# Calc02_3 - 2.3 Continuity Grand Canyon Arizona Photo by...

This preview shows pages 1–5. Sign up to view the full content.

2.3 Continuity Grand Canyon, Arizona Greg Kelly, Hanford High School, Richland, Washington Photo by Vickie Kelly, 2002

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

View Full Document
Most of the techniques of calculus require that functions be continuous . A function is continuous if you can draw it in one motion without picking up your pencil. A function is continuous at a point if the limit is the same as the value of the function. This function has discontinuities at x=1 and x=2. It is continuous at x=0 and x=4, because the one-sided limits match the value of the function 1 2 3 4 1 2
jump infinite oscillating Essential Discontinuities: Removable Discontinuities: (You can fill the hole.)

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

View Full Document
Removing a discontinuity: ( 29 3 2 1 1 x f x x - = - has a discontinuity at . 1 x = Write an extended function that is continuous at . 1 x = 3 2 1 1 lim 1 x x x - - ( 29 ( 29 ( 29 ( 29 2 1 1 1 1 1 x x x x x x - + + = + - 1 1 1 2 + + = 3 2 = ( 29 3 2 1 , 1 1 3 , 1 2 x x x f x x - - = = Note: There is another discontinuity at that can not be removed.
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### Page1 / 10

Calc02_3 - 2.3 Continuity Grand Canyon Arizona Photo by...

This preview shows document pages 1 - 5. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online