Mister Exam
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How to use it?
- Limit of the function:
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Limit of -2+x^3+6*x
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Limit of ((-2+x)/x)^(2*x)
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Limit of (-2+x)*log(-2+x)
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Limit of -6+x^2+5*x
- Sum of series:
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tan(pi/(4*n))
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Identical expressions
- tan(pi/(four *n))
- tangent of ( Pi divide by (4 multiply by n))
- tangent of ( Pi divide by (four multiply by n))
- tan(pi/(4n))
- tanpi/4n
- tan(pi divide by (4*n))
Limit of the function tan(pi/(4*n))
The solution
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/ pi\ lim tan|---| n->oo \4*n/
$$\lim_{n \to \infty} \tan{\left(\frac{\pi}{4 n} \right)}$$
Limit(tan(pi/((4*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
$$\lim_{n \to \infty} \tan{\left(\frac{\pi}{4 n} \right)} = 0$$
$$\lim_{n \to 0^-} \tan{\left(\frac{\pi}{4 n} \right)} = \left\langle -\infty, \infty\right\rangle$$
More at n→0 from the left
$$\lim_{n \to 0^+} \tan{\left(\frac{\pi}{4 n} \right)} = \left\langle -\infty, \infty\right\rangle$$
More at n→0 from the right
$$\lim_{n \to 1^-} \tan{\left(\frac{\pi}{4 n} \right)} = 1$$
More at n→1 from the left
$$\lim_{n \to 1^+} \tan{\left(\frac{\pi}{4 n} \right)} = 1$$
More at n→1 from the right
$$\lim_{n \to -\infty} \tan{\left(\frac{\pi}{4 n} \right)} = 0$$
More at n→-oo
$$\lim_{n \to 0^-} \tan{\left(\frac{\pi}{4 n} \right)} = \left\langle -\infty, \infty\right\rangle$$
More at n→0 from the left
$$\lim_{n \to 0^+} \tan{\left(\frac{\pi}{4 n} \right)} = \left\langle -\infty, \infty\right\rangle$$
More at n→0 from the right
$$\lim_{n \to 1^-} \tan{\left(\frac{\pi}{4 n} \right)} = 1$$
More at n→1 from the left
$$\lim_{n \to 1^+} \tan{\left(\frac{\pi}{4 n} \right)} = 1$$
More at n→1 from the right
$$\lim_{n \to -\infty} \tan{\left(\frac{\pi}{4 n} \right)} = 0$$
More at n→-oo
The graph