Unformatted text preview: x →-2 ( x + 2)( x-4) x + 2 = lim x →-2 ( x-4) =-6 . Next you try to compute f (-2) = , so f (-2) is undeﬁned. In partic-ular, 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 every-where except at x =-2. I’ll do this with a piecewise function. Let g ( x ) = x 2-2 x-8 x + 2 x 6 = 2 x-4 x = 2 . Now you can check an see that g ( x ) is continuous everywhere and agrees with f ( x ) except at x =-2. 1...
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- Spring '06
- Continuity, Continuous function, 2 g, partic0 ular