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Formula for Average Velocity
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The slopes of the _______ line is the ______ of the slopes of the secant lines.
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The slope of the tangent equals _______________
instantaneous velocity
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if and only if _________ and __________
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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)
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Limit Laws
Suppose that c is a constant and the limits
and
exist, Then:
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- c
- The limit of a constant is the constant
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=
where n is a positive integer
if n is even, we assume that a > 0.
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where n is a positive integer
if n is even, we assume that
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If a polynomial or a rational function and a is in the domain of f, then
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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
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Squeeze theorem:
If for all x in an open interval that contains a (except possibly at a) and
THEN:
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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| <
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Definition of Left-Hand Limit
if for every number > 0 there is a corresponding number > 0 such that:
|f(x)-L| < whenever < x < a
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Definition of Right-Hand limit
if for every number > 0 there is a corresponding number > 0 such that:
|f(x) - L| < whenever a < x < a +
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When a limit = 1/0 it is:
undefined
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When a limit = 0/0 it is
Indeterminate
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