MATH 1712: WEEK 3

Topics for this week are:

• Limits and Continuity
• Tangent Lines and Definition of the Derivative

Objectives for this week:

• Find the limits and one-sided limits of rational functions graphically and algebraically
• Determine the intervals over which a function is continuous
• Use the limit definition of the derivative to find the derivative of a given function
• Find the tangent line to a curve at a specified point using the limit definition of a derivative

Text coverage:     Sections 2.4 - 2.6 of S. Tan.

Online resources:

• Week 3 Formula Sheet
• Week 3 Practice Problems
• Maple worksheets
  • Limits: This worksheet introduces the Maple commands for finding one- and two-sided limits of functions.  In this worksheet, the reader also learns how to examine the graphs of functions to find the limit graphically.
  • Slopes, Tangent Lines, and Derivatives: This worksheet gives animated visualization for the computation and role of a tangent line. The worksheet is appropriate at an early stage in a study of differential calculus.
  • Solving Equations: This worksheet is about continuity--the intermediate value property of continuous functions, etc. Equations are solved using "bisection," regula falsi, and Newton's method. This assignment help you understand the Maple procedures.
  • Solving f(a) = b: The Method of Bisection: The Method of Bisection for finding roots of an equation is not conceptually hard. It has two especially good features: first, it is easily understood, and second, it can provide initial guesses for methods which might converge faster -- such as Newton's Method. We illustrate the method and provide an example to show that a little care must be taken.
• Java Projects
  • Continuity for functions of one variable: This applet is designed for experimenting with the "epsilon-delta" definition of continuity, and with quantitative measures of continuity.
  • Tangent lines to graphs of a single variable: This applet is designed for experimenting with tangent lines and the linear approximation to a function.
  • Secant lines and their relation to tangent lines for graphs of a single variable: This applet is designed for experimenting with secant lines and the secant line approximation to the tangent.

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Last Modified: . School of Mathematics, Georgia Institute of Technology.