3.7 Optimization
Monday, January 4, 2016
7:20 AM
Procedure:
1. Understand the problem
a. What is the unknown? What are the given quantities?
2. Draw a diagram
3. Notation: Assign a symbol to the quantity that is to be maximized or minimized. Then ass
var
Math 1552(1-4) Spring 2011 Final Exam
Answer any 10 questions.
1. Use integration by parts to evaluate the following integrals
(a)
!
x cos 5xdx
!
(b)
(2x + 1)e3x dx.
2. (a) Use a suitable trigonometric substitution to evaluate the integral
(b) Evaluate th
Math 1552 (11-15) Final Exam Fall 2012
Answer any 10 questions. In order to earn partial credit, please show all of your
work.
1. (a) Use integration by parts to evaluate the integral
!
(b) Evaluate the integral
!
x2 lnxdx.
cos2 x sin3 xdx
2. (a) Use a su
Math 1552(5-8) Final Exam Fall 2011
Answer any 10 questions. In order to earn partial credit, please show all of your
work.
1. (a) Use integration by parts to evaluate the integral
!
xe2x dx
!
cos3 x
dx
sin x
.
(b) Evaluate the integral
2. (a) Use a suita
2MATH 1550,
REVIEW for FINAL
1. Evaluate each limit. You may use LHospitals rule where applicable. If the limit does
not exist, justify your answer.
(a)
sin x x
x 0
x3
lim
(b)
lim x ln x
x 0
2 Find all values of k so that the following function is contin
Calculus Cheat Sheet
Limits
Definitions
Precise Definition : We say lim f ( x ) = L if
Limit at Infinity : We say lim f ( x ) = L if we
x a
x
for every > 0 there is a > 0 such that
whenever 0 < x a < then f ( x ) L < .
can make f ( x ) as close to L as w
Calculus Final
December 10, 2014
7:30 AM
Anything questions on test reviews/tests are fair game to study
Chapter Two
I.
Limits
Limits to infinity
One-sided limits
Infinite limits (vertical asymptotes, the limit of f(x) as xc equals +
or infinity, c=Ver
Related Rate-Word Problems
. Draw a diagram and label the quantities that don’t change with their respective values and quantities
that do change with respect to time as variables.
2. Mathematically specify the rate of change that you are looking for and
TEST1Review
2.1 2.3
LimitsandRateofChange
Findtheslopeofasecantline.
Findaveragerateofchangeoraveragevelocity)
f (x h) f (x)
Avg. Rate of change =
, over the interval [x,x +h]
h
Beabletofindaveragerateofchangeoveranintervaloraveragevelocityoveran
interva
Test 3 Review
3.10 Linear Approximations and Differentials. P255 #s 1-4,11-14,1518,19-22,23-28
4.1Extreme Value Thm: If is f(x) continuous on a closed interval [a,b] then
f(x) has both an absolute max and an absolute min.
How to find: The Absolute max and