What is the limit of cos of x as x approaches infinity?

[ellivis]

I understand that it osculates between 1 and -1, so is there a limit? Thanks for your help!

 

[mathsmanretired]

There is no limit. As you have said the cosine function continually moves between -1 and 1. This means that it does not get continually closer to some fixed value which is the definition of a limit.

 

[mathsmanretired]

There is no limit. As you have said the cosine function continually moves between -1 and 1. This means that it does not get continually closer to some fixed value which is the definition of a limit.

 

[mathsmanretired]

There is no limit. As you have said the cosine function continually moves between -1 and 1. This means that it does not get continually closer to some fixed value which is the definition of a limit.

 

[DragosDumitru]

The sense of limits approaching infinity in periodic functions

Very good question. I also asked myself how much is
lim (cos x) .
x-->∞

 

[Unregistered]

thanks

 

[Unregistered]

Lim (cos(1/x))^(x^2) as x--> infinity

 

[Unregistered]

I WOULD SAY THE ANSWER IS NO LIMIT, OR D.N.E. DOES NOT EXIST

 

[Unregistered]

i need help with a question:
the minute hand on a watch is 8mm long and the hour hand is 4mm long. how fast it the distance between the tips of the hands changing at 1 oclock? Thanks !

 

[Unregistered]

"Lim (cos(1/x))^(x^2) as x--> infinity"

Well, first look at what's put inside the cosine function. As x approaches infinity when you have 1/x, that's 1 being divided by VERY large numbers which we can thus conclude is equivalent to 0. Taking the cos(0) you'll get 1.

So now we have 1^(x^2) as x approaches infinity, but the (x^2) is now kinda useless at this point; 1 raised to any power is 1.

Thus, the limit is 1.