Уравнение касательной: у = f(x₀) + f'(x₀)(x-x₀)
y = ln(x²+2x)
y(2) = ln(4+4) = ln8
y' = (1/(x²+2x))*(2x+2) = (2x+2)/(x²+2x)
y'(2) = (4+2)/(4+4) = 6/8 = 0.75
y кас = ln8 + 0.75*(x-2) = ln8 + 0.75x - 1.5
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Уравнение касательной: у = f(x₀) + f'(x₀)(x-x₀)
y = ln(x²+2x)
y(2) = ln(4+4) = ln8
y' = (1/(x²+2x))*(2x+2) = (2x+2)/(x²+2x)
y'(2) = (4+2)/(4+4) = 6/8 = 0.75
y кас = ln8 + 0.75*(x-2) = ln8 + 0.75x - 1.5