Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (1+x^2+9*x)/(-5+2*x+7*x^2)
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Limit of (-tan(2*x)+sin(2*x))/x^3
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Limit of 3/n^4
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Limit of (1-cos(x)^2)/(x^2*sin(x)^2)
- Sum of series:
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cos(pi*n)/n
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Identical expressions
- cos(pi*n)/n
- co sinus of e of ( Pi multiply by n) divide by n
- cos(pin)/n
- cospin/n
- cos(pi*n) divide by n
Limit of the function cos(pi*n)/n
The solution
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/cos(pi*n)\ lim |---------| n->oo\ 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
Other limits n→0, -oo, +oo, 1
$$\lim_{n \to \infty}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = 0$$
$$\lim_{n \to 0^-}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = -\infty$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = \infty$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = -1$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = -1$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = 0$$
More at n→-oo
$$\lim_{n \to 0^-}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = -\infty$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = \infty$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = -1$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = -1$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(\frac{\cos{\left(\pi n \right)}}{n}\right) = 0$$
More at n→-oo
The graph