Final answer:
The limit of arctan(1/3) as x approaches infinity is simply the value of arctan(1/3), which is a constant angle. The options provided do not accurately represent the value, and a calculator is needed for the exact angle.
Step-by-step explanation:
The question asks to evaluate the limit of the function arctan(1/3) as x approaches infinity. The function arctan(1/3) is constant since it does not depend on x, meaning the limit as x approaches infinity is simply the value of the function itself. Therefore, the answer to the question is the arctan of 1/3, which is a constant angle whose tangent is 1/3.
Since the arctan function is defined for all real numbers and the arctan of 0 is 0, the arctan of any real number is a number between -π/2 and π/2. Hence, the correct answer is the arctan of 1/3, which can be calculated using a calculator or by recognizing it as a known angle if applicable. However, the provided options (A, B, C, D) do not include the correct value, assuming a typo, the answer closest to the actual value would be the arctan of 1/3, but none of the options correctly represent this value.