F '(x0) = - 2 find the following limits: (1) Lim Δ X - > 0 f (x0 + 3 Δ x) - f (x0) / Δ x (2) limh - > 0 f (x0) - f (x0-h) / h

F '(x0) = - 2 find the following limits: (1) Lim Δ X - > 0 f (x0 + 3 Δ x) - f (x0) / Δ x (2) limh - > 0 f (x0) - f (x0-h) / h

1. LIM (Δ x → 0) f (x0 + 3 Δ x) - f (x0) / Δ x = 3 * Lim f (x0 + 3 Δ x) - f (x0) / 3 Δ x according to the definition of derivative: = 3 * f '(x0) = 3 * (- 2) = - 62, LIM (H → 0) f (x0) - f (x0-h) / h = LIM (- H → 0) f (x0 + (- H)) - f (x0) / (- H) according to the definition of derivative: = f' (x0) = - 2 if you don't understand, please ask