Continuity: Determine a parameter: Find the value of a so that f(x) is continuous where

The polynomials are continuous, so that the problem is the continuity at x = 2.

The Definition of Continuity requires

1. the function be defined at x = 2. It is.
2. The limit must exist at x = 2. To determine this, we need to determine the two 1-sided limits and choose a value of a so that these limits are equal.
   Limit from the left:
   Limit from the right:
   Setting these equal, we get
   4a = 32, or a = 8.
   Now the two 1-sided limits are equal, so that the limit exists:
   .
3. This latter equality completes the definition of continuity. Hence we conclude that if the value of a is chosen as 8, then f(x) will be continuous.