Math Video | Calculus Lesson | Differential Calculus 433

Author

centerofmath

Title

2: Limits and Continuity

Video Description

After you understand what it means to write limx→b f(x) = L, then you should understand one main point: essentially every function f(x) that you have ever seen, which was not explicitly defined in cases or pieces, is a continuous function, which means that, if b is in the domain of f, then limx→b f(x) simply equals f(b), i.e., to calculate the limit, you simply plug in x = b. (Here, we have assumed that an open interval around b is contained in the domain of f; the preceding statement needs to be modified a bit otherwise.) What do we mean by “essentially every function f(x) that you have ever seen”? We mean any elementary function: a function which is a constant function, a power function (with an arbitrary real exponent), a polynomial function, an exponential function, a logarithmic function, a trigonometric function, or inverse trigonometric function, or any finite combination of such functions using addition, subtraction, multiplication, division, or composition.

Video Keywords

Differential Calculus, Center of Math, David B. Massey, Calc 1, Limits and Continuity, Single-Variable Calculus

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