Questions about calculating marginal revenue

MR=△TR/△Q
△TR=TR(after)-TR(before)=(P+△P)(Q+△Q)-PQ=P△Q+Q△P+△P△Q
therefore, MR=△TR/△Q=P+△P+Q△P/△Q.

BUT the actual function of MR is MR=P+Q△P/△Q

Why there is a difference △P between these two functions?

What you’re calling the actual function is an approximation, when ∆P is small enough to ignore.

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Thank you!

My pleasure.