Question

Find ∂z/∂y at (1, ln2, ln3) if xe^y+ye^z+2 ln〖y-ln〖3=0〗 〗

Answer #1

find the solution of the first order differential equation
(e^x+y + ye^y)dx +(xe^y - 1)dy =0 with initial value y(0)= -1

Evaluate the iterated integral.
∫ln4 0 ∫ln3 0 ∫ln2 0 e^(0.5x+y−z) dzdydx

find the volume of the solid under the surface z =
2xex + yey that projects onto the region
D={0≤x≤ln2,0≤y≤ln3}
a. 11(ln2)(ln3)−ln32411(ln2)(ln3)−ln324
b. 7(ln2)(ln3)−ln367(ln2)(ln3)−ln36
c. 8(ln2ln3)−ln558(ln2ln3)−ln55
d. 9(ln2)(ln3)−ln1089(ln2)(ln3)−ln108
e. None of these.
f. 10(ln2ln3)−ln545

F(x, y, z) =< 3xy^2 , xe^z , z^3 >, S is the solid bounded
by the cylinder y2 + z2 = 1 and the planes x
= −1 and x = 2 Find he surface area using surface integrals. DO NOT
USE Divergence Theorem. Answer: 9π/2

The jpdf of X and Y is
?(1/8)xe−(x+y)/2 if x > 0 and y > 0,
0 elsewhere.
Find E(Y/X).

F(x, y, z) = xye^zˆi + xy^2 z^3ˆj − ye^zˆk,S is the surface of
the box bounded by the coordinate planes and the planes x = 3, y =
2, and z = 1. Find the surface area using surface integrals. DO NOT
use divergence theorem.

f(x, y, z) =
xe4yz, P(1, 0, 3),
u = <2/3, -1/3, 2/3>
(a) Find the gradient of f.
∇f(x, y, z) =
< , , >
(b) Evaluate the gradient at the point P.
∇f(1, 0, 3) = < , ,
>
(c) Find the rate of change of f at P in the
direction of the vector u.
Duf(1, 0, 3) =

1. [20 pts.] Solve (t +1)e^t + (ye^y −te^t )y' 0 = 0

Consider the following. f(x, y, z) = xe5yz, P(1, 0, 2),
u=1/3,-2/3,2/3. (a) Find the gradient of f. ∇f(x, y, z) = (b)
Evaluate the gradient at the point P. ∇f(1, 0, 2) = (c) Find the
rate of change of f at P in the direction of the vector u. Duf(1,
0, 2) =

solve by separation variable
3, xydx-(1+x^2) dy=0
4, xy'+y=y^2
5,yy'=xe^2+y^2
6, xsiny.y'=cosy
7, y'=x^2 y/1+x^3 xsiny.y'+cosy

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