I will try to answer with one try as much as I can.
「できる限り」は英語で as much as I can とか to the best of my ability などの言い方がございます。リスニングとかで一回だけ聞いた上で答えてみます、という場合は I will try to answer with one try でも良いですが、「できる限り」と言いたい場合は I will try to answer with one try as much as I can. とか I'm going to try my best to answer after listening once. のようにいえます。
ご参考に。