To determine

To evaluate : limx→−∞xln(1−1x)

Answer

limx→−∞xln(1−1x)=−1

Explanation

The following limit is in indeterminate form, Applying l’Hospital’s Rule, we get

limx→−∞xln(1−1x)=limx→−∞ln(1−1x)1x =limx→−∞11−1x×1x2−1x2=−limx→−∞11−1x=−11−0=−1

Conclusion: The value of the limit is limx→−∞xln(1−1x)=−1