Provide a list of questions to motivate the study of calculus.
1. What are the different representations of functions and models?
2. How are limits and derivatives related to the problems of tangent lines and velocity?
3. What are the basic rules of differentiation, including exponential, logarithmic, and inverse trigonometric functions?
4. How can derivatives be applied to finding extreme values and analyzing families of curves?
5. What are the problems of area and distance that motivate the study of definite integrals?
6. How can integrals be applied to finding area, volume, work, and average value?
7. What are the standard techniques of integration and how can they be applied to various contexts?
8. What are some additional applications of integration, such as polar coordinates, vectors, and differential equations?