We know that cosines are always between -1 and +1.

`-1<=cos(4x)<=+1`

So we can say;

`-1<=[lim_(xrarroo) cos(4x)]<=+1`

Let us say `lim_(xrarroo)cos4x = p` where `-1<=p<=+1.`

`lim_(xrarroo)(cos(4x))/x = p/oo = 0`

** So the answer is** `lim_(xrarroo)(cos(4x))/x = 0`

**Further Reading**

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