Limits of quotients
Guided practice — solve each problem, check, then generate a fresh one.
Formula to apply
lim_{x→a} (x² − a²)/(x − a) = 2a
Problem
Evaluate lim_{x→4} (x² − 16) / (x − 4).
Working
- 1Factor the numerator: x² − 16 = (x − 4)(x + 4).
- 2Cancel: f(x) = x + 4 for x ≠ 4.
- 3Substitute x = 4: the limit is 4 + 4 = 8.