These 50 challenging calculus problems involve applying a variety of calculus skills. The exercises come with a good range of difficulty from milder challenges to very hard problems. On the page following each problem you can find the full solution with explanations.
- derivatives of polynomials, trig functions, exponentials, and logarithms
- the chain rule, product rule, and quotient rule
- second derivatives (and beyond)
- applications such as related rates, extreme values, and optimization
- limits, including l'Hopital's rule
- antiderivatives of polynomials, trig functions, exponentials, and logarithms
- definite and indefinite integrals
- techniques of integration, including substitution, trig sub, and integration by parts
- multiple integrals
- non-Cartesian coordinate systems
