$\displaystyle lim_{x\rightarrow{\infty}}(\frac{x+1}{x})^x$ therefore i applied l'hopital s rule to make $\displaystyle lim_{x\rightarrow{\infty}}\frac{-(x+1)^{x-1}}{x^2}$ I hope my differentiation is correct. So do i keep differentiating till I remove the x term from the denominator before i apply the limit?