Tim Challies new blog post entitled, “Preaching the Gospel with TULIP’s Tricky ‘L’ in Mind” he answers well, the question of how do you preach in light of limited atonement. He begins his post with:
It’s a fair question for the Arminian to ask: How can you preach the free offer of the gospel when you believe in a limited atonement? How can you preach the “whosoever” of John 3:16 if you cannot be certain that Christ’s atonement was for every person? How can you say, “Turn to Christ and be saved all the ends of the earth” if Christ’s atoning sacrifice does not extend to all humanity?”
These are good questions that he answers well. So definitely check out his post here and I hope you find at as helpful as I did.