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Piecewise functions are defined by different formulas on different intervals. To determine the limit as $x$ approaches a boundary point $a$, you must use the formula valid for $x < a$ for the left-hand limit and the formula valid for $x > a$ for the right-hand limit.

Conditions: The function is defined piecewise.; The point $a$ is a boundary between branches.

Piecewise functions are defined by different formulas on different intervals. To determine the limit as $x$ approaches a boundary point $a$, you must use the formula valid for $x < a$ for the left-hand limit and the formula valid for $x > a$ for the right-hand limit.

Conditions: The function is defined piecewise.; The point $a$ is a boundary between branches.