arctan1x2x

arctan1x2x refers to the mathematical function arctangent evaluated at the expression 1/x^2x. The arctangent function, also known as inverse tangent or tan^-1, is the inverse of the tangent function. For any real number y, arctan(y) is the angle x such that tan(x) = y, and -pi/2 < x < pi/2.

In the expression arctan1x2x, the argument of the arctangent function is 1 divided by x raised to the power of 2x. This expression is defined for real values of x where x^2x is not zero and the result of 1/x^2x is within the domain of the arctangent function, which is all real numbers. The term x^2x itself involves exponentiation where the base and the exponent are variables. The behavior of x^2x depends significantly on the value of x. For positive x, x^2x is well-defined. For x=0, 0^0 is often considered indeterminate, but in some contexts, it is defined as 1. For negative x, x^2x can lead to complex numbers or be undefined depending on the specific value and conventions used.

Therefore, the function arctan1x2x is typically considered for positive real numbers x, where 1/x^2x yields a real number. The output of this function will be an angle in radians, specifically between -pi/2 and pi/2. The graphical representation of arctan1x2x would show how the output angle changes as the input x varies.