The first problem, x=2, is a discontinuous point, and the first kind of discontinuous point jumps discontinuously.

Because x=2, the left limit is 2 and the right limit is 4.

The second question x= 1 is a discontinuous point, because the left and right limits of this point are 1.

But this point is not defined, so it is a discontinuous point. Let f( 1)= 1 and it becomes continuous.

The denominator of the third question is multiplied by (x+ 1)+ 1 under the root sign at the same time, which is equivalent to finding.

The limit 1/ ((x+ 1)+ root sign 1) when x tends to 0, and the limit is 0.5.

The discontinuity of the fourth question is x=0. When x tends to 0, the limit of f(x) is 1, so

Let f(0)= 1 become continuous.