Evaluating Limits by Factoring/Cancelling

when can you factor out

when x is at least raised to a power of two

when can you use a conjugate

when something is a square root or imaginary number added to another number

when can you simplify

if two fractions with different denominators are being added

when is a function continuous

1. f’(α) is defined

2. lim f(x) exists
   ^{x → α}

3. lim f(x) = f(α)
   ^{x → α}