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is an option for Asymptotic, DiscreteAsymptotic and similar functions that specifies the number of desired terms in an asymptotic approximation.
Find the leading asymptotic approximation for Sin at 0:
Plot the function and the approximation:
Use SeriesTermGoal to obtain a better approximation:
Asymptotic DiscreteAsymptotic AsymptoticSolve AsymptoticDSolveValue AsymptoticIntegrate AsymptoticRSolveValue AsymptoticSum AsymptoticProduct