To evaluate the limit \(\lim_{{x \to \infty}} \frac{\arctan(x)}{x}\), let's follow these steps:

### Step 1: Behavior of \(\arctan(x)\) as \(x \to \infty\)
The arctangent function \(\arctan(x)\) approaches \(\frac{\pi}{2}\) as \(x \to \infty\). So:

\[
\lim_{{x \to \infty}} \arctan(x) = \frac{\pi}{2}
\]

### Step 2: Apply the limit to the given expression
Now, let's consider the ratio \(\frac{\arctan(x)}{x}\). As \(x\) grows very large:
- The numerator, \(\arctan(x)\), approaches \(\frac{\pi}{2}\), which is a constant.
- The denominator, \(x\), grows without bound.

This means we are essentially dividing a constant by an infinitely large number:

\[
\lim_{{x \to \infty}} \frac{\arct

Find the limit of arctan(x)/x as x approaches infinity. This problem involves calculus concepts like limits and the behavior of trigonometric functions, specifically the arctangent function. Suitable for Grades 11-12 students studying limits.

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