Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of sin(pi/n)
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Limit of cot(n)
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Limit of x^5
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Limit of sec(x)
- Sum of series:
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sin(pi/n)
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Identical expressions
- sin(pi/n)
- sinus of ( Pi divide by n)
- sinpi/n
- sin(pi divide by n)
Limit of the function sin(pi/n)
The solution
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/pi\ lim sin|--| n->oo \n /
$$\lim_{n \to \infty} \sin{\left(\frac{\pi}{n} \right)}$$
Limit(sin(pi/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
$$\lim_{n \to \infty} \sin{\left(\frac{\pi}{n} \right)} = 0$$
$$\lim_{n \to 0^-} \sin{\left(\frac{\pi}{n} \right)} = \left\langle -1, 1\right\rangle$$
More at n→0 from the left
$$\lim_{n \to 0^+} \sin{\left(\frac{\pi}{n} \right)} = \left\langle -1, 1\right\rangle$$
More at n→0 from the right
$$\lim_{n \to 1^-} \sin{\left(\frac{\pi}{n} \right)} = 0$$
More at n→1 from the left
$$\lim_{n \to 1^+} \sin{\left(\frac{\pi}{n} \right)} = 0$$
More at n→1 from the right
$$\lim_{n \to -\infty} \sin{\left(\frac{\pi}{n} \right)} = 0$$
More at n→-oo
$$\lim_{n \to 0^-} \sin{\left(\frac{\pi}{n} \right)} = \left\langle -1, 1\right\rangle$$
More at n→0 from the left
$$\lim_{n \to 0^+} \sin{\left(\frac{\pi}{n} \right)} = \left\langle -1, 1\right\rangle$$
More at n→0 from the right
$$\lim_{n \to 1^-} \sin{\left(\frac{\pi}{n} \right)} = 0$$
More at n→1 from the left
$$\lim_{n \to 1^+} \sin{\left(\frac{\pi}{n} \right)} = 0$$
More at n→1 from the right
$$\lim_{n \to -\infty} \sin{\left(\frac{\pi}{n} \right)} = 0$$
More at n→-oo
The graph