MATH 31A Lecture Notes - Lecture 1: Massu Engira Masilamani
Document Summary
The word calculus: latin for pebbles/small stones that people use for counting. Credit to: newton, leibniz (d/dx), greeks, china, india, middle east, etc. Area of a circle: *r2 = 0. 5* *circumference. A hexagon inscribed in a circle, there are many spare areas outside. Keep making more sides to the polygon, and the spare space gets smaller. Divide the polygon into triangles: as n become large, the height of the triangles become the radius of the circle. Z(cid:28664)no"s p(cid:28660)r(cid:28660)(cid:28663)ox: t(cid:28667)(cid:28664) turtl(cid:28664) (cid:28668)s (cid:28660)(cid:28663)(cid:28663)(cid:28668)n(cid:28666) sm(cid:28660)ll (cid:28661)ut (cid:28668)n(cid:28665)(cid:28668)n(cid:28668)t(cid:28664) num(cid:28661)(cid:28664)rs, so achilles can never outrun the turtle. Here, we need to calculate the limit to solve this problem. X approaches a, what happens to f(x)? a limit is a prediction. A jump disconnection: the left/right limit may not equal to the real value of f(x). When the left limit=right limit and that they both exist, the limit exists.
