, 5, 1) = G(5, 1).
In depth Explanation please! 4. A potential is given as V(x,y,z) Az^2x + Be^-ex + Dy3z^-2, where A, B, C, D What is Ex, Ey, and Ez?
Let F(x, y, z) = x2y3 + y 2 sin(π z) /π + z2ex-1 a) Find the equation of the tangent plane to the graph of the function z = z(x, y) at the point (x, y) = (1, 1), if z satisfies the equation F(x, y, z) = 2 with z(1, 1) = 1. b) At the point P(1, 1, 1), determine in which of the two directions ~u = h−4, 3, 0i or ~v = h−3, 0, 4i...
f a random sample X,X, X, from the 2. Let Y, < Y.< Y, be the order statistics o exponential distribution with mean β. Let (i) Are the random variables U,V,W independent? (ii) What is the distribution of each of U,V and W.
The contour diagram in Figure 6(a) describes the hyperbolic paraboloid z = f(x, y) = I y. The bold lines represent the r and y axes. (a) (b) Figure 6 i) Through a change of variables u = r+y and v = r-y, show that f can be rewrit- ten in the standard form of a hyperbolic paraboloid. Such a transformation is shown in Figure 6(b) where the bold lines now represent the u and v axes. az ii) Use...
(c) Let F be the vector field on R given by F(x, y, z) = (2x +3y, z, 3y + z). (i) Calculate the divergence of F and the curl of F (ii) Let V be the region in IR enclosed by the plane I +2y +z S denote the closed surface that is the boundary of this region V. Sketch a picture of V and S. Then, using the Divergence Theorem, or otherwise, calculate 3 and the XY, YZ...
Let z equals f left parenthesis x comma y right parenthesis commaz=f(x,y) , where x equals u squared plus v squared and y equals StartFraction u Over v EndFractionx=u2+v2 and y=uv. Find StartFraction partial derivative z Over partial derivative u EndFraction and StartFraction partial derivative z Over partial derivative v EndFraction∂z∂u and ∂z∂v at left parenthesis u comma v right parenthesis equals left parenthesis negative 6 comma negative 6 right parenthesis(u,v)=(−6,−6) , given that : f Subscript x Baseline left parenthesis negative 6 comma...