Question

limx→∞{x[ln(x+1)−lnx]}

Answer 1

lim. [x(In(x + 1) - In x]
x→∞

lim. xIn . x + 1/x
x→∞

Regra do L'

d/dx . (x + 1)/d/dx . (1/In . x + 1/x)

d/dx(x)/In(x + 1/x)d/dx - d/dx(In(x + 1/x)/(In x + 1/x)²

Regra de Derivado para Quociente (u/v)'


lim (In x + 1/x)²/x/(x+1)x²
x→∞

lim d/dx(x) . (In x + 1/x)²/In (x + 1/x)d/dx - d/dx(In x + 1/x)
x→∞

Simplifique a soma: In (x + 1/x) - In(x + 1/x)

lim. (in x + 1/x)²/x/(x + 1)x²
x→∞

lim. x²(In x + 1/x)² + x(In x + 1/x)²
x→∞