 # CALCULUS

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The Lessons

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.

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.

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.

The derivative of a constant. The derivative of y = x.
The product rule.
The power rule.
The derivative of the square root function.

The derivative of a function of a function.

The quotient rule.
Implicit differentiation.
The derivative of inverse functions.

The second derivative.

The turning points of a graph. Critical values.

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? Home