A PREVIEW OF CALCULUS

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A PREVIEW OF CALCULUS

• Section 1.1

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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

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

• 5.45
• 0.02

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

6
Determine if the following problem is solved
using precalculus or calculus.Find the slope of
the secant line of a curve.

• Precalculus
• Calculus

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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 .

• Precalculus
• Calculus

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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

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THE AREA PROBLEM

• What you are asked to find
• The area of a plane region that is bounded by the
  graph of functions