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Should we divide by 0 in limited question

I got a huge argument between me and me doctor. ends me kicked from the classroom. It was a limit question and we was have e to the power 1 divided be x and the x was get closer to zero and the doctor end the question by dividing by zero and saying infinite and e to power infinite is also infinite and because we was have one divided by the above formula it will equal one and I said that this is a mistake.

Here how the doctor solved the question

I am still think that he is wrong and we should not divide by zero even if in this example the answer was right but the steps still wrong .
I wanna hear your opinion guys . and even if I was completely wrong I still think that he shouldn’t kicked me out because I told him that he is wrong

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