Question

Решить 43.32а и 43.33б

Answer 1

1) y1 = (x^3/3 - 2)
Y = y1(x0) + y1 '(x0)*(x - x0) - уравнение касательной
y1(x0) = (x0)^3/3 - 2
y1 '(x0) = (x0)^2
Y = (x0)^2/3 - 2 + x*(x0)^2 - (x0)^3 = x*(x0)^2 + ((x0)^2/3 - (x0)^3 - 2)
y2 = x - 3
Y || y2 - когда равны коэффициенты при х
1 = (x0)^2
x0 = +-1
x0 = 1, Y = x + (1/3) - 1 - 2 = x - (8/3)
x0 = -1, Y = x + (1/3) + 1 - 2 = x - (2/3)
2) y1 = arcsinx
y1(x0) = arcsin(x0)
y1 '(x0) = 1/(√(1 - (x0)^2))
Y = arcsin(x0) + (x - x0)/(√(1 - (x0)^2)) = x/(√(1 - (x0)^2)) + arcsin(x0) - (x0)/(√(1 - (x0)^2))
y2 = x + 2
Y || y2
1/(√(1 - (x0)^2)) = 1
1 - (x0)^2 = 1
x0 = 0
Y = x + arcsin(0) = x