1.1 A Preview of Calculus Main Idea Understand what calculus is and how it compares with precalculus.

What is Calculus? The mathematics of change- velocities and accelerations. Furthermore the math of tangent lines, slopes, areas, volumes, arc lengths, cetroids, curvatures, and many others that have enabled scientists, engineers, and economists to model real-life situations.

Study Tips 1.Be sure you understand the question. What is given? What are you asked to find? 2.Make a Plan. There are many approaches: look for a pattern, solve a simpler problem, work backwards, draw a diagram, or use technology. 3.Make sure you answer the question. Verbalize your answer. 4.Does your answer make sense? Is your answer reasonable?

PrecalculusCalculus Find constant velocityAnalyze the velocity of an accelerating object Slope of a lineSlope of a curve Tangent line to a circleTangent line to a curve Find area of rectangleFind area under a curve

What is the mathematical difference between precalculus and calculus? The Limit Process!! So understanding chapter 1 is critical to understanding not just doing calculus. Calculus has two major concepts 1.Tangent line problem – Differentiation 2.Area problem - Integration

Tangent Line Problem Given a function f and a point P on its graph Find the equation of the tangent line to the graph at point P.

How can you estimate the slope of the tangent line? Secant lines Page 45 Exploration

The Area Problem Find the area of a plane region that is bounded by the graphs of functions.

How can we get a better estimation of the area? How many rectangles would make the best estimation? Page 46 exploration