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. Topics include: 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; and non-Cartesian coordinate systems.
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. Topics include: 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; and non-Cartesian coordinate systems.