MATH 157 Study Guide - Final Guide: Wellington Koo, Periodic Function, Inflection Point

• School: Simon Fraser University
• Department: Mathematics
• Course: MATH 157
• Professor: Shiva Gol Tabaghi

Document Summary

Special limits: limit definition of continuity of a function. A function is continuous at a number a if. Note. a belongs to the domain of f . b) exist . c) If: f is defined on an open interval containing a, except perhaps at a, and, f is not continuous at a we say that f is discontinuous at a. Suppose that f is continuous on the closed interval. [a,b] and let n be any number between f(a) and f(b), where f(a) number c in (a,b) such that f(c)=n. f(b). Theorem: existence of zeros of a continuous function. If f is a continuous function on a closed interval [a,b], and if f(a) and f(b) have opposite signs, then there is at least on solution of the equation f(x)=0 in the interval (a,b). axlxf )(lim axaxaxlxfandlxflxf))(lim)(lim()(lim01sinlim71828. 2. )11(lim xnxxeennaxafxf )()(limaxxf )(limaxafxf )()(lim : limit definition of derivative at the point (a, f(a)). The derivative of a function f at a defined as.