Functions Contents - E
      Sequences and limits
      Infinite sequences
         Sequences notation - the rule for the n-th term of a sequence
         Graphing the terms of a sequence on the number line
      The limit of a sequence
         The definition of the limit of a sequence
         Convergence of a sequence
         Verifying the convergence of a sequence from the definition, examples
      The limit of a sequence theorems
      The cluster point or accumulation point
      Divergent sequences
      Sufficient condition for convergence of a sequence
         The Cauchy criterion (general principle of convergence)
      Some important limits
      Operations with limits
         Operations with limits examples
      Series
      Infinite series
         The sequence of partial sums
         The sum of the series
         Convergence of infinite series
         Divergence of infinite series
         Convergent and divergent series examples
      Harmonic series
      The remainder or tail of the series
         Necessary and sufficient condition for the convergence of a series
         Necessary condition for the convergence of a series
         The n-th term test for divergence
      Properties of series
         The product of two series or the Cauchy product
      Geometric series
      P-series
      Alternating series
         Alternating series test or Leibnitz's alternating series test
         Absolute convergence
         Conditional convergence
      Series of positive terms
      Power series
      Power series or polynomial with infinitely many terms
         The sum of a power series is a function
      Maclaurin and Taylor series
         Representing polynomial using Maclaurin's and Taylor's formula
         Representing polynomial using Maclaurin's and Taylor's formula examples
      The power series expansion of the exponential function
         Properties of the power series expansion of the exponential function
         The radius of convergence or the interval of convergence
      The limit of a function
      The limit of a function
         The definition of the limit of a function
         A limit on the left (a left-hand limit) and a limit on the right (a right-hand limit)
         Continuous function
         Limits at infinity (or limits of functions as x approaches positive or negative infinity)
         Infinite limits
         The limit of a function examples
         Vertical, horizontal and slant (or oblique) asymptotes
         Monotone functions - increasing or decreasing in value
      Limit of a function properties (theorems or laws)
         Squeeze rule
         Composition rule
         Limits of functions properties use examples
      Limits of rational functions
         Evaluating the limit of a rational function at infinity
         Evaluating the limit of a rational function at a point
         The limit of a rational function that is defined at the given point
         The limit of a rational function that is not defined at the given point
         The limit of a rational function at infinity containing roots (irrational expressions)
         The limit of a rational function at a point containing irrational expressions, use of substitution
         Evaluating the limit of a rational function containing irrational expressions using rationalization
      Limits of trigonometric functions
         Evaluating trigonometric limits examples
      Limits of functions based on the definition of the natural number e
         Evaluating limits of functions based on the definition of the natural number e
         Use of the composition rule to evaluate limits of functions
       Properties of continuous functions
      Continuous function definition
         Intermediate value theorem - Bolzano's theorem
         Existence of roots
         Extreme value theorem
         Monotone function
   
 
 
 
   
   
 
   
   
 
 
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