Smith took part in ITA Fall Nats, while trio played at So Cal Intercollegiates.
Smith will get underway at Fall Nationals in Newport Beach, Calif. on Wednesday.
Goldberg, Hance reached singles, doubles quarterfinal rounds at Kramer Club.
Eight players will compete in Southern California, Las Vegas beginning Thursday.
Goldberg turned in two singles wins, while Rapp/Wild won a pair of doubles matches.
Smith reached ITA All-Americans round of 16; Hovenier turned in his first-career win.