Evaluate lim x→a f(x) for a function you type, including limits at infinity (enter inf or -inf for a).
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Evaluate limx→3 (x² − 9) / (x² − x − 6).
Step 1 — check the form. Numerator at x = 3: 9 − 9 = 0. Denominator at x = 3: 9 − 3 − 6 = 0. So it is 0/0 — indeterminate, work needed.
Step 2 — factorise both.
x² − 9 = (x − 3)(x + 3)
x² − x − 6 = (x − 3)(x + 2)
Step 3 — cancel (x − 3). This is legal because x ≠ 3 inside the limit — x only approaches 3. Write that line down; examiners look for it.
= limx→3 (x + 3)/(x + 2) = (3 + 3)/(3 + 2) = 6/5 = 1.2
Check at x = 3.001: 0.006001 / 0.005001 = 1.19996 ✔
Worked in full in Limits — The Idea Behind lim x→a f(x).
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