Sinx/x is a bounded function divided by infinity.

Of course, the preference is 0, and the b option is wrong.

The second problem is to find the limit limx tends to 0 sinx/|x|

The left and right limits are-1 and 1 respectively.

Both the left limit and the right limit exist, which is the first discontinuity. Choose C.

The third problem is that |xn| tends to |a|

It may be convergence

It is also possible that xn jumps between A and -a, so D is chosen for divergence.