A PREVIEW OF CALCULUS Section 1.1. When you have finished your homework you should be able to… Understand what calculus is and how it compares with precalculus.

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Presentation transcript:

A PREVIEW OF CALCULUS Section 1.1

When you have finished your homework you should be able to… Understand what calculus is and how it compares with precalculus Understand that the tangent line problem is basic to calculus Understand that the area problem is also basic to calculus

Find the area of the triangle with vertices Round to the nearest hundredth.

WHAT IS CALCULUS? Consider the following function. Using tools you learned in precalculus, what can you tell me about this function?

CALCULUS IS THE MATHEMATICS OF CHANGE Think of calculus as a “limit machine” with 3 stages 1st Stage: Precalculus mathematics Example: The slope of a line The area of a rectangle 2nd Stage: Limit Process 3rd Stage: A new calculus Formation Example: Derivative Integral

Determine if the following problem is solved using precalculus or calculus. Find the slope of the secant line of a curve. A.Precalculus B.Calculus

Determine if the following problem is solved using precalculus or calculus. Find the area bounded by the graph of, the x-axis, and the lines and. A.Precalculus B.Calculus

THE TANGENT LINE PROBLEM What You are Given: –A function –A point on its graph What You are Asked to Find: –An equation of the tangent line to the graph at the point With the exception of vertical lines, this is equivalent to finding the SLOPE of the tangent line at x. –You can approximate this slope by using the point of tangency and a second point on the curve. Such a line is called a secant line

THE AREA PROBLEM –What you are asked to find: The area of a plane region that is bounded by the graph of functions