I am having trouble with the following type of problem. Will you please explain with steps how to learn this? I put two examples to make sure i can understand it.

Example Problem 1:

lim x> 1 f(x), where f(x) = {4 - x, x < 1

4x - x^2, x > 1

Example Problem 2:

lim x> -1 f(x) = {x + 3, x <_ -1

2x + k, x > -1