how to solve this indeterminate form ( use L'hospital) , please show me the steps

Question

anonymous · Answer

$$\lim_{x \rightarrow o}( \sin x \log x^2)$$

ganeshie8 · Answer

$$\large  \lim_{x \rightarrow 0} \left( \sin x \log x^2\right) $$

$$\large  \lim_{x \rightarrow 0} \left( \dfrac{\sin x}{x} \right)\times    \lim_{x \rightarrow 0}\left(x\log x^2\right) $$

ganeshie8 · Answer

$$\large    \lim_{x \rightarrow 0}\left(x\log x^2\right) $$

ganeshie8 · Answer

$$\large    \lim_{x \rightarrow 0}\left( \dfrac{\log x^2}{1/x}\right) $$

ganeshie8 · Answer

use L'Hopital now

ganeshie8 · Answer

$$\large    \lim_{x \rightarrow 0}\left( \dfrac{1/x^2 (2x)}{-1/x^2}\right) $$


$$\large    \lim_{x \rightarrow 0}\left(-2x\right) $$

$$\large   0$$

ganeshie8 · Answer

see if that makes more or less sense..

anonymous · Answer

you are amazing @ganeshie8  .. made the sum look so easy :) ..thanks a lot !!

ganeshie8 · Answer

yw :)