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

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Presentation on theme: "1.1 A Preview of Calculus Main Idea Understand what calculus is and how it compares with precalculus."— Presentation transcript:

1 1.1 A Preview of Calculus Main Idea Understand what calculus is and how it compares with precalculus.

2 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.

3 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?

4 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

5 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

6 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.

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

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

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


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