(b) Use part (a) to solve the DE x32"-8xZ'+8Z = 0 , (x> 0) Question 4....
Problem 3 Use series expansion to find the slope of the following function at 0. f(x) = V2 + x - V2 - x Problem 5 Solve the equation in the complex space: z-i|z| = Re{z} and represent the solution in the complex plane. Problem 6 What is the locus of points that satisfy the following equation in the complex plane Re[7z - 8z* – 31m{z} + z2 + zz*] = 0
By show it means prove not solve for the if again Thank you! (a) Show that eis an integrating factor for the DE (b) Show that a general solution y y(z) of the DE (1) is given implicitly by the equation F(x, y) c where c is a constant and where F(x, y) = e-r2(y2(z"y + 2)-1 ) (a) Show that eis an integrating factor for the DE (b) Show that a general solution y y(z) of the DE (1)...
Find the volume of the following regions bounded by the planes: a). 3x+8y+8z=9, 3x+8y+8z=9, y=x, x=0, z=0. b). 5x+3y+5z=2, 5x+3y+5z=2, y=x, x=0, z=0.
Let S be the part of the sphere x^2 + y^2 + z^2 = 4 that lies between the cones z = √x^2 + y^2 and z = √3x^2 + 3y^2. (1) Let S be the part of the sphere x2 + y2 + Z2-4 that lies between the cones X +y and z a) Find a differentiable parametrization of S b) Find the area of S c) Find 22 dS. (1) Let S be the part of the sphere...
solve the system x-y+8z =-107 8) 6x +z=17 8) 3y-5に89 9),2-y2 = 39 x-y 3 9)
Consider the function T: K3 K3 defined by T(x, y, z) = (0, y,0). This kind of function is called a projection, since we are 'projecting' the vector (2, y, z) onto the y-axis. In this problem, you will prove that the function T is linear. In the first part, you will prove that T preserves addition. In the second part, you will prove that T preserves scalar multiplication. There is only one correct answer for each part, so be...
(b) The surface of the quarter sphere 2+y2+z2=4, y >0, z 2 0, is made of a thin metal with density p (x+y). py S Plx, y, z) ds. Calculate its mass (b) The surface of the quarter sphere 2+y2+z2=4, y >0, z 2 0, is made of a thin metal with density p (x+y). py S Plx, y, z) ds. Calculate its mass
You are given the following multivariate PDF (z, y, z) ES else fxx,z(x, y, z) = ) 0 where S-((x, y, z) | x2 + y2 + z2-1) (a) (5 points) Let T be the set of all points that lie inside the largest cylinder by volume that can be inscribed in the region of S. Similarly let U be the set of all points that lie inside the largest cube that can be inscribed in the region of s....
Very very urgent !!! need a detailed explanation of solving this problem. we need to solve using the formula like integral of f(x,y) . r_x* r_y. Let F(z, y, z)-z tan 1 (уг) i + z3ln(z2 + 9) j + z k. Find the flux of F across the part of the paraboloid z2 + y2 + z = 4 that lies above the plane z = 3 and is oriented upward. Let F(z, y, z)-z tan 1 (уг) i...
7. Use Green's Theorem to find Jc F.nds, where C is the boundary of the region bounded by y = 4-x2 and y = 0, oriented counter-clockwise and F(x,y) = (y,-3z). what about if F(r, y) (2,3)? x2 + y2 that lies inside x2 + y2-1. Find the surface area of this 8. Consider the part of z surface. 9. Use Green's Theorem to find Find J F Tds, where F(x, y) (ry,e"), and C consists of the line segment...