Calculus of a Single Variable, Chapter 5, 5.8, Section 5.8, Problem 19

Given,
lim_(x->oo) sech(x)
to find the value of lim_(x->oo)sechx
we need to find the value of
lim_(x->-oo) sechx and lim_(x->+oo)sechx
so,
the value of
lim_(x->-oo)sechx is as x tends to negative infinity the sech(x) -> 0
and similarly as
lim_(x->+oo)sechx is as x tends to positive infinity the sech(x) -> 0
So,
lim_(x->-oo)sechx=lim_(x->+oo) sechx=0
the limit exits forlim_(x->oo)sechx
and the value islim_(x->oo)sechx=0