lim x-->0
also it says assume as x--> 0 xlnx --> 0
my answer is its 0/0 type since anything to the power of 0 is 1 including ?
using L H Rule you get
then again the anything to the power of zero thing gives you that --> 1
There is no such "thing". 0 to the 0 power is NOT 1. What L'Hopital's rule says is that the limit is the same as the limit of . To find that limit, let so that . If you are allowed to "assume" the limit of that is 0, then the limit of ln(y) is 0 so the limit of is, indeed, 1.
Actually the limit $\displaystyle \begin{align*} \lim_{x \to 0} x\ln{(x)} \end{align*}$ DOES NOT EXIST as $\displaystyle \begin{align*} x\ln{(x)} \end{align*}$ is only defined where $\displaystyle \begin{align*} x > 0 \end{align*}$. However, $\displaystyle \begin{align*} \lim_{x \to 0^+} x\ln{(x)} = 0 \end{align*}$.