arctg(x)

+ inequation

Solve the inequality!

A inequation with variable

The solution

You have entered [src]

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atan(x) < \/ 3 

$$\operatorname{atan}{\left(x \right)} < \sqrt{3}$$

atan(x) < sqrt(3)

Detail solution

Given the inequality:
$$\operatorname{atan}{\left(x \right)} < \sqrt{3}$$
To solve this inequality, we must first solve the corresponding equation:
$$\operatorname{atan}{\left(x \right)} = \sqrt{3}$$
Solve:
This equation has no roots,
this inequality is executed for any x value or has no solutions
check it
subtitute random point x, for example

x0 = 0

$$\operatorname{atan}{\left(0 \right)} < \sqrt{3}$$

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0 < \/ 3 
    

so the inequality is always executed

Solving inequality on a graph

Rapid solution [src]

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And\x > -oo, x < oo, x != tan\\/ 3 //

$$x > -\infty \wedge x < \infty \wedge x \neq \tan{\left(\sqrt{3} \right)}$$

(x > -oo)∧(x < oo)∧(Ne(x, tan(sqrt(3))))

Rapid solution 2 [src]

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(-oo, tan\\/ 3 /) U (tan\\/ 3 /, oo)

$$x\ in\ \left(-\infty, \tan{\left(\sqrt{3} \right)}\right) \cup \left(\tan{\left(\sqrt{3} \right)}, \infty\right)$$

x in Union(Interval.open(-oo, tan(sqrt(3))), Interval.open(tan(sqrt(3)), oo))