What is the limit of $(x / cos (-3x))$ as x approaches infinity?

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Answer 1 · 2016-07-08T22:00:01

the limit wiil alternate between $-oo$ and $oo$

$lim_{x to oo} (x / cos(-3x))$

$=lim_{x to oo} (x / cos (3x))$ as $cos psi = cos (- psi)$

$= 1/( cos (3x)) lim_{x to oo} x$

because cos (3 x) is bounded and periodic, ie $cos(-3 x) in [-1,1]$ it can be taken out of the limit

but note that, as $x to oo$ , the limit wiil alternate between $-oo$ and $oo$ as the cosine term changes sign with frequency $3/pi$

What is the limit of (x / cos (-3x)) (x / cos (-3x)) as x approaches infinity?