Archive for June, 2010

Continuity & One-Sided Limits

Student 09_10
Jun 1 |18:28
There are 3 conditions for a function to be continuous: definition of continuity-
         • Lim f(x) = f(c) (limit must exist)
            x—-> c
         • Lim f(x) = f(c) or lim must equal the function value
            x —-> c
         • F(c)must be defined
 -one clue is to make sure there are no holes or asymptotes so you can easily “walk” across the function.
Definition of a limit states that in order to have a limit at a point, the function must get close to a value at that point from both side
• This implies that we have to check the limit reaches a certain number from both sides of the function .
Also we learned the notation for one-sided limits
As x approaches c from the left side it’s
 Lim f(x)
 x —->c-
As x approaches c from the right side it’s
         Lim f(x)
         x —-> c +