Iam taking advanced math to learn new methods for solving equations. what is the complete infinitive phrase in the sentence?

Ipronounced his name, offering him at the same time my hand: he took it, smiling and saying, “we shall do very well by-and-by.” then he laid me down, and addressing bessie, charged her to be very careful that i was not disturbed during the night. having given some further directions, and intimates that he should call again the next day, he departed; to my grief: i felt so sheltered and befriended while he sat in the chair near my pillow… (chapter 3) this passage, in which jane first meets the doctor, is an example of