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

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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J. Physical Oceanography, 1984 "A Numerical Model for Low-Frequency Equatorial Dynamics", with M. Cane**Education/Credentials**

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