This topic feeds directly into your retention score for Mathematics — the recall check after your next session will pull from what's written here.
Definition of a limit
Informally, the limit of a function as x approaches a value a describes the value the function gets close to — not necessarily the value it actually takes at a. Continuity means those two values match.
Left-hand and right-hand limits must be equal for the limit to exist
A function can have a limit at a point even if it's undefined there
Continuity requires: the limit exists, the function is defined, and they're equal
To revise before the next test
Epsilon-delta definition — worked through 5 problems
One-sided limits practice set
Removable vs. non-removable discontinuities
Past paper — 2023 Section B, Q4–Q6
Common mistakes (click to expand)
Forgetting to check both one-sided limits before concluding a limit exists. Confusing "undefined at a point" with "limit doesn't exist" — these are different things. Dropping the algebraic simplification step when the direct substitution gives 0/0.
"Continuity is what lets you draw the graph without lifting your pen." — how our tutor first explained it, and it stuck.
lim(x→2) (x² - 4)/(x - 2)
= lim(x→2) (x - 2)(x + 2)/(x - 2)
= lim(x→2) (x + 2)
= 4
| Session date | Focus | Confidence |
|---|---|---|
| 18 Jul | Epsilon-delta proofs | Medium |
| 21 Jul | One-sided limits | High |
| 23 Jul | Discontinuity types | Low |
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