A good example of an earnest prayer can be found in the book of Nehemiah chapter 1, which states:
Nehemiah 1: (NAS)
 I said, "I beseech You, O LORD God of heaven, the great and awesome God, who preserves the covenant and lovingkindness for those who love Him and keep His commandments,
 let Your ear now be attentive and Your eyes open to hear the prayer of Your servant which I am praying before You now, day and night, on behalf of the sons of Israel Your servants, confessing the sins of the sons of Israel which we have sinned against You; I and my father's house have sinned.
 "We have acted very corruptly against You and have not kept the commandments, nor the statutes, nor the ordinances which You commanded Your servant Moses.
 "Remember the word which You commanded Your servant Moses, saying, 'If you are unfaithful I will scatter you among the peoples;
 but if you return to Me and keep My commandments and do them, though those of you who have been scattered were in the most remote part of the heavens, I will gather them from there and will bring them to the place where * I have chosen to cause My name to dwell.'
 "They are Your servants and Your people whom You redeemed by Your great power and by Your strong hand.
 "O Lord, I beseech You, may Your ear be attentive to the prayer of Your servant and the prayer of Your servants who delight to revere Your name, and make Your servant successful today and grant him compassion before this man." Now I was the cupbearer to the king.
From the verses above, we can learn valuable lessons on the way we should pray.
v5 - Acknowledge God's sovereignty and lovingkindness
v6, 7 - Pray attentively, for ourselves and others, 'on behalf' in intercession, confessing others' sins and ours
v9 - Accept God's forgiveness and return to Him in repentance
v10 - Acknowledge God's redemption
v11 - Revere God and His name
The keywords here are:
If you died today, are you absolutely certain that you would go to heaven? You can be! TRUST JESUS NOW
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