TI-89 Graphing Calculator: Limits at Infinity

This tutorial explains how to determine limits at infinity using the TI-89 graphing calculator. It covers accessing the calculus menu, entering functions, and interpreting results. The video demonstrates calculating three limits: one as x approaches positive infinity, another as x approaches negative infinity, and a third where the limit does not exist. Key concepts include recognizing when limits equal the ratio of leading coefficients and understanding when limits do not exist.

What is the first step to access the calculus menu on the TI-89 calculator?

• Press F1

• Press F4

• Press F2

• Press F3

When entering a function for limit calculation, what must be enclosed in parentheses?

• Only the numerator

• Only the denominator

• Both numerator and denominator

• Neither

What is the result of the first limit calculation as x approaches positive infinity?

• 1/3

• 2/5

• 3/4

• 1/2

Why does the limit equal the ratio of the leading coefficients when the degrees of the numerator and denominator are the same?

• Because the limit approaches zero

• Because the degrees cancel out

• Because the degrees are irrelevant

• Because the coefficients are equal

What happens to the function value when the degree of the denominator is greater than the numerator as x approaches infinity?

• It approaches zero

• It approaches infinity

• It becomes undefined

• It remains constant

In the second limit calculation, what is the result as x approaches negative infinity?

• Zero

• Negative infinity

• Infinity

• One

What is the function used in the third limit calculation?

• x minus one divided by x cubed

• x plus five divided by x squared

• x cubed divided by x plus two

• x squared divided by x minus three

What does the calculator indicate when the limit is equal to positive infinity?

• The limit is negative infinity

• The limit exists

• The limit does not exist

• The limit is zero

What notation is used to indicate that a limit does not exist?

• NULL

• INF

• DNE

• N/A

Why is it useful to write a limit as equals infinity even if it does not exist?

• It simplifies calculations

• It provides more information about the behavior

• It is a standard practice

• It is required by the calculator