Find the limits

Question

lim x approaches 0 ( (1/(e^x-1)) -1/x )

find =

Answer 1

Reading the given limit as lim_(x→0+)[1/(e^x − 1) − 1/x] and sampling with x equal to 1×10^-11, a calculator gives 1×10¹¹ − 1×10¹¹ or 0 as the result.

Reading the given limit as lim_(x→0+)[1/(e^(x−1)) − 1/x] and sampling with x equal to 1×10^-11, a calculator gives

2.718281828 − 1/10^-11 or -10¹¹, which indicates negative infinity as the result.