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| MATHEMATICS Formulas, Graphs,
Tables, . . . < High School to University Level > |
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CONTENTS H
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71
Rational functions
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Basic
properties of rational functions
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Vertical,
horizontal and oblique or slant asymptotes
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The
graph of the reciprocal
function, equilateral or rectangular hyperbola
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Translation
of the reciprocal function, linear rational function
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Oblique or slant
asymptote
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The
graph of a rational function example
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72
Sequences
and limits
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Infinite
sequences
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Graphing the terms of a sequence
on the number line
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The limit of a sequence
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The definition of the limit of a
sequence
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Convergence of a sequence
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73
Verifying
the convergence of a sequence from the definition examples
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Properties of
convergent sequences
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Bounded
sequences
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74
Increasing, decreasing, monotonic
sequence
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Monotonic
sequence theorem
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Sandwich
theorem (result) or squeeze rule
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Least
upper bound (or supremum, abbrev. lub, sup) and greatest lower bound (or
infimum, abbrev. glb, inf)
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75
The
definition of the real number
e
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The
limit of
sequence
theorems
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The
cluster point or accumulation point
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Divergent
sequences
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76
Sufficient condition for convergence of a sequence
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The Cauchy criterion
or
general principle of
convergence
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The Cauchy criterion
or general principle of convergence example
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Some
important limits
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77
Operations
with limits
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Operations
with limits examples
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The
limit of a function
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The
definition of the limit of a function
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A
limit on the left (a left-hand limit) and a limit
on the right (a right-hand limit)
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78
Continuous
function
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Limits
at infinity (or limits of functions as x approaches
positive or negative infinity)
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Infinite limits
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The
limit of a function examples
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Vertical, horizontal
and slant (or oblique) asymptotes
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Vertical
asymptote
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Horizontal
asymptote
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Slant
or oblique asymptote
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Slant
or oblique asymptote example
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Monotone
functions - increasing or decreasing in value
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79
Limits of
functions
properties (theorems or laws)
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Limits of
functions
properties use examples
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Evaluating
the limit of a rational function at infinity
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Evaluating
the limit of a rational function at infinity examples
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80
Evaluating
the limit of a rational function at a point
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The limit of a rational function that is defined at the given point
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The limit of a rational function that is not defined at the
given point
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The limit of a rational function at infinity
containing roots (irrational expressions)
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The limit of a rational function at a point containing
irrational expressions, use of substitution
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Evaluating
the limit of a rational function
containing irrational expressions using rationalization
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