san14 san14
  • 07-12-2017
  • Mathematics
contestada

Find the limit please

Find the limit please class=

Respuesta :

wizard123
wizard123 wizard123
  • 07-12-2017
use identity
[tex]\lim f(x) = \lim e^{ln f(x)} = e^{\lim ln f(x)}[/tex]

The limit now is:
[tex]e^{\lim ln x^{e^{-x}}} \\ \\ =e^{\lim e^{-x} ln x} \\ \\ =e^{\lim \frac{ln x}{e^x}} \\ \\ =e^0 = 1[/tex]

The limit of lnx/e^x is 0 because e^x is exponentially greater than ln(x) as x
goes to infinity.  You could also use L'Hopitals rule here to obtain the limit of 0.
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