Given the following vector force field, F, is
conservative:
F(x,y)=(2x2y4+x)i+(2x4y3+y)j,
determine the work done subject to the force while traveling along
any piecewise smooth curve from (-2,1) to (-1,0)
Find the work done by the force field F in moving a
particle through the path C. That is, find Where
C is the compound path given by r(t)=<t,0,t> from (0,0,0) to
(2,0,2) followed by r(t)=<2,t,2> from (2,0,2) to
(2,2,2)
Let
f(x,y) = 3x^2 + 6xy
a) find the rate of change of f at the point P(3,2) in the
direction of u = [3,4]
b) In what direction does f have the maximum rate of change?
what is the maximum rate of change?
Suppose that F= -xyI
-yzJ-xzK. Find
the work done by this vector field on an object moving once
counterclockwise (when viewed from above) around the path from
(2,3,1) to (-4,6,2) to (1,-3,8) and back to (2,3,1). Solve using
Stokes' theorem.
Clearly label all work, do not crowd work together f(x) =
3x−3x^3. For f(x), find (a) Domain: (b) Intercepts (if possible) (c)
End behavior (d) Any vertical or horizontal asymptotes (e)
Intervals of increasing/decreasing and Relative max/min and (f)
Intervals of concavity and Points of inflection (g) Use all of the
above to create a detailed graph of the function
Given:
f(x,y) = 5 - 3x - y for 0 < x,y < 1 and x + y < 1, 0
otherwise
1) find the covariance of x and y
2) find the marginal probability density function for x
c) find the probability that x >= 0.6 given that y <=
0.2
Consider the function y = f(x) = 2x3 − 3x2 − 9x − 2.
(a) [2] Specify the (open) intervals on which f(x) is increasing,
and the intervals on which f(x) is decreasing.
(b) [2] Specify all local maxima and local minima, giving both
x-coordinates and y-coordinates for them.
(c) [2] Specify the intervals on which f(x) is concave up and on
which f(x) is concave down.
(d) [2] List the inflection point(s).
(e) [2] Sketch a graph of y...