If f:R/{1,-1} -> R, f(x) = arctg[1/(x^2 - 1) calculate lim f(x) = ? when x->1 , x>1.

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lim f(X) = lim arctg (1/(1-x^2) when x-->1

Substitute with x=1

lim f(x) = arctg lim (1/0)

But we know that arctg = arcsin/arccos

==> arctg (1/0) = arc(sin(pi/2)/cos(pi/2)

                     = arctg(pi/2)

                      = pi/2

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