Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of x^(4/x)
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Limit of (-6+x^2-x)/(-4+x^2)
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Limit of (-6+x^2-x)/(-21+x+2*x^2)
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Limit of e^(3-x)*(-2+x)
- Sum of series:
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cos(1/n)
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Identical expressions
- cos(one /n)
- co sinus of e of (1 divide by n)
- co sinus of e of (one divide by n)
- cos1/n
- cos(1 divide by n)
Limit of the function cos(1/n)
The solution
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/1\ lim cos|-| n->oo \n/
$$\lim_{n \to \infty} \cos{\left(\frac{1}{n} \right)}$$
Limit(cos(1/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
$$\lim_{n \to \infty} \cos{\left(\frac{1}{n} \right)} = 1$$
$$\lim_{n \to 0^-} \cos{\left(\frac{1}{n} \right)} = \left\langle -1, 1\right\rangle$$
More at n→0 from the left
$$\lim_{n \to 0^+} \cos{\left(\frac{1}{n} \right)} = \left\langle -1, 1\right\rangle$$
More at n→0 from the right
$$\lim_{n \to 1^-} \cos{\left(\frac{1}{n} \right)} = \cos{\left(1 \right)}$$
More at n→1 from the left
$$\lim_{n \to 1^+} \cos{\left(\frac{1}{n} \right)} = \cos{\left(1 \right)}$$
More at n→1 from the right
$$\lim_{n \to -\infty} \cos{\left(\frac{1}{n} \right)} = 1$$
More at n→-oo
$$\lim_{n \to 0^-} \cos{\left(\frac{1}{n} \right)} = \left\langle -1, 1\right\rangle$$
More at n→0 from the left
$$\lim_{n \to 0^+} \cos{\left(\frac{1}{n} \right)} = \left\langle -1, 1\right\rangle$$
More at n→0 from the right
$$\lim_{n \to 1^-} \cos{\left(\frac{1}{n} \right)} = \cos{\left(1 \right)}$$
More at n→1 from the left
$$\lim_{n \to 1^+} \cos{\left(\frac{1}{n} \right)} = \cos{\left(1 \right)}$$
More at n→1 from the right
$$\lim_{n \to -\infty} \cos{\left(\frac{1}{n} \right)} = 1$$
More at n→-oo
The graph