1. Let f (x) = (x 2 + 4x − 21)/(x − 3) for x ≠ 3. How should f (3) be defined so that f will be continuous at 3? 2. Define f :  →  by f (x) = x 2 + 3x – 5. Use Definition 2.1 to prove that f is...

1. Let f (x) = (x²
+ 4x − 21)/(x − 3) for x ≠ 3. How should f (3) be defined so that f will be continuous at 3?

2. Define f :
 →
 by f (x) = x²
+ 3x – 5. Use Definition 2.1 to prove that f is continuous at 3.

3. Find an example of a function f :
 →
 that is continuous at exactly one Point