MHB Find the limit of 1/(n•cosn) as n tends to +∞.

[harpazo]

Find the limit of 1/(n•cosn) as n tends to +∞.

I say the following:

1/[(∞)cos (∞)]

1/∞ = 0

The limit is 0.

 

[Prove It]

Find the limit of 1/(n•cosn) as n tends to +∞.

I say the following:

1/[(∞)cos (∞)]

1/∞ = 0

The limit is 0.

Not even close I'm afraid. You can NOT plug in infinity as though it's a number!

You are trying to use the fact that the product of a function that goes to 0 (in this case, 1/n) with a BOUNDED function has a limit of 0. But 1/cos(x) is not bounded.

I would be inclined to think that the limit does not exist.

 

[harpazo]

Is there a more mathematical way to show the limit DNE?