Now a lot of new technology can be applied to ---- problems

Now a lot of new technology can be applied to ____ problems in industry.A.solve B.solving选哪个?
to do不是不定式吗？apply后面不是跟不定式吗？难道是分开看？apply to / doing?我分不清哪个是不定式，那个是介词后跟ing
那什么时候用to do,什么时候用doing呢？used to do和used doing 不是都有吗？