Question

Let f(x) = |x+3 | / x+3 find each limit if possible
lim x --> -3

Answer 1

well the definition of
|x+3|=x+3 if x+3>=0
=-(x+3) if x+3<0

or
let's write it as
|x+3|=x+3 if x>=-3
=-(x+3) if x<-3


Now since you have x approaching -3
and your function doesn't exist at x equal 3
you are going to need to look at the left and the right of -3
since we actually do have two different functions
the function before -3 is -(x+3) and
the function after -3 is x+3

Answer 2

So you don't apply |u| = -u if u <0 ?
It is the same function and I need to find the answers from the right and from the left, but all I get is undefined because 0/0

Answer 3

I did apply |u|=-u if u<0 above

Answer 4

you need to look at the right and left limit

Answer 5

Exactly, so from the left it would be undefined? I'm having trouble understanding this chapter

Answer 6

\[\lim_{x \rightarrow -3^+}\frac{|x+3|}{x+3} \text{ and } \lim_{x \rightarrow -3^-}\frac{|x+3|}{x+3}\]

Now what is |x+3| for numbers to the right of -3?
I actually already told you when I wrote the definition of |x+3|