Can someone tell me if i got these questions correct or wrong :

Both of your answers are correct.
In the first question, there is a discontinuity in the graph; however, the limit does indeed exist and its value is 2.

In the second question, lim x→4 does not exist, while all of the other do. The options then just involve checking if the correct value of the limit is stated with the value of x, and you did this well.