Continuity

⏱ 15 min★ Up to 80 XP📝 3 questions

Game

Can the bacterium reach the destination

without ever leaving the path?

A tiny bacterium needs to travel from START to END. Watch what happens on each path.

PATH A — Smooth curve

PATH B — Curve with a gap

BacteriumGap (missing path)

Graph A

Can you draw this graph without lifting your pen?

Biotech Context

Something doesn't add up.

Bioreactor population — 4-hour window:

Time	Cell Count
1 PM	1,000
2 PM	1,100
3 PM	1,200
4 PM	1,300

Simulation

Watch continuity break.

Drag the slider to introduce a gap.

Continuous

Gap Sizenone

Limits vs Continuity

When a limit exists

but continuity doesn't.

From left x → 2⁻

→ 4

From right x → 2⁺

→ 4

Limit

lim

x → 2

f(x) = 4

If both sides agree,

why isn't the graph continuous?

Formal Definition

Continuity requires three things.

A function is continuous at x = a if all three hold. Click any condition to see what breaks.

Continuous at x = a

All three required.

Remove any one condition and continuity breaks.

Practice Questions

ConceptQuestion 1 of 3

Can a function have a limit at a point but still be discontinuous there?

Coming up

Two roads. Both continuous.

Road A

Smooth

Road B

Sharp corner

Both roads are continuous.

But which road has a well-defined direction
at every point?

Next concept

Differentiability

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