Got a midterm worksheet. Realized how confused I am.

Question

Here are some questions:

lim x^3 + 12x^2 - 5x/5x
x->0

Find the indicated limit:
lim 11x/absolute value x
x->0+

Answer 1

I am not sure if you mean
lim x^3 + 12x^2 - 5x/5x
x->0
or
lim (x^3 + 12x^2 - 5x) /5x
x->0
but either way
as x ---> 0 you end up with -5x/5x
which is -1
all those higher order terms go to zero faster than 5x
like if x = .1
x^2 = .01
x^3 = .001

Answer 2

Now if you are given that you are on the POSITIVE side of the origin, then |x| = x
then
11x/x = 11 for any old x if x>0