Question

calcule o limite da forma: 0.infinito

Answer 1

a)

Lim ( x * e^(1/x))

x-->0⁺

Lim   (e^(1/x))/(1/x)

x-->0⁺

Usando L'Hopital

d(e^(1/x)) / dx  = (1/x)' * e^(1/x) = (-1/x²) * e^(1/x)

d(1/x)/dx = (-1/x²)

Lim   (-1/x²) * e^(1/x)/(-1/x²)

x-->0+

Lim    e^(1/x) =e^(∞) = ∞

x-->0+