Section 2.1 A Preview of Calculus

Text for Section 2.1 A Preview of Calculus

Learning Outcomes

• Describe the tangent problem and how it led to the idea of a derivative.
• Explain how the idea of a limit is involved in solving the tangent problem.
• Recognize a tangent to a curve at a point as the limit of secant lines.
• Identify instantaneous velocity as the limit of average velocity over a small time interval.
• Describe the area problem and how it was solved by the integral.
• Explain how the idea of a limit is involved in solving the area problem.
• Recognize how the ideas of limit, derivative, and integral led to the studies of infinite series and multivariable calculus.

• The Essence of Calculus
• What is Calculus?
• Use average velocity to predict instantaneous velocity
• Finding average rate of change (secant slope) in the form of a difference quotient