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
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