Question

Let ?(?, ?, ?) = 2???? + (? 3 + ? 3 )? − 3? 2? ?,

(?) Find div ? at (1, 2, −1).

(?) Find curl ?. Is ? irrotational?

Answer #1

A)
Consider the vector field F(x,y,z)=(9yz,−8xz,8xy).
Find the divergence and curl of F.
div(F)=∇⋅F= ?
curl(F)=∇×F=( ? , ? , ?)
B)
Consider the vector field
F(x,y,z)=(−4x2,0,3(x+y+z)2).
Find the divergence and curl of F.
div(F)=∇⋅F= ?
curl(F)=∇×F=( ? , ? , ?).

17
Find curl F
A) F=z^2xi+y^2zj-z^2yk
B) given vector field F= (x+xz^2)I +xyj +yzk, Find div and curl
of F.

Let M = ( (−3 1 3 4), (1 2 −1 −2), (−3 8 4 2))
14. (3 points) Let B1 be the basis for M you found by row
reducing M and let B2 be the basis for M you found by row reducing
M Transpose . Find the change of coordinate matrix from B2 to
B1.

for
0(x,y,z) = (x^2 y^2 z^2) / 2. calculate div(grad 0) and curl(grad
0) pretend the zero is a fata symbol

1. Let ?(?)=8(sin(?))? find f′(2).
2. Let ?(?)=3?sin−1(?) find f′(x) and f'(0.6).

Let P be the point (2, 3, -2). Suppose that the point P0(-3, -2,
7) is 1/4 of the way from P to Q. Find the point Q.

Let u = (−3, 2, 1, 0), v = (4, 7, −3, 2), w = (5, −2, 8, 1).
Find the vector x that satisfies 2u − ||v||v = 3(w − 2x).

Consider the vector field.
F(x, y, z) =
7ex sin(y), 7ey sin(z), 8ez sin(x)
(a) Find the curl of the vector field.
curl F =
(b) Find the divergence of the vector field.
div F =

Let X = {1, 2, 3, 4} and Y = {2, 3, 4, 5}. Define f : X → Y by
1, 2, 3, 4 → 4, 2, 5, 3. Check that f is one to one and onto and
find the inverse function f -1.

3. Let ?1, ?2, ?3 be 3 independent random variables with
standard normal distribution. Find the conditional probability

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