Suppose f(x,y)=sqrt(tan(x)+y) and u is the unit vector in the
direction of 〈2,−1〉. Then,
(a) ∇f(x,y)=∇f(x,y)=...
Suppose f(x,y)=sqrt(tan(x)+y) and u is the unit vector in the
direction of 〈2,−1〉. Then,
(a) ∇f(x,y)=∇f(x,y)=
(b) ∇f(0.4,9)=∇f(0.4,9)=
(c) fu(0.4,9)=Duf(0.4,9)=
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 .
A. Find unit vector u1 perpendicular to u. Find unit vector w1
in the direction of...
A. Find unit vector u1 perpendicular to u. Find unit vector w1
in the direction of w. u=(1,1), w=(-2,3)
B. Describe the set span {(1,0,0),(1,1,0),(1,1,1)}
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)
Consider the following. f(x, y, z) = xe5yz, P(1, 0, 2),
u=1/3,-2/3,2/3. (a) Find the gradient...
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) =