How do I solve this limit when x -> 0: (2^x-1)/x

The answer is ln(2) according to my book, but I have no idea how to get there

Guest Jun 17, 2014

#2**+5 **

Chris has reminded me that L'Hopital's rule may also be used here.

This says differentiate the numerator and denominator separately, and form the ratio of the resulting two expressions, then take the limit of this as x tends to zero.

So, if you are familiar with L'Hopital's rule, this would be the better approach.

Alan
Jun 18, 2014

#2**+5 **

Best Answer

Chris has reminded me that L'Hopital's rule may also be used here.

This says differentiate the numerator and denominator separately, and form the ratio of the resulting two expressions, then take the limit of this as x tends to zero.

So, if you are familiar with L'Hopital's rule, this would be the better approach.

Alan
Jun 18, 2014