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what is the limit of:  (cos 4x)/x as the lim x goes to - infinity 

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ntretheway | (Level 2) Adjunct Educator

Posted September 18, 2013 at 4:52 AM via web

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what is the limit of:  (cos 4x)/x as the lim x goes to - infinity 

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jeew-m | College Teacher | (Level 1) Educator Emeritus

Posted September 18, 2013 at 5:00 AM (Answer #1)

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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`

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