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atan(x)
Limit of the function/ atan(x)

Limit of the function atan(x)

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The solution

You have entered [src] 
 lim atan(x)
x->oo
lim⁡x→∞atan⁡(x)\lim_{x \to \infty} \operatorname{atan}{\left(x \right)} 
Limit(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
02468-8-6-4-2-10105-5
Plot the graph
Rapid solution [src] 
pi
--
2
π2\frac{\pi}{2}
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞atan⁡(x)=π2\lim_{x \to \infty} \operatorname{atan}{\left(x \right)} = \frac{\pi}{2}
lim⁡x→0−atan⁡(x)=0\lim_{x \to 0^-} \operatorname{atan}{\left(x \right)} = 0
More at x→0 from the left
lim⁡x→0+atan⁡(x)=0\lim_{x \to 0^+} \operatorname{atan}{\left(x \right)} = 0
More at x→0 from the right
lim⁡x→1−atan⁡(x)=π4\lim_{x \to 1^-} \operatorname{atan}{\left(x \right)} = \frac{\pi}{4}
More at x→1 from the left
lim⁡x→1+atan⁡(x)=π4\lim_{x \to 1^+} \operatorname{atan}{\left(x \right)} = \frac{\pi}{4}
More at x→1 from the right
lim⁡x→−∞atan⁡(x)=−π2\lim_{x \to -\infty} \operatorname{atan}{\left(x \right)} = - \frac{\pi}{2}
More at x→-oo
The graph
Limit of the function atan(x)
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