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cos(pi*n)/n
Limit of the function/ cos(pi*n)/n

Limit of the function cos(pi*n)/n

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You have entered [src] 
     /cos(pi*n)\
 lim |---------|
n->oo\    n    /
lim⁡n→∞(cos⁡(πn)n)\lim_{n \to \infty}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) 
Limit(cos(pi*n)/n, n, oo, dir='-')
Lopital's rule
There is no sense to apply Lopital's rule to this function since there is no indeterminateness of 0/0 or oo/oo type
The graph
02468-8-6-4-2-1010-2020
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Rapid solution [src] 
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Expand and simplify
Other limits n→0, -oo, +oo, 1
lim⁡n→∞(cos⁡(πn)n)=0\lim_{n \to \infty}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = 0
lim⁡n→0−(cos⁡(πn)n)=−∞\lim_{n \to 0^-}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = -\infty
More at n→0 from the left
lim⁡n→0+(cos⁡(πn)n)=∞\lim_{n \to 0^+}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = \infty
More at n→0 from the right
lim⁡n→1−(cos⁡(πn)n)=−1\lim_{n \to 1^-}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = -1
More at n→1 from the left
lim⁡n→1+(cos⁡(πn)n)=−1\lim_{n \to 1^+}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = -1
More at n→1 from the right
lim⁡n→−∞(cos⁡(πn)n)=0\lim_{n \to -\infty}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = 0
More at n→-oo
The graph
Limit of the function cos(pi*n)/n
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