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This distinction arises from different conventions regarding what constitutes a valid limit. Strictly speaking, a limit must be a finite real number; since the branch grows without bound, the finite limit 'does not exist'.

Conditions: The function is unbounded near the target input.; Context specifies whether seeking a strict finite real limit or using extended infinite-limit notation.

This distinction arises from different conventions regarding what constitutes a valid limit. Strictly speaking, a limit must be a finite real number; since the branch grows without bound, the finite limit 'does not exist'.

Conditions: The function is unbounded near the target input.; Context specifies whether seeking a strict finite real limit or using extended infinite-limit notation.

Writing a limit as infinity ($\infty$) is descriptive notation indicating that the function's output grows without bound, eventually exceeding any finite threshold. It does not mean the limit evaluates to a specific real number, because infinity is not a member of the set of real numbers.

Conditions: Working within standard calculus definitions over real numbers.; The function exhibits unbounded behavior near the target input.

Writing a limit as infinity ($\infty$) is descriptive notation indicating that the function's output grows without bound, eventually exceeding any finite threshold. It does not mean the limit evaluates to a specific real number, because infinity is not a member of the set of real numbers.

Conditions: Working within standard calculus definitions over real numbers.; The function exhibits unbounded behavior near the target input.