Calc 1, Lec 10A: Applications of Rational Functions, Limit Definition, Continuity, Discontinuities

(0:00) Exam 1 soon.
(1:14) Inversely proportional quantities (a common situation where rational functions arise).
(5:21) Yield rate of a two coupon bond (can be thought of as the root of a rational function related to equating present values of inflow and outflow).
(13:17) Intuitive description and precise definition of the limit of a function, with pictures and Mathematica Manipulate visual. It's necessary because of difficulties that arose from Fourier series (very important in modern applied mathematics, especially signal processing).
(21:48) Continuity of a function at a point and over a set.
(24:06) Ways a function can fail to be continuous, including a wild example with infinitely many oscillations over any tiny open interval containing zero.
(29:52) Example where a discontinuity can be "fixed" by choosing a parameter value appropriately (set the left- and right-hand limits equal to each other and solve for the parameter).