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Bonjour,

Réponse :

1. She has been walking in the mountains since the beginning of the afternoon.

2. He wanted her to take some medicine.

3. Did he remember to bring the biscuits?

1- Smoking in class is forbidden. ( interdiction ) 

→ You mustn’t smoke in class.

2- My mother needn’t call the doctor. ( absence d'obligation )

→ My mother doesn’t have to call the doctor.

3- Perhaps he will come tomorrow. ( possibilité, éventualité )

→ He may come tomorrow.