What is the limit for cos (n pi) and sin (n pi)?

teng125
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may i know how to solve [ n^2 cos(n(pi)) ]/ n^2 + 42??

i have divided it by n^2 and get cos(n pi) / (42/n^2) and i can't solve already.pls help

what is the limit for cos (n pi) and sin (n pi)??
 
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Please use latex or make the expressions more clear, using paranthesis since a/b+c isn't the same as a/(b+c), you see?
Also, the limit for what (of course n here) going to what?

I'm guessing you mean the something which looks like

\mathop {\lim }\limits_{n \to ?} \frac{{n^2 \cos \left( {n\pi } \right)}}{{n^2 + 42}}
 
Last edited:
[ n^2 cos(n pi ) ] / (n^2 + 42) for n >1

what is the limit for cos (n pi) and sin (n pi) for n>1 also??
 
teng125 said:
what is the limit for cos (n pi) and sin (n pi) for n>1 also??
Again, the limit of those expressions for n going to what? To 0, pi, infinity, ...? You can't say "the limit for n>1"...
 
oh...yaya for n to infinity
 
teng125 said:
oh...yaya for n to infinity
Ah :smile:

In that case, the limit doesn't exist since sin as well as cos will keep oscilating between -1 and 1.
 
Except for sin(n pi) which is identically zero for all n.
 
daveb said:
Except for sin(n pi) which is identically zero for all n.
That's only true for integer values of n, we're letting n go to infinity here.
 
so,what is the answer for my first question??
 
  • #10
The answer to this?

\mathop {\lim }\limits_{n \to +\infty} \frac{{n^2 \cos \left( {n\pi } \right)}}{{n^2 + 42}}

The limit doesn't exist for the reason I gave above.
 
  • #11
TD said:
That's only true for integer values of n, we're letting n go to infinity here.
True, but I had always been taught that if you have a limit as "n" goes to infinity, then you are talking about integer values for "n". If you want all values, then you use "x" instead of n. Hence, the reason I made the statement.
 
  • #12
is it possible to obtain an answer if n goes to 1 ??
 
  • #13
teng125 said:
is it possible to obtain an answer if n goes to 1 ??
Sure, just fill in n = 1.
 
  • #14
Gah, shake head, look askance. limit as n goes to 1... n is taken to be integer valued, it makes no sense to ask 'as n tends to 1'. See Daveb's very important interjection, TD.
 
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