Question

What's the value of the limit? `lim_(x->oo) (2*e^3/(e^2+1))^(1/x)`

Answer 1

`1`

Explanation:

Notice, `x^0=1\forall \ \ x\ne 0`

Assuming `x\to \infty`, then we have

`\lim_{x\to \infty}(2\frac{e^3}{e^2+1})^{1/x}`

`=(2\frac{e^3}{e^2+1})^{0}`

`=1`