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