[tex]f(x)=e^x-x+2 \\ f'(x)=e^x-1 \\ \lim_{x \to \infty} \frac{f(x)}{f'(x)}= \lim_{x \to \infty} \frac{e^x-x+2}{e^x-1 \\ } \\ (L'Hopital) \\ = \lim_{x \to \infty} \frac{e^x-1}{e^x} \\ = \lim_{x \to \infty} a_n \frac{e^x(1- \frac{1}{e^x}) }{e^x} =1 [/tex]
