Question

Find the urge of the function f over the given region. F(x,y) = 3x+7y over the triangle (0,0) (6,0) and (0,10)

Answer #1

Integrate the function f over the given region
f(x,y) =xy over the triangular region with vertices (0,0) (6,0)
and(0,9)

Consider the vector field →F=〈3x+7y,7x+5y〉F→=〈3x+7y,7x+5y〉
Is this vector field Conservative? yes or no
If so:
Find a function ff so that →F=∇fF→=∇f
f(x,y) =_____ + K
Use your answer to evaluate ∫C→F⋅d→r∫CF→⋅dr→ along the curve C:
→r(t)=t2→i+t3→j, 0≤t≤3r→(t)=t2i→+t3j→, 0≤t≤3

Find the absolute maximum, and minimum values of the function:
f(x, y) = x + y − xy Defined over the closed rectangular region D
with vertices (0,0), (4,0), (4,2), and (0,2)

Find the absolute min and max values of the function
f(x, y) =x + y− x^2y on the closed triangular region with
vertices (0,0), (3,0), and (0,3).

Find the absolute minimum and absolute maximum of
f(x,y)=10−3x+8y
on the closed triangular region with vertices (0,0),(8,0) and
(8,12).
List the minimum/maximum values as well as the point(s) at which
they occur. If a min or max occurs at multiple points separate the
points with commas.

Let X and Y have a joint density function given by f(x; y) = 3x;
0 <= y <= x <= 1
(a) Find P(X<2Y).
(b) Find cov(X,Y).
(c) Find P(X < 1/2 |Y = 1/3).
(d) Find P(X = 1/2|Y = 1/3).
(e) Find P(X > 1/2|Y > 1/3).
(f) Find the conditional expectation E(X|Y = y).

The real part of a f (z) complex function is given as
(x,y)=y^3-3x^2y. Show the harmonic function u(x,y) and find the
expressions v(x,y) and f(z). Calculate f'(1+2i) and write x+iy
algebraically.

Use Lagrange Multiplers to find the minimum of the function
subject to the given constraint(s).
f(x,y,z,t)=7x+7y+7z+7t,
7(x2+y2+z2+t2)=8

. (X,Y ) is uniformly distributed over the triangle with
vertices (0,0),(2,0),(0,1). Find the density f(z) of X −Y for z ≤
0.

The average value of a function f(x, y, z) over a solid region E
is defined to be fave = 1 V(E) E f(x, y, z) dV where V(E) is the
volume of E. For instance, if ρ is a density function, then ρave is
the average density of E. Find the average value of the function
f(x, y, z) = 5x2z + 5y2z over the region enclosed by the paraboloid
z = 4 − x2 − y2 and the...

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