Evaluate the limit using L'Hospital's rule

Question

lim 2xe^(1/x)-2x

x--›oo

Answer 1

2x(e^1/x-1) = e^1/x-1/(1/2x)

The derivative of the numerator is -(1/x²)e^1/x

The derivative of the denominator is -1/(2x²)

The limit is 2.