Advanced Math/limits

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Question
lim x->0 1-cosx/sin(x/2)

Answer
Taking the limit as x -> 0 gives

lim x->0 cosx = 1
lim x->0 sin(x/2) = lim x->0 x = 0 since, for x small, sin(x) ≈ x.

Its also OK to write lim x->0 (1/x) = ∞, so that

lim x->0 (1 - cosx/sin(x/2)) = lim x->0 (1 - 1/x) = 1 - ∞ = -∞.

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randy patton

Expertise

college mathematics, applied math, advanced calculus, complex analysis, linear and abstract algebra, probability theory, signal processing, undergraduate physics, physical oceanography

Experience

26 years as a professional scientist conducting academic quality research on mostly classified projects involving math/physics modeling and simulation, data analysis and signal processing, instrument development; often ocean related

Publications
J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane

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M.S. MIT Physical Oceanography, B.S. UC Berkeley Applied Math

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Also an Expert in Oceanography

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