Question 1028776
0 =< (x+1)/e^x =< (x+1)/(x^2 + 1), for all the values of x >= 0

And Limit x approaches to inf (x+1)/(x^2 + 1) = limit (1/x + 1/x^2)/(1 + 1/x^2) 
                              =(0+0)/(1+0) = 0.

So by Boundness Theorem the Limit proposed is also 0.