It seems like you are trying to express a function \( h(t) \), but the formatting of the equation isn't clear. From what I see, it looks like you might want to express a fraction involving powers of \( t \). Could you confirm if this is what you're trying to write?

Is the function something like this?

\[
h(t) = \frac{t^3}{t^6 + 1}
\]

If this is correct, I can help you analyze and solve the equation, or provide further details like finding limits, derivatives, or behavior as \( t \to \infty \). Let me know if you need any specific assistance with this equation.

Would you like me to proceed with solving or analyzing this?

### 5 Related Questions:
1. What is the derivative of \( h(t) = \frac{t^3}{t^6 + 1} \)?
2. What happens to \( h(t) \) as \( t \to \infty \)?
3. How can we find the critical points of \( h(t) \)?
4. What is the behavior of \( h(t) \) for large and small values of \( t \)?
5. How would you integrate \( h(t) \)?

### Tip:
To simplify the analysis of rational functions, look at the degrees of the polynomials in the numerator and denominator to quickly understand behavior as \( t \) becomes large or small.

Explore the rational function h(t) = t^3 / (t^6 + 1), including its derivative, limits, and behavior as t approaches infinity. This problem involves advanced calculus concepts suitable for Grades 11-12 or first-year calculus students.

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