由衷

例句：

1. 1. He expressed his sincere gratitude to the teacher for her help.
   他真诚地感谢老师对他的帮助。
2. 2. She spoke with utmost sincerity, showing her deep affection for her friend.
   她说话非常真诚，表现出对她朋友的深厚感情。
3. 3. The manager sincerely apologized for the mistake made by his team.
   经理真诚地为他的团队犯的错误道歉。