1. Statistics b: Identities involving averages

    03:43

    from David Liao Added 14 0 0

    The average of a sum is the sum of the averages. The average of a constant multiplied against a function is the constant multiplied by the average of the function. The average of a constant is the…

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    • Statistics c: Dispersion and variance

      05:33

      from David Liao Added 13 0 0

      The variance of a function is the average of the square of the function. For the purposes of theoretic calculations, it might be useful to express the variance using the "inside-out" computation…

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      • Limits f: Outline of epsilon-delta proof of a limit of a linear function

        07:00

        from David Liao Added 65 0 0

        In this video, the outline for using the epsilon-delta definition to prove that the limit of a function has a particular value y = L at x = a has two main parts. First, we determine what range of…

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        • Limits e: Limits do not always exist

          02:40

          from David Liao Added 22 0 0

          An example of a situation in which a function can fail to have a limit at a value of x = a is when the function jumps discontinuously in height at that value of x. One example of a situation in which…

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          • Limits d: Infinite limits "at" infinity

            03:32

            from David Liao Added 20 0 0

            When we say that a function has an infinite limit "at" infinity, we mean that as x becomes arbitrarily large, the function becomes arbitrarily large.

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            • Limits c: Limits "at" infinity"

              03:30

              from David Liao Added 21 0 0

              When we say that a function has a limit of L "at" infinity, we mean that as x becomes arbitrarily large, the function becomes arbitrarily close to L.

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              • Limits b: Improper (infinite) limits

                03:58

                from David Liao Added 19 0 0

                When we say that the limit of a function at a value of x = a is infinity, we mean that as x becomes arbitrarily close to a, the value of the function becomes arbitrarily large.

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                • The Theorem of the Mean Policeman (1966)

                  13:38

                  from Eric Cornwell Added 2,298 2 0

                  One of several films produced by Bruce and Katharine Cornwell for the Mathematical Association of America in the mid-1960s addressing topics in calculus. This film explores the mean value, and Rolle's…

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                  • A Function is a Mapping (1965)

                    09:58

                    from Eric Cornwell Added 177 1 0

                    One of several films produced by Bruce and Katharine Cornwell for the Mathematical Association of America in the mid-1960s addressing topics in calculus. This film explores the concept of limits.…

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