Module 4 - Limit as x Approaches a |
Introduction | Lesson 1 | Lesson 2 | Lesson 3 | Self-Test |
Lesson 4.3: TI-89 Limit Function |
The TI-89 computer algebra system has a limit function. In this lesson you will use the TI-89 computer algebra system to find limits. Using the Limit Function
From the Home screen, evaluate
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So,
4.3.1 Use the limit( command to evaluate
4.3.2
The Angle mode makes a difference in the evaluation of
The Sandwich Theorem
The Sandwich Theorem is used in many Calculus books to prove
This theorem can be visualized by graphing the three terms in the inequality simultaneously.
![]() The graph format needs to be changed to simultaneous.
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Seeing the three graphs simultaneously converge to 1 around x = 0 illustrates the Sandwich Theorem argument that
Left- and Right-Hand Limits The limit( command can also be used to evaluate a left-hand limit or a right-hand limit, which is the value approached by a function as x approaches a specific value from the left or from the right.
4.3.3 Interpret
4.3.4 Interpret
Using the Trace Feature
The Trace feature may be used to estimate limits. As the Trace cursor moves along a curve, the x- and y-values appear at the bottom of the Graph screen. Look at the y-values of y =
Moving the Trace cursor toward zero from the left or the right provides dynamic graphical and numeric reinforcement for the left- and right-hand limits. ![]() Entering a Specific x-Value While the Trace cursor is active, you can move it to a particular point by typing in the x-coordinate of that point. For example, to move to the point with x = 0.001,
This value should appear by "xc" in the lower left corner of the screen. ![]()
The cursor is not visible since it is below the viewing window, but the coordinates of the cursor are shown giving further evidence that
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