Topic explanation

Standard explanation

A two-sided limit exists only when the left-hand and right-hand limits both exist and are equal.

Key points

• Left-hand and right-hand limits
• rule
• worked example
• Left-hand and right-hand limits: A two-sided limit exists only when the left-hand and right-hand limits both exist and are equal.
• CONCEPT AND RULE: A two-sided limit exists only when the left-hand and right-hand limits both exist and are equal.
• METHOD: For left-hand and right-hand limits, identify the given information and required result. Select the
• A two-sided limit exists only when the left-hand and right-hand limits both exist and are equal.
• Worked pattern: For sign(x) at 0, left limit is -1 and right limit is 1, so no limit exists.

Labelled diagram