Question

check the existence of limit x-1\|x-1| at x=1​

Answer 1

Answer:

a pretty basic question i assume, but i'm very confused. my textbook just says that it does have a limit (that was the original question) but i can't get to the same answer.

here's something i've come up with:

|x-1|=x-1, if x>1 and -(x-1) if x<1

the limit of |x-1|/(x-1)as x->0 from the left would be -(x-1)/(x-1)=-1

the limit of |x-1|/(x-1) as x-> from the right would be (x-1)/(x-1)=1

which then says that the limit of |x-1|/(x-1) as x->0 doesn't exist