The idea of a limit
Answers are for parents and teachers.
1
Compute lim (x² − 25)/(x − 5) as x → 5.
10
2
Find lim (4h² + 7h)/h as h → 0.
7
3
For f(x) = 2x + 3 (x < 1), f(x) = x + 4 (x ≥ 1) find the left and right limits as x → 1. Does the limit exist?
From the left 2 · 1 + 3 = 5, from the right 1 + 4 = 5; they are equal, so the limit exists and equals 5.
4
For f(x) = x when x ≤ 0 and f(x) = x + 2 when x > 0, is there a limit as x → 0? Explain.
No: the left limit is 0, the right limit is 2; the one-sided limits are not equal.
5
Find lim (x² − 2x − 8)/(x − 4) as x → 4.
6