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The given function is:

\[
f(x) = \frac{1}{(x+1)^2}, \quad \text{where} \quad x \geq 0
\]

This is a rational function that involves a denominator of \((x+1)^2\). It is defined for \(x \geq 0\) as specified.

### Key features of this function:
1. **Domain**: The function is defined for \(x \geq 0\). The expression in the denominator, \((x+1)^2\), is always positive and does not cause division by zero for \(x \geq 0\).
   
2. **Asymptotes**: 
   - **Horizontal asymptote**: As \(x \to \infty\), the function approaches 0 because the denominator grows much faster than the numerator. Thus, \(y = 0\) is a horizontal asymptote.
   - **No vertical asymptote**: Since the denominator does not become zero for \(x \geq 0\), there is no vertical asymptote.

3. **Behavior near \(x = 0\)**: When \(x = 0\), \(f(0) = \frac{1}{(0+1)^2} = 1\). The function is decreasing as \(x\) increases from 0 onwards.

4. **Monotonicity**: The function is strictly decreasing for all \(x \geq 0\) because as \(x\) increases, the denominator increases, making \(f(x)\) smaller.

Would you like a detailed derivative analysis or more information on another feature of the function?

### Relative Questions:
1. What is the derivative of \(f(x) = \frac{1}{(x+1)^2}\)?
2. How would you find the minimum value of the function \(f(x)\)?
3. Can you explain the concavity of this function based on the second derivative?
4. What is the behavior of the function as \(x \to 0^+\)?
5. How would you integrate the function \(f(x)\) over a given interval?

### Tip:
Always check for asymptotic behavior in rational functions—both horizontal and vertical asymptotes give important information about the limits of the function.

Explore the detailed behavior of the rational function f(x) = 1 / (x + 1)^2, defined for x ≥ 0. Key topics include domain, asymptotic behavior, monotonicity, and function limits. This solution is suitable for students in Grades 10-12.

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