You are correct for 1)

For 2) you must split it into two limits. The absoulte value of a function, f(x) is but

So treat it as two cases:

The first case is when x approaches 8 through positive values, when this happens f(x) > 0, hence |f(x)| = f(x).

Now through negative values, when this happens f(x) <0, hence |f(x)| = -f(x).

Since these limits are not equal, the limit does not exist!

For 3):

Use the rules and the rules

This gives:

. Limit no existy!

For 4) Is this the equation you meant?

If so:

Now the only limit you have to handle is .