Question

lim x->infinity (e^x+x)^(2/x)

Answer 1

Hint : factor out \(e^x\)

Answer 2

that may not be a very useful hint, one sec..

Answer 3

I was thinking maybe manipulating it into an indeterminate form for l'hopitals rule
\( (e^x + x)^{2/x}= e^{\ln (e^x+x)^{2/x}} =e^{2/x \cdot \ln (e^x + x) }\)
and taking the limit would mean taking the limit of that power, which needs l'hopital's rule

Answer 4

nice thats working out smoothly ! xD

Answer 5

Isn't this like infinity^0

Answer 6

I think it's 2. Maybe...

Answer 7

It's actually \(\mathrm{e}^2\)

Answer 8

yes \(\lim f(x_n) = f(\lim x_n)\) as e^x is a continuous function

Answer 9

Yeah e^2 seems more legit
Also the graph agrees

Answer 10

\[\lim\limits_{x\to \infty} \left(e^x+x\right)^{2/x} = e^{\lim\limits_{x\to \infty} ~\ln \left(e^x+x\right)^{2/x} }\]

Answer 11

Oh right lnL=2 so L=e^2