Let f ( x , y ) = x^ 2 + y ^3 + sin ( x ^2 + y ^3 ). Determine
the line integral of f ( x , y ) with respect to arc length over
the unit circle centered at the origin (0, 0).
Write as a MatLab script
For X=-2π~2π with intervals of π/100.
a. Plot Y1=sin(X) as a red line. Add a grid. b. Plot Y2=cos(X) as a
black dotted line. Add a grid. c. Plot Y1 and Y2 in the same plot
without using the hold on/off command. d. For Y3= Y1 times Y2, plot
Y1, Y2 and Y3 in the same graph. Y3 will be green line. Add title,
axis label and a legend.
part 1)
Let f(x) = x^4 − 2x^2 + 3. Find the intervals of concavity of f
and determine its inflection point(s).
part 2)
Find the absolute extrema of f(x) = x^4 + 4x^3 − 8x^2 + 3 on
[−1, 2].
Consider the function f(x, y) = 4xy − 2x 4 − y
2 .
(a) Find the critical points of f.
(b) Use the second partials test to classify the critical
points.
(c) Show that f does not have a global minimum.
f(x,y) = 2/7(2x + 5y) for 0 < x < 1, 0 < y < 1
given X is the number of students who get an A on test 1
given Y is the number of students who get an A on test 2
find the probability that more then 90% students got an A test 2
given that 85 % got an A on test 1