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📈 Optional Mathematics - Class 10
Lesson 12 · Continuity and Discontinuity of a Function

Continuity and Discontinuity of a Function Presentation

Optional MathematicsSubject
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Optional Mathematics · Class 10

Continuity and Discontinuity of a Function

One-sided limits · Three conditions · Four worked examples

By the end of this lesson you can

📈

Spot where a graph is broken

↔️

Find left-hand and right-hand limits from a table

⚖️

Decide when a limit exists

✅

Test continuity with three conditions

🧩

Handle piecewise and 0/0 functions

Unbroken or broken?

✏️Continuous
y = x² never breaks
The pencil never lifts
A sharp corner still counts
VS
🕳️Discontinuous
y = (x² − 4)/(x − 2) has a hole at x = 2
A hole, gap or jump
The pencil must lift

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Presenter notes: Today we ask a simple question about graphs: can this graph be drawn without lifting the pencil at a given point? By the end you will be able to answer it with limits instead of guesses.