An Approach to CALCULUS

An Approach to CALCULUS The Lessons 11.  Continuous versus discrete The definition of a "continuous" quantity. 12.  Limits A sequence of rational numbers. The definition of the limit of a variable. The limit of a function. Theorems on limits. Limits of polynomials. 13.  Continuous functions The definition of "a function is continuous at a value of x." 14.  Infinity (∞) The definition of "a variable becomes infinite." Limits of rational functions. 15.  The derivative The slope of a tangent line to a curve. The difference quotient and the definition of the derivative. Notations for the derivative. The equation of a tangent to a curve. 16.  Rules for derivatives The derivative of a constant. The derivative of y = x. The product rule. The power rule. The derivative of the square root function. 17.  The chain rule The derivative of a function of a function. 18.  More rules for derivatives The quotient rule. Implicit differentiation. The derivative of inverse functions. 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. The general power rule. 15.  Evaluating e Appendix 1.  Are the real numbers really numbers? Appendix 2.  Is a line really composed of points?