Question

Let f(x,y) = xe^sin(x^2y+xy^2) /(x^2 + x^2y^2 + y^4)^3 . Compute ∂f ∂x (√2,0) pointwise.

Answer #1

let
f(x,y) = xe^(xy)
Find the directional derivative of f at point (2,0) in the
direction of vector <-6,8>. Find the maximum rate of change
of f at point (2,0) and the direction in which it occurs.

Let f (x, y) =
xe xy. Find the maximum rate
of change of f at the point (3, -2).

Let f (x, y) = 100 sin(π(x−2y))/(1+x^2+y^2) . Find the
directional derivative of f 1+x^2+y^2 at the point (10, 6) in the
direction of: (a) u = 3 i − 2 j (b) v = −i + 4 j

Let F be the defined by the function F(x, y) = 3 + xy - x - 2y,
with (x, y) in the segment L of vertices A (5,0) and B (1,4). Find
the absolute maximums and minimums.

Let f(x, y) = x tan(xy^2) + ln(2y). Find the equation of the
tangent plane at (π, 1⁄2).

Find fxx, fxy, fyy when f(x, y) = xe^(x^2−xy+y^2)

Let F (x, y) =
2xyi + (x –
2y)j, r (t) =
sin ti – 2 cos t
j, 0 ≤ t ≤ π. Then C
F•dr is

Let (1，1) be the initial approximation of a solution of
(x + y) sin(xy) = 1
(x - y) cos(x^2y) = 1:
Use the Newton's method to find, and report, the next two
approximations of the
solution.

Let f(x, y) = sqrt( x^2 − y − 4) ln(xy).
• Plot the domain of f(x, y) on the xy-plane.
• Find the equation for the tangent plane to the surface at the
point (4, 1/4 , 0).
Give full explanation of your work

1. for 0<= x <=3 0<=x<=1 f(x,y) = k(x^2y+ xy^2)
a. Find K joint probablity density function.
b. Find marginal distribution respect to x
c. Find the marginal distribution respect to y
d. compute E(x) and E(y) e. compute E(xy)
f. Find the covariance and interpret the result.

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