Mister Exam
Other calculators:
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How to use it?
- Limit of the function:
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Limit of (2+sqrt(x)-sqrt(2))/x
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Limit of (2-x)/(-1+x)^2
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Limit of e^(x^2)-cos(x)/x^2
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Limit of (-44-x+3*x^2)/(-16+x^2)
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Identical expressions
- four *atan(x/ two)
- 4 multiply by arc tangent of gent of (x divide by 2)
- four multiply by arc tangent of gent of (x divide by two)
- 4atan(x/2)
- 4atanx/2
- 4*atan(x divide by 2)
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Similar expressions
- 2*x^4*atan(x)/(2+x^4+sin(x))
- 4*arctan(x/2)
Limit of the function 4*atan(x/2)
The solution
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/ /x\\ lim |4*atan|-|| x->oo\ \2//
$$\lim_{x \to \infty}\left(4 \operatorname{atan}{\left(\frac{x}{2} \right)}\right)$$
Limit(4*atan(x/2), 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
$$\lim_{x \to \infty}\left(4 \operatorname{atan}{\left(\frac{x}{2} \right)}\right) = 2 \pi$$
$$\lim_{x \to 0^-}\left(4 \operatorname{atan}{\left(\frac{x}{2} \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(4 \operatorname{atan}{\left(\frac{x}{2} \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(4 \operatorname{atan}{\left(\frac{x}{2} \right)}\right) = 4 \operatorname{atan}{\left(\frac{1}{2} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(4 \operatorname{atan}{\left(\frac{x}{2} \right)}\right) = 4 \operatorname{atan}{\left(\frac{1}{2} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(4 \operatorname{atan}{\left(\frac{x}{2} \right)}\right) = - 2 \pi$$
More at x→-oo
$$\lim_{x \to 0^-}\left(4 \operatorname{atan}{\left(\frac{x}{2} \right)}\right) = 0$$
More at x→0 from the left
$$\lim_{x \to 0^+}\left(4 \operatorname{atan}{\left(\frac{x}{2} \right)}\right) = 0$$
More at x→0 from the right
$$\lim_{x \to 1^-}\left(4 \operatorname{atan}{\left(\frac{x}{2} \right)}\right) = 4 \operatorname{atan}{\left(\frac{1}{2} \right)}$$
More at x→1 from the left
$$\lim_{x \to 1^+}\left(4 \operatorname{atan}{\left(\frac{x}{2} \right)}\right) = 4 \operatorname{atan}{\left(\frac{1}{2} \right)}$$
More at x→1 from the right
$$\lim_{x \to -\infty}\left(4 \operatorname{atan}{\left(\frac{x}{2} \right)}\right) = - 2 \pi$$
More at x→-oo
The graph