Show that if z = xy, then gz ≈ gx +gy, and if z = x/y, then gz ≈ gx −gy. Apply these rules to equation in the lecture: M/P = kY. M/P = k(i)Y = k(¯ i)Y = kY
If you turn on a gradient value of G=(Gx,Gy,Gz) in a main magnetic field strength of B0 what is the frequency of the precession of spins at location r=(x,y,z)? Do not use dot product notation. freq(x,y,z) = ??
nd gy be m x 1 vectors. Show that A 42 Let z and y be m x y is diagonalizable f and only
Consider the following function 6 f(x, y,z)=z - x? cos(my) + xy? (i) Find the gradient of the function f(x, y, z) at the point P,(2,-1,-7). (ii) Find the directional derivative of f(x, y, z) at P,(2,-1,-7) along the direction of the vector ū = 2î+j+2k. (iii) Find the equation of the tangent plane to the surface given below at the point P,(2,-1, -7). 6 :- xcos(ty) + = 0 xy
Find the directional derivative of f at p in the direction of a. f(x,y,z)=xy+z^2; P(2,-2,2);A=i+j+k
Consider differential equation (x - 1)y" – xy' + y = 0. a). Show that yi = el is a solution of this equation. Use the method of reduction of order to find second linearly independent solution y2 of this equation. (2P.) b). Find solution of the initial value problem (1P.) y(1) = 0, y'(1) = 1. c). Find solution of the initial value problem (1P.) y(1) = 0, y'(1) = 0. d). Does your answer in b) and c)...
i need to show that Z forms a ring under new addition x+y=(x+y+1) and new multiplication x*y=x+y+xy
i need to show that Z forms a ring under new addition x+y=(x+y+1) and new multiplication x*y=x+y+xy and thanx
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)...
Var(Y) =y Var(X)=x Cov(X,Y) =z What is Cov(XY,XY)
Let F(x, y, z) = (yza, x, xy +z) and answer the following questions. Show all work for each part. Q4.3 5 Points Let the surface Si be the part of the unit sphere which sits above the xy-plane. Use Stokes' Theorem to find SSs, curl(F).dS. Please select file(s) Select file(s)