The problem of continuity and differentiability of binary functions 1. F (x, y) - f (0,0) + 2x-y = O (ρ), (when (x, y) → (0,0)), we can get that f (x, y) is differentiable at point (0,0). Why? How? 2. LIM (x, y) → (0,0) (f (x, y) - f (0,0) + 2x-y) = 0 can get f (x, y) continuous at point (0,0). Why? How?

The problem of continuity and differentiability of binary functions 1. F (x, y) - f (0,0) + 2x-y = O (ρ), (when (x, y) → (0,0)), we can get that f (x, y) is differentiable at point (0,0). Why? How? 2. LIM (x, y) → (0,0) (f (x, y) - f (0,0) + 2x-y) = 0 can get f (x, y) continuous at point (0,0). Why? How?

1. If f (x, y) - f (0,0) + 2x-y = O (ρ) (when (x, y) → (0,0), then there is the expression f (0 + Δ x, 0 + Δ y) - f (0,0) = - 2 Δ x + Δ y + O (ρ) (ρ→ 0), where ρ = SQR [Δ x ^ 2 + Δ y ^ 2], then according to the definition of total differential of multivariate function, f (x, y) must be differentiable at point (0,0), and DF (0,0)

At present, 450 books are lent to students, 5 for each. The relationship between the remaining books y and the number of students x is, the independent variable here is, the function is

Y = 450-5x, the independent variable is X