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!
Use the rules and the rules
. Limit no existy!
For 4) Is this the equation you meant?
Now the only limit you have to handle is .