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--% Limits involving trig and inverse trig functions
-- Some of these limits were taken from bug reports submitted before
-- changes were made to limit and related series packages.
-- Author: Clifton J. Williamson
-- Date Created: 27 August 1992
-- Date Last Updated: 27 August 1992
-- Keywords: limit, trigonometric function, inverse trigonometric function
-- References:
)clear all
-- in each case, the argument to 'atan' has a pole and the left-hand
-- and right-hand limits differ
limit(atan(1/sin(x)),x = 0)
limit(atan(sqrt(1 - x**2)/x),x = 0)
limit(atan(-sin(x)/(cos(x) + a)),x = acos(-a))
limit(atan(sin(x)/(cos(x) + a)),x = acos(-a))
-- we'll get these next two if sqrt(1 - a**2) is considered to be
-- positive by SIGNEF
limit(atan(1/(cos(x) + a)),x = acos(-a))
limit(atan(1/(sin(x) + a)),x = asin(-a))
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