Question

What is lim (x -> 0) of (e^x) / x

Thank you!!

Answer 1

The limit of a quotient is the quotient of the limits.

limit ( e ^ x ) / x as x -> 0 =

[ limit ( e ^ x ) as x -> 0 ] / [ limit x as x -> 0 ] =

1 / 0 which is undefined.

limit ( e ^ x ) / x as x -> 0 = + OR - infinity

OR

limit ( e ^ x ) / x as x -> 0- = - infinity

limit ( e ^ x ) / x as x -> 0+ = infinity