I don't need Tongji's book, so it's not difficult to answer your first question … I'll explain it to you and ask you later! In fact, the concept that the partial derivative of multivariate function is continuous at a certain point is the same as that of univariate function, which can be obtained from the definition of partial derivative: when we find the partial derivative of multivariate function to a variable, we always regard other variables as constants temporarily, so that the original multivariate function becomes univariate function, and the discussion on the partial derivative of multivariate function is the same as that of univariate function.