Using limit laws to prove a limit

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.

Quote:

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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.

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The limit of a product is equal to the product of the limits. doesn't exist, but the function oscillates between -1 and 1. . The product of 0 with something that oscillates is still 0.