Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (4+x^2)/(-6+2*x)
-
Limit of ((1+x)/(1+2*x))^x
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Limit of (n/(1+n))^(5+3*n)
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Limit of (9^x-8^x)/asin(3*x)
- Graphing y =:
- x*atan(x)
- Derivative of:
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x*atan(x)
- Integral of d{x}:
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x*atan(x)
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Identical expressions
- x*atan(x)
- x multiply by arc tangent of gent of (x)
- xatan(x)
- xatanx
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Similar expressions
- x*atan(x/3)
- x*arctan(x)
- x*arctanx
Limit of the function x*atan(x)
The solution
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lim (x*atan(x)) x->oo
$$\lim_{x \to \infty}\left(x \operatorname{atan}{\left(x \right)}\right)$$
Limit(x*atan(x), x, 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 x→0, -oo, +oo, 1
$$\lim_{x \to \infty}\left(x \operatorname{atan}{\left(x \right)}\right) = \infty$$
$$\lim_{x \to 0^-}\left(x \operatorname{atan}{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \operatorname{atan}{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \operatorname{atan}{\left(x \right)}\right) = \frac{\pi}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \operatorname{atan}{\left(x \right)}\right) = \frac{\pi}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \operatorname{atan}{\left(x \right)}\right) = \infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x \operatorname{atan}{\left(x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x \operatorname{atan}{\left(x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x \operatorname{atan}{\left(x \right)}\right) = \frac{\pi}{4}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x \operatorname{atan}{\left(x \right)}\right) = \frac{\pi}{4}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x \operatorname{atan}{\left(x \right)}\right) = \infty$$
More at x→-oo
The graph