Відповіді АЛГЕБРА: 18.22

18.22

1) f(x) = x + 9x, x₀ = 3.

f’(x₀) = lim fxo+ ∆x- f(x0)∆x

∆x → 0

f(x₀ + ∆x) – f(x₀) = x₀ + ∆x + 9x0+ ∆x – x₀ – 9x0

x₀ = 3

f’(3) = lim 3+ ∆x+ 93+ ∆x- 3- 93∆x = lim ∆x+ 93+ ∆x- 3∆x = lim

∆x → 0 ∆x → 0 ∆x → 0

3∆x+ ∆x2+ 9-9-3∆x3+ ∆x∆x = lim∆x2(3+ ∆x)∆x = lim ∆x2∆x2+ 3∆x = 1.

∆x → 0 ∆x → 0

2) f(x) = x-2 x₀ = 6

f’(x) = lim 6+ ∆x-2- 6-2∆x = lim 4+ ∆x- 6-2∆x = lim

∆x → 0 ∆x → 0 ∆x → 0

(4+ ∆x- 2)(4+ ∆x+ 2)∆x(4+ ∆x+2 = lim 4+ ∆x-4∆x(4+ ∆x+2) = lim ∆x∆x(4+ ∆x+ 2) =

∆x → 0 ∆x → 0

= [14+0+2] = 14