Understanding Limits and Asymptotes

This tutorial explains how to calculate limits using the TI-89 graphing calculator. It covers accessing the calculus menu, entering functions, and handling special cases like division by zero and undefined limits. The video also discusses limits approaching infinity and the concept of vertical asymptotes.

What menu on the TI-89 calculator contains the limit function?

• Algebra

• Calculus

• Statistics

• Graph

Which key combination is used to access the square root function on the TI-89?

• Second and Add

• Second and Divide

• Second and Subtract

• Second and Multiply

What is the result of the limit as x approaches 2 for the function sqrt(4x + 1)?

• 5

• 4

• 3

• 2

What should be done if direct substitution in a limit results in division by zero?

• Ignore the result

• Edit the previous entry

• Use a different calculator

• Try a different function

What is the limit of (x^2 - x - 12) / (x - 4) as x approaches 4?

• 5

• 6

• 7

• 8

What does it mean when the calculator indicates a limit is undefined?

• The limit is zero

• The limit is infinite

• The limit is negative

• The limit does not exist

What is the vertical asymptote for the function 1/(x + 3)?

• x = 3

• x = -3

• x = 0

• x = 1

What is the limit of 1/x^2 as x approaches zero?

• Zero

• One

• Infinity

• Negative Infinity

What does DNE stand for in the context of limits?

• Does Not Enter

• Does Not End

• Does Not Equal

• Does Not Exist

When a limit approaches infinity, what additional information does this provide?

• The function grows without bound

• The function is constant

• The function is undefined

• The limit is zero