One-Sided Limits

AP Calculus · Axiom Academy

Approach a point from only one direction Left-Sided and Right-Sided Limits Sometimes a function approaches different values from the left and right. We describe this with one-sided limits. Relationship to Two-Sided Limits The two-sided limit exists if and only if the one-sided limits exist and are equal: This is crucial: if left limit ≠ right limit, the two-sided limit does NOT exist. Example: Absolute Value Function From the right: When x > 0, , so Since the left limit equals the right limit (both equal 0), we have . Some functions have different one-sided limits (a jump): The two-sided limit does not exist at a jump discontinuity.

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