Mister Exam
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How to use it?
- Limit of the function:
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Limit of (-3+sqrt(1+4*x))/(-2+x)
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Limit of x^2+(sqrt(1+3*x)-sqrt(1-2*x))/x
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Limit of ((11+7*x+7*x^2)/(14+9*x+13*x^2))^(4*x)
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Limit of (-1+x+6*x^2)/(1/2+x)
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Identical expressions
- x*acot(x/n^ two)
- x multiply by arcco tangent of gent of (x divide by n squared )
- x multiply by arcco tangent of gent of (x divide by n to the power of two)
- x*acot(x/n2)
- x*acotx/n2
- x*acot(x/n²)
- x*acot(x/n to the power of 2)
- xacot(x/n^2)
- xacot(x/n2)
- xacotx/n2
- xacotx/n^2
- x*acot(x divide by n^2)
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Similar expressions
- x*arccot(x/n^2)
Limit of the function x*acot(x/n^2)
The solution
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/ /x \\
lim |x*acot|--||
n->oo| | 2||
\ \n //
$$\lim_{n \to \infty}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right)$$
Limit(x*acot(x/n^2), 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
Other limits n→0, -oo, +oo, 1
$$\lim_{n \to \infty}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = \frac{\pi x}{2}$$
$$\lim_{n \to 0^-}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = x \operatorname{acot}{\left(\tilde{\infty} x \right)}$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = x \operatorname{acot}{\left(\tilde{\infty} x \right)}$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = x \operatorname{acot}{\left(x \right)}$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = x \operatorname{acot}{\left(x \right)}$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = \frac{\pi x}{2}$$
More at n→-oo
$$\lim_{n \to 0^-}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = x \operatorname{acot}{\left(\tilde{\infty} x \right)}$$
More at n→0 from the left
$$\lim_{n \to 0^+}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = x \operatorname{acot}{\left(\tilde{\infty} x \right)}$$
More at n→0 from the right
$$\lim_{n \to 1^-}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = x \operatorname{acot}{\left(x \right)}$$
More at n→1 from the left
$$\lim_{n \to 1^+}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = x \operatorname{acot}{\left(x \right)}$$
More at n→1 from the right
$$\lim_{n \to -\infty}\left(x \operatorname{acot}{\left(\frac{x}{n^{2}} \right)}\right) = \frac{\pi x}{2}$$
More at n→-oo