I need help on this problem:
Also please explain how to do it. I started out by graphing the first function but not sure how to do the others/what its asking for.
This looks like an assignment of some sort so I won't give direct answers.
By definition of conitnuity, limit x-> a f(x) = f(a)
The key here is to find a,b such that the limit from the left of 2 and the limit from the right of 2 correseponds to f(2).
Basically you'll need to find this:
exists if and only if and both exist and are the same.
Yes, . That is " , the limit from below, because that fraction form is true only for x< 2. In order that the limit at 2 (from both directions) exist, we must get the same limit "from above": must equal 4. That gives you one equation.
Do the same with and to get a second equation.