2.5 continuity

2.5 continuity - infinity (vertical asymptote) One sided...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon
2.5 Continuity Def: a function f(x) is Continuous at x = a Def: a function is continuous if a line can be drawn if you can trace it without picking up your pencil. This extends direct sub to other continuous functions This means 3 Things : 1. f(a) exists 2. Lim f(x) exists 3. they are the same We say f has a discontinuity at x = a, or f is discontinuous at x = a if f is no continuous at x = a Def: a function f(x) is continuous on the interval, I, if it is continuous at each x in I Discontinuities are one of 3 types 1. Removable – if I can define the function or redefine the function (hole) 2. jump – in order to finish the graph, it has to jump to a different spot (jump) 3. unbounded – when the function approaches positive or negative
Background image of page 1

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
Background image of page 2
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: infinity (vertical asymptote) One sided Continuity one sided limit Theorem: f and g continuous implies 1. f + or g continuous 2. f * g continuous 3. f/g or g/f continuous where defined 4. c*f continuous Theorem: 1. Polynomials are continuous everywhere 2. Rational functions are continuous where defined 3. Roots are continuous where defined 4. Trigs are continuous where defined Theorem: if f(x) is continuous then lim f(g(x)) is f(lim g(x)) The intermediate Value Theorem: Given: f(x) continuous on [a,b] and N between f(a) and f(b). Then: there exists a C so that a<c<b and f(c) = N...
View Full Document

This note was uploaded on 04/07/2008 for the course MATH 161 taught by Professor Algier during the Spring '08 term at Grove City.

Page1 / 2

2.5 continuity - infinity (vertical asymptote) One sided...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online