For Maine’s remaining Olympic hopeful freestyle skiers, the final week of qualifying competition comes down to one thing: skiing to their potential.

Moguls skiers Jeremy Cota (Greenville), Troy Murphy (Bethel) and David DiGravio (Farmington) and halfpipe skier Simon Dumont (Bethel) have chances to secure berths on the U.S. Olympic freestyle team for the Winter Olympics in Sochi, Russia, next month.

The three moguls skiers will compete on Lake Placid’s Whiteface Mountain Wednesday, with Murphy currently holding the third – and final – spot for Olympic qualification. Dumont returns to action at Park City, Utah, with events on Friday and Saturday. He currently also holds the third spot.

Murphy, 21, was a long shot to make the Olympic team when the qualifying races began. But he jumped into contention with a fifth-place finish in his first race last week in Deer Valley, Utah. He finished 46th in the next event, but his fifth place has him sitting in a good position. Only Patrick Dineen, with a third and fourth among his finishes, and Sho Kashima, with a fifth, have scored as high as Murphy on the U.S. team.

“I’m excited,’’ said Murphy. “I just have to ski as best as I can. If I ski to my ability, and do well, chances are with me.’’

Murphy wasn’t disappointed with his 46th place finish, saying, “You can’t win them all.’’

And he was still riding high off his fifth.

“It just showed all my hard work and training paid off,’’ said Murphy. “I always knew I could compete at this level. And it all came together that night.’’

Cota, 25, was one of the leading U.S. Olympic contenders entering the World Cup races that are used for qualifying. And while he still feels he’s skiing well, he knows he has to ski better. He has an additional chance to qualify for the U.S. team after Lake Placid in a World Cup event at Val St.-Come, Quebec, next Sunday. Murphy may also be invited to participate then.

“My skiing has gone well, I just keep making little mistakes in the events,’’ said Cota, whose best finish in four events has been a 19th (he didn’t finish one). “I’m still confident enough in my skiing. I know if I ski good enough in one event, it’s good enough (to qualify). But in our sport that’s easier said than done.

“It’s competitive enough that I can’t make a mistake and expect to do well.’’

Cota, who has done well historically at Lake Placid, said the team is so competitive that there are a number of skiers who could reach the podium and secure a berth. While only three moguls skiers are guaranteed a berth in Sochi, U.S. Skiing could also add a fourth depending on results in other freestyle disciplines.

“It’s really all on me at this point, just a matter of executing,’’ he said. “We’ll see what happens. Hopefully all of us will ski well there tomorrow.’’

Dumont, meanwhile, pulled off a fourth in miserable weather conditions at Breckenridge, Colo., last Sunday to improve his chances. He said there were 6 inches of snow at the bottom of the halfpipe, making it difficult for all competitors.

“I got lucky we ran it,’’ he said. “It put me in a better place. It gave me a little more confidence going into the next events.’’

David Wise clinched a spot on the Olympic halfpipe team with a first at Breckenridge. Aaron Blunck has also met the qualifying criteria. Dumont is being challenged by Gus Kenworthy, Lyman Currier and Alex Ferreira.

Dumont, 27, said this is the time of year when he usually starts skiing his best. He’s healthier than he has been in years and in the best shape of his life because of his physical therapy for a shattered ankle last summer.

“I feel good,’’ he said. “I’m hoping to get a podium (top-three finish) and get some momentum going forward.’’

Mike Lowe can be reached at 791-6422 or at:

mlowe@pressherald.com

Twitter: MikeLowePPH