Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of 2+((-1+x)/(3+x))^x
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Limit of (-1+x)/(x+x^2)
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Limit of ((1+x)^4-(-1+x)^4)/((1+x)^4+(-1+x)^4)
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Limit of tan(6*x)/(3*x)
- Sum of series:
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sin(pi*n/3)
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Identical expressions
- sin(pi*n/ three)
- sinus of ( Pi multiply by n divide by 3)
- sinus of ( Pi multiply by n divide by three)
- sin(pin/3)
- sinpin/3
- sin(pi*n divide by 3)
Limit of the function sin(pi*n/3)
The solution
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/pi*n\ lim sin|----| n->oo \ 3 /
$$\lim_{n \to \infty} \sin{\left(\frac{\pi n}{3} \right)}$$
Limit(sin((pi*n)/3), 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
$$\lim_{n \to \infty} \sin{\left(\frac{\pi n}{3} \right)} = \left\langle -1, 1\right\rangle$$
$$\lim_{n \to 0^-} \sin{\left(\frac{\pi n}{3} \right)} = 0$$
More at n→0 from the left
$$\lim_{n \to 0^+} \sin{\left(\frac{\pi n}{3} \right)} = 0$$
More at n→0 from the right
$$\lim_{n \to 1^-} \sin{\left(\frac{\pi n}{3} \right)} = \frac{\sqrt{3}}{2}$$
More at n→1 from the left
$$\lim_{n \to 1^+} \sin{\left(\frac{\pi n}{3} \right)} = \frac{\sqrt{3}}{2}$$
More at n→1 from the right
$$\lim_{n \to -\infty} \sin{\left(\frac{\pi n}{3} \right)} = \left\langle -1, 1\right\rangle$$
More at n→-oo
$$\lim_{n \to 0^-} \sin{\left(\frac{\pi n}{3} \right)} = 0$$
More at n→0 from the left
$$\lim_{n \to 0^+} \sin{\left(\frac{\pi n}{3} \right)} = 0$$
More at n→0 from the right
$$\lim_{n \to 1^-} \sin{\left(\frac{\pi n}{3} \right)} = \frac{\sqrt{3}}{2}$$
More at n→1 from the left
$$\lim_{n \to 1^+} \sin{\left(\frac{\pi n}{3} \right)} = \frac{\sqrt{3}}{2}$$
More at n→1 from the right
$$\lim_{n \to -\infty} \sin{\left(\frac{\pi n}{3} \right)} = \left\langle -1, 1\right\rangle$$
More at n→-oo
The graph