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The 60 pages that link to Limit of a function, each with the reason it gives.

• DerivativeNarrower topic: The derivative is defined by a limit of average rates of change.

• Partial derivativeNarrower topic: The derivative is defined by taking a limit of difference quotients.

• Asymptotic analysisNarrower topic: Asymptotic statements describe behavior precisely through limits.

• DifferentiabilityNarrower topic: A derivative is defined through a limit of difference quotients.

• Directional derivativeNarrower topic: The directional derivative exists only when its difference quotient has the required limit.

• Improper integralNarrower topic: The limit defines an improper integral by moving a cutoff toward the problematic point.

• Riemann integralNarrower topic: The integral is defined by the limit of approximating sums.

• Cauchy principal valueNarrower topic: A principal value is defined by a particular arrangement of limits.

• Method of exhaustionNarrower topic: Convergence captures the idea behind shrinking the gap between bounding figures.

• Asymptotic expansionNarrower topic: An asymptotic expansion is defined by behavior in a chosen limiting regime.

• Euler's NumberNarrower topic: The defining compound-growth expression reaches e through a limit.

• Comparison testNarrower topic: Limit comparison uses the limiting ratio of the two term sequences.

• History of calculusNarrower topic: The limit concept eventually supplied a precise foundation for derivatives and integrals.

• Complex derivativeNarrower topic: The derivative is defined by a limit whose input is the complex increment.

• Squeeze theoremNarrower topic: The theorem establishes this kind of limit by trapping the function between two bounds.

• Indeterminate formNarrower topic: An indeterminate form arises when evaluating a limit from the expressions of its parts.

• L'Hôpital's ruleNarrower topic: The theorem is a method for finding particular limits of quotients.

• Linear approximationNarrower topic: Limits define the derivative and the small-error condition behind first-order accuracy.

• One-sided limitNarrower topic: A two-sided limit combines the behavior from both directions.

• Differentiable functionNarrower topic: Differentiability is defined through a limit of the linear-approximation error.

• Euler–Mascheroni constantNarrower topic: The constant is defined by a sequence limit rather than a finite closed expression.

• Slutsky's theoremNarrower topic: Different notions of convergence determine the theorem’s distinct hypotheses.

• Differentiation rulesNarrower topic: The derivative’s definition uses a limit of average rates of change.