Agile means for someone to have the ability to move easily and be energetic. It means having an adaptable and resourceful character. The antonyms of agile are slow clumsy and stiff.
Therefore, the sentence "The agile youth sprang into the chariot, stood erect and grasped the reins with delight, pouring out thanks to his reluctant parent" can be written as "The energetic youth sprang into the chariot, stood erect and grasped the reins with delight, pouring out thanks to his reluctant parent".
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Eulogy is when the audience is here to hear about the life of the person who passed away. This is not some inspirational speech or some issue, its to honor the dead.