Math 1210-5: TEST 3
Name:
This exam is closed books and notes, no electronic devices. Please turn off your cell phones!
Write clearly, explain what you are doing, and show all work. All problems have equal
weight. Good luck!
1. Find the indicated integrals.
a.
b.
Z π/2
0
cos3 x sin x dx
Z 1
q
0
x
(x2 + 4)
dx
2. Find the area of the rectangle with maximum perimeter that can be inscribed in a circle
of a radius r.
3. Solve the differential equation subject to the indicated condition
dy
= y 2 cos(x),
dx
y=1
at
x = 0.
4. Find where the function f is increasing and where it is decreasing, where it is concave up
and where it is concave down. Find the inflection point. Find where the function reaches
local minimum and maximum values. Sketch the graph.
f (x) = x2 (x − 1)
5. Find G0 for each function G.
(a). G(x) =
(b). G(x) =
Z x 2
t −1
1
Z x2
x
t
dt
sin(z) cos(z)dz