Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (-2+x)/(-2+x^2-x)
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Limit of cos(5*x)*sin(2*x)/tan(x)
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Limit of 3*sin(x)^2/(4*x)
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Limit of log(1+e^x)
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Identical expressions
- x-atan(five *x)
- x minus arc tangent of gent of (5 multiply by x)
- x minus arc tangent of gent of (five multiply by x)
- x-atan(5x)
- x-atan5x
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Similar expressions
- x+atan(5*x)
- pi/2-atan(2*x)-atan(5*x)-atan(10*x)
- x-arctan(5*x)
Limit of the function x-atan(5*x)
The solution
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lim (x - atan(5*x)) x->oo
$$\lim_{x \to \infty}\left(x - \operatorname{atan}{\left(5 x \right)}\right)$$
Limit(x - atan(5*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
$$\lim_{x \to \infty}\left(x - \operatorname{atan}{\left(5 x \right)}\right) = \infty$$
$$\lim_{x \to 0^-}\left(x - \operatorname{atan}{\left(5 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x - \operatorname{atan}{\left(5 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x - \operatorname{atan}{\left(5 x \right)}\right) = 1 - \operatorname{atan}{\left(5 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x - \operatorname{atan}{\left(5 x \right)}\right) = 1 - \operatorname{atan}{\left(5 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x - \operatorname{atan}{\left(5 x \right)}\right) = -\infty$$
More at x→-oo
$$\lim_{x \to 0^-}\left(x - \operatorname{atan}{\left(5 x \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(x - \operatorname{atan}{\left(5 x \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(x - \operatorname{atan}{\left(5 x \right)}\right) = 1 - \operatorname{atan}{\left(5 \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(x - \operatorname{atan}{\left(5 x \right)}\right) = 1 - \operatorname{atan}{\left(5 \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(x - \operatorname{atan}{\left(5 x \right)}\right) = -\infty$$
More at x→-oo
The graph