Using limit laws to prove a limit

**devilray1018** · September 11th 2012, 05:41 AM

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.

**Prove It** · September 11th 2012, 05:50 AM

Originally Posted by devilray1018

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. $\displaystyle \begin{align*} \lim_{x \to 0}\sin{\frac{1}{x}} \end{align*}$ doesn't exist, but the function oscillates between -1 and 1. $\displaystyle \begin{align*} \lim_{x \to 0}x^4 = 0 \end{align*}$ . The product of 0 with something that oscillates is still 0.

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