Mister Exam

Other calculators:

atan(x)/(1+x^2)
Limit of the function/ atan(x)/(1+x^2)

Limit of the function atan(x)/(1+x^2)

at →
v

For end points:

The graph:

from to

Piecewise:

The solution

You have entered [src] 
     /atan(x)\
 lim |-------|
x->oo|      2|
     \ 1 + x /
lim⁡x→∞(atan⁡(x)x2+1)\lim_{x \to \infty}\left(\frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\right) 
Limit(atan(x)/(1 + 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
02468-8-6-4-2-10101.0-1.0
Plot the graph
Rapid solution [src] 
0
00
Expand and simplify
Other limits x→0, -oo, +oo, 1
lim⁡x→∞(atan⁡(x)x2+1)=0\lim_{x \to \infty}\left(\frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\right) = 0
lim⁡x→0−(atan⁡(x)x2+1)=0\lim_{x \to 0^-}\left(\frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\right) = 0
More at x→0 from the left
lim⁡x→0+(atan⁡(x)x2+1)=0\lim_{x \to 0^+}\left(\frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\right) = 0
More at x→0 from the right
lim⁡x→1−(atan⁡(x)x2+1)=π8\lim_{x \to 1^-}\left(\frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\right) = \frac{\pi}{8}
More at x→1 from the left
lim⁡x→1+(atan⁡(x)x2+1)=π8\lim_{x \to 1^+}\left(\frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\right) = \frac{\pi}{8}
More at x→1 from the right
lim⁡x→−∞(atan⁡(x)x2+1)=0\lim_{x \to -\infty}\left(\frac{\operatorname{atan}{\left(x \right)}}{x^{2} + 1}\right) = 0
More at x→-oo
The graph
Limit of the function atan(x)/(1+x^2)
    © Mister Exam – Calculator