find d limit as x ->∞

{x +e^x +e^2x}^(1/x)

plz show step

(e2x)1/x < (x+ex+e2x)1/x < (2e2x)1/x

e2 < (x+ex+e2x)1/x < 21/xe2

Now take the limits, and since 21/x-> 1,

e2 < (x+ex+e2x)1/x < e2

so

(x+ex+e2x)1/x = e2

Or, you can take the log of the limit, and then use l'Hospital's Rule