Calculus I
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Formula for Average Velocity

The slopes of the _______ line is the ______ of the slopes of the secant lines.

The slope of the tangent equals _______________
instantaneous velocity

if and only if _________ and __________

The line x=a is called a vertical symptote of the curve y = f(x) if at least one of the following is true: (6)



 c
 The limit of a constant is the constant


=
where n is a positive integer
if n is even, we assume that a > 0.

where n is a positive integer
if n is even, we assume that

If a polynomial or a rational function and a is in the domain of f, then

If
for all
x in an open interval that conatins a (except possibly at a) and the limits of
f and
g both exist as
x approaches
a, then

Squeeze theorem:
If
for all x in an open interval that contains a (except possibly at a) and
THEN:

Let
f be a function on some open interval that contains the number
a, except possibly at
a itself.
if for every number
> 0 there is a corresponding number
> 0 such that:
f(x)  L <
whenever 0 <  x  a <

Definition of LeftHand Limit
if for every number
> 0 there is a corresponding number
> 0 such that:
f(x)L <
whenever
< x < a

Definition of RightHand limit
if for every number
> 0 there is a corresponding number
> 0 such that:
f(x)  L <
whenever a < x < a +

When a limit = 1/0 it is:
undefined

When a limit = 0/0 it is
Indeterminate