evaluate 0 (e - (1+x) )/x
i used l'hopitals rule for the case but i get the limit as infinity but when i graph this function the lim is 1.25... any sort of insight would be helpful.
The derivative is a product of two functions. The limit of the first function in the product is readily recognised as e. The limit of the second function is 1/2: see limit of 1/(x(1+x)) - Log[1+x]/x^2 as x approaches 0 - Wolfram|Alpha (click on show steps).