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| MATHEMATICS Formulas, Graphs,
Tables, . . . < High School to University Level > |
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CONTENTS I
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81
Limits of trigonometric functions
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Evaluating
trigonometric
limits examples
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Evaluating
limits of functions
based on the definition of the natural number e
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Use of the composition
rule to evaluate limits of functions
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Use of the composition
rule to evaluate limits of functions
examples
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82
Series
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Infinite series
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The
sequence of partial
sums
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The
sum of the series
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Convergence
of infinite series
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Divergence
of infinite series
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Convergent
and divergent series
examples
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Harmonic
series
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83
The remainder
or tail
of the series
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Necessary
and sufficient
condition for the convergence of a series - Cauchy's convergence test
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Necessary
condition for the convergence of a series
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The
nth
term test for divergence
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Properties
of series
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The
product of two series or the Cauchy product
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84
Geometric
series
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Geometric
series examples
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P-series
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Alternating
series
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Alternating series test
or Leibnitz's
alternating series test
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85
Absolute convergence
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Conditional
convergence
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Series
of positive terms
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Tests
for convergence
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Comparison
test
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86
The
limit
comparison test
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The
ratio test
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Tests
for convergence examples
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Root
test or Cauchy's root test
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Root
test or Cauchy's root test examples
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87
Power
series
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Power
series or polynomial with infinitely many terms
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The
sum of a power series is a function
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Maclaurin and Taylor series
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Representing
polynomial using Maclaurin's and Taylor's formula
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88
The power series expansion of the exponential function
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Properties
of the power series expansion of the exponential function
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The radius of convergence or the interval of
convergence
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89
The power series expansion of the logarithmic function
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Properties
of the power series expansion of the logarithmic function
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The
binomial series
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The binomial
series expansions to the power series
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The binomial
series expansion to the power series example
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90
Differential calculus
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Properties
of continuous functions
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Continuous
function definition
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Intermediate value theorem - Bolzano's theorem
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Existence of roots
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Extreme value theorem
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Monotone function
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The
derivative of a function
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Definition of the derivative of a function
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