What is the limit of (1- e^(x) )/(1+2e^x) as x approaches infinity. Steps PLEASE.

Question

What is the limit of
`(1- e^(x) )/(1+2e^x)` as x approaches infinity. Steps PLEASE.

Answer 1

Hello,


`\lim_(x \to \infty) (1-e^x)/(1+2e^x)\\ = \lim_(x \to \infty) ( (1-e^x)/(e^x))/( (1+2e^x)/(e^x))\\ = \lim_(x \to \infty) ( (1)/(e^x)-1)/((1)/(e^x)+2)\\ = (0-1)/(0+2) =- (1)/(2)`