--Copyright The Numerical Algorithms Group Limited MCMXCII.

--% 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))
