# 1 Limits and Their Properties 1.1 A Preview 1 Limits and Their Properties 1.1 A Preview of Calculus 1.1

1. Understand what calculus is and how it compares with precalculus 2. Understand the tangent line problem 3. Understand the area problem The tangent line and area problems are two classic problems of Calculus

SoWhat is Calculus? Calculus is the math of change Pre-calculus and Calculus deal with the same topics But calculus deals with them in a dynamic way 1.1

Examples 1.1 Examples

1.1 Examples 1.1 Examples

1.1 The tangent line problem A secant of a curve is a line that intersects the curve in at least two points. The word secant comes from the Latin word secare, meaning to cut.

1.1 The tangent line (or simply tangent) to a plane curve at a given point is the straight line that "just touches" the curve at that point. Leibniz defined it as the line through a pair of infinitely close points on the curve.

https://teacher.desmos.com/activitybuilder/custom/5d6a03190e2f7f26e3775f8d The area problem Just like the tangent line problem we can use the idea of limit to approximate areas under curves

1.1 We do that by calculating areas of rectangles https://www.desmos.com/calculator/7kb3z4mc10