Explanation

Sometimes direct substitution gives 0/0. Use algebra:

1. Factor & cancel

2. Rationalize

3. Simplify

Example:
lim (x → 2) (x²−4)/(x−2) → factor numerator: (x−2)(x+2)/(x−2) → cancel → lim = 4

Quiz

1. What indeterminate form often appears?

2. Factor x²−4 = ?

3. lim (x → 1) (x²−1)/(x−1) = ?

4. Can you simplify before substituting?

5. Is 0/0 defined?

Answer Key

1. 0/0

2. (x−2)(x+2)

3. (x−1)(x+1)/(x−1) → lim = 2

4. Yes

5. No