To determine
To evaluate: the limit limx→0(1−2x)1/x
Answer
The value of the limit is limx→0(1−2x)1/x=e−2
Explanation
We know that limx→0(1+nx)1/x=en
(The given limit is in indeterminate form, so we have to use l’Hospital’s Rule, and carry out the simplification).
Comparing from the formula, we see that n=−2
Therefore limx→0(1−2x)1/x=e−2
Conclusion: limx→0(1−2x)1/x=e−2