The document you've uploaded is an assignment booklet for a Calculus course (BMTC-131) with a series of calculus problems. Here is a breakdown of the types of problems in the assignment:

1. True/False questions with proofs or counterexamples:

   • Analyze statements regarding odd functions, logarithmic differentiation, differentiability, inflection points, and increasing/decreasing behavior.

2. Differentiation and Integration:

   • Finding derivatives, evaluating integrals, and solving limits.

3. Curve tracing:

   • Trace a given curve by analyzing its properties.

4. Parametric curves:

   • Find the length of parametric curves and calculate the angle between curves.

5. Integration techniques:

   • Apply methods like Simpson's rule, integration of polynomial expressions, and solving using limits.

6. Applications of calculus:

   • Find areas under curves, largest possible domains, and expand functions in power series.

7. Rolle's Theorem and Continuity:

   • Verify Rolle’s theorem for a given function and check the continuity at a particular point.

8. Numerical methods:

   • Use the Trapezoidal rule to evaluate an integral.

9. Maclaurin series and extrema:

   • Approximate functions using series and find minimum values using trigonometric identities.

10. Advanced calculus:

    • Solve problems involving normal slopes, points of inflection, and integrals involving exponential and rational functions.

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Would you like help with a specific problem from the assignment? Feel free to let me know which one you want to focus on!

Here are 5 related questions that may expand on this:

1. How do you trace a curve step-by-step using calculus?
2. What are the steps to verify Rolle's Theorem?
3. Can you explain Simpson's rule for approximating integrals?
4. How can you find the area under a curve using definite integrals?
5. What is the Maclaurin series, and how is it applied?

Tip: When solving problems involving the derivative, always check if the function is continuous and differentiable in the domain of interest.