This preview shows page 1. Sign up to view the full content.
Unformatted text preview: x 2 ( x + 2)( x4) x + 2 = lim x 2 ( x4) =6 . Next you try to compute f (2) = , so f (2) is undened. In particular, this means the limit of the function and the value of the function are not equal. So f ( x ) has a removable discontinuity at x =2. Now I want a continuous function g ( x ) which agrees with f everywhere except at x =2. Ill do this with a piecewise function. Let g ( x ) = x 22 x8 x + 2 x 6 = 2 x4 x = 2 . Now you can check an see that g ( x ) is continuous everywhere and agrees with f ( x ) except at x =2. 1...
View Full
Document
 Spring '06
 YUKICH
 Continuity

Click to edit the document details