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→5} (x² − 25) / (x − 5).
Working
- 1Factor the numerator: x² − 25 = (x − 5)(x + 5).
- 2Cancel: f(x) = x + 5 for x ≠ 5.
- 3Substitute x = 5: the limit is 5 + 5 = 10.