An ApproachtoCALCULUSThe Lessons 11. Continuous versus discrete The definition of a "continuous" quantity. 12. Limits A sequence of rational numbers. The definition of "a function is continuous at a value of x." 14. Infinity (∞) The definition of "a variable becomes infinite." 15. The derivative The slope of a tangent line to a curve. The derivative of a constant. The derivative of y = x. 17. The chain rule The derivative of a function of a function. 18. More rules for derivatives The quotient rule. 19. Instantaneous velocity and Related rates The second derivative. 10. Maximum and minimum values The turning points of a graph. Critical values. 11. Applications of maximum and minimum values 12. Derivatives of trigonometric functions 13. Derivatives of inverse trigonometric functions 14. Derivatives of exponential and logarithmic functions The system of natural logarithms. 15. Evaluating e Appendix 1. Rational and irrational numbers Appendix 2. Are the real numbers really numbers? Appendix 3. Is a line really composed of points?
