Let U1, U2, . . . , Un be independent U(0, 1) random
variables.
(a) Find...
Let U1, U2, . . . , Un be independent U(0, 1) random
variables.
(a) Find the marginal CDFs and then the marginal PDFs of X =
min(U1, U2, . . . , Un) and Y = max(U1, U2, . . . , Un).
(b) Find the joint PDF of X and Y .
Find a unit normal vector for the following function at the
point P(−1,3,−10): f(x,y)=ln(−x/(−3y−z))
Find a unit normal vector for the following function at the
point P(−1,3,−10): f(x,y)=ln(−x/(−3y−z))
Consider the vector u1=(2,0,2), u2=(4,1,-1), u3=( 0,1,-5),
u4=(3,0,2)
a) Find the dimension and a basis for...
Consider the vector u1=(2,0,2), u2=(4,1,-1), u3=( 0,1,-5),
u4=(3,0,2)
a) Find the dimension and a basis for U= span{ u1,u2,u3,u4}
b) Does the vector u=(2,-1,4) belong to U. Justify!
c) Is it true that U = span{ u1,u2,u3} justify the answer!
f(x, y, z) =
xe4yz, P(1, 0, 3),
u = <2/3, -1/3, 2/3>
(a) Find the...
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) =
Consider the function f(x, y) = sin(2x − 2y) (a) Solve and find
the gradient of...
Consider the function f(x, y) = sin(2x − 2y) (a) Solve and find
the gradient of the function.
(b) Find the directional derivative of the function at the point
P(π/2,π/6) in the direction of the vector
v = <sqrt(3), −1>
(c) Compute the unit vector in the direction of the steepest
ascent at A (π/2,π/2)
Let f(x, y) =sqrt(1−xy) and consider the surface S defined by
z=f(x, y).
find a vector...
Let f(x, y) =sqrt(1−xy) and consider the surface S defined by
z=f(x, y).
find a vector normal to S at (1,-3)
For f(x,y,z) = sqrt(35-x^2-4y^2-2z) 1. Find the gradient of
f(x,y,z) 2. Evaluate delta f(x,y,z) 3. Find...
For f(x,y,z) = sqrt(35-x^2-4y^2-2z) 1. Find the gradient of
f(x,y,z) 2. Evaluate delta f(x,y,z) 3. Find the unit vectors U+ and
U- , that give the direction of steepest ascent and the steepest
descent respectively.