Using limit laws prove that:
The limit as x approaches 0 of the function (x^4)(sin(1/x))=0
Please state each law used.
The limit of a product is equal to the product of the limits. $\displaystyle \displaystyle \begin{align*} \lim_{x \to 0}\sin{\frac{1}{x}} \end{align*}$ doesn't exist, but the function oscillates between -1 and 1. $\displaystyle \displaystyle \begin{align*} \lim_{x \to 0}x^4 = 0 \end{align*}$. The product of 0 with something that oscillates is still 0.