Topic explanation

Standard explanation

f is continuous at a when f(a) exists, lim(x->a)f(x) exists, and both are equal.

Key points

• Continuity at a point
• rule
• worked example
• Continuity at a point: f is continuous at a when f(a) exists, lim(x->a)f(x) exists, and both are equal.
• CONCEPT AND RULE: f is continuous at a when f(a) exists, lim(x->a)f(x) exists, and both are equal.
• METHOD: For continuity at a point, identify the given information and required result. Select the matching d
• f is continuous at a when f(a) exists, lim(x->a)f(x) exists, and both are equal.
• Worked pattern: Choose k=4 in f(x)=x²-4x-2 for x!=2 and f(2)=k.

Labelled diagram