Can someone give me the answers to problems a-l? i already finished it but i don't have an answer key so i want to check with someone.

If we approach 1 from the left, we're using the blue function, but if we approach 1 from the right, we're using the green function. So, we have

Since the left and right limits are different, the limit

does not exist.

When we approach 0, we always use the blue function. Both halves of the blue function tend to 1 as x approaches zero. So, in this case, we have

Note that the fact that, by definition, we have doesn't mean that the limit is wrong, or that it doesn't exist. It simply means that the function is not continuous, because we have

As for -2, x can approach this value only from the left, because the function is not defined between -2 and -1. So, we have

The limit as x approaches 3 is similar to the one where x approaches zero: the function is not defined at x=3, but the limit from both sides approaches -1:

As for the limits as x approaches infinity, we have to deduce from the graph that the funtion grows indefinitely as x grows, i.e.

And that the function has no limit as , because it has a sinusoidal behaviour, with an ever-growing amplitude.