lim_(x->-oo)(x*|__(1/x)__|)?

1 Answer
Jun 17, 2018

The limit does not exist (diverges to +oo)

Explanation:

For x<-1, we have

0>1/x> -1

and hence

|__ (1/x) __| = -1

So, for x < -1, we have

x\ |__ 1/x __| = -x

and the limit we are seeking is

lim_{x to -oo } x\ |__ 1/x __| = lim_{x to -oo} (-x)

It is clear that this limit does not exist (diverges to +oo)