GRADE 12 · MATHEMATICS · TOPIC 5

Continuity and Differentiability

A function is continuous if its value agrees with its limit at a point.

CONCEPT EXPLAINED

Understand the concept

A function is continuous if its value agrees with its limit at a point.

SOLVED EXAMPLE

Is f(x)=x² continuous at x=2?

  1. Step 1: Limit as x→2 is 4
  2. Step 2: f(2)=4.

Final answer: Yes

PRACTISE YOURSELF

Derivative of x³

Show the answer

3x²

Try another similar question and explain each step aloud. Refer to your school syllabus for topic level and notation.