Final answer:
In the sentence provided, the gerund is 'dancing,' functioning as a direct object, as it receives the action of the verb 'has given.'
Step-by-step explanation:
The gerund in the sentence 'Carson has given underwater dancing her best effort' is 'dancing.' A gerund is a verb form ending in -ing that functions as a noun, and in this sentence, 'dancing' is the direct object of the verb 'has given.' The sentence shows an action (has given) performed by the subject (Carson) on a direct object (underwater dancing), wherein 'underwater' is an adjective modifying the gerund 'dancing.' Therefore, the gerund 'dancing' acts as a direct object.