Staff, Lewisedd,A, Scott collins, fraboni, Boguszak, ROBERTACASPER, MicheleAnderson, Daniel Mark Rosser, Charles Zhang, Theresa Riel, MARY MINKE, Jorge Guarin
Exam I(Practice)
Math 231
Spring 2015
Charles Z.
Name_
Show work to get partial credit, and show enough work to get full credit!
1. Find each of the following integrals:
(a) sin 4 x cos 2 xdx
(b) sin
8/28/2017
3
Energy and
1st Law of Thermodynamics
Objective:
1. Discuss energy
2. Develop equations for applying the principle
of conservation of energy in closed systems.
1
3
Energy and
1st Law of The
Derivative Rules
Constant Rule
Sum and Difference Rule
Product Rule
Quotient Rule
Chain Rule
d
[cf ( x)] cf '( x)
dx
d
[ f ( x ) g ( x )] f '( x ) g '( x)
dx
d
[ f ( x) g ( x)] f '( x) g ( x) f ( x) g
Integration Rules
Constant Rule
kf ( x)dx k f ( x)dx
Sum and Difference Rule
kdx kx c
e dx e
x
x
1
x
n
x dx
c
a dx ln a a
[ f ( x) g ( x)]dx f ( x)dx g ( x)dx
e
x
c
ax
dx
x n 1
c
n 1
1 ax
e c
A triangular plate with height 6 ft and a base of 3 it is submerged vertically in water so that the top is 3 it below the
surface. Express the hydrostatic: force against ene side of the plate as an in
Final(Practice)
Math 231
Charles Z.
Spring 2015
Name_
(Show work to get partial credit, and show enough work to get full credit!)
1. Find
5
( x 1)( x
2
9)
2. Find 25 x 2 dx
dx
(Use Partial fractions
Exam III(Practice)
Math 231
Spring 2014
Charles Z.
Name_
Show work to get partial credit, and show enough work to get full credit!
1. Verify that y = -2 sin5x + 7 cos5x is the solution to the differen
Exam II(Practice)
Math 231 Spring 2015
Charles Z.
Name_
Show work to get partial credit, and show enough work to get full credit!
1. What to do first for each of the following integrals?
1
earctan x
(
Exam IV(Practice)
Math 231
Spring 2015
Charles Z.
Name_
Show work to get partial credit, and show enough work to get full credit!
a
1. Let cfw_an be a positive sequence such that n 2 .
an 1
Select am