Understanding Limits Graphically

The video tutorial explains how to determine limits graphically, focusing on one-sided and regular limits. It begins with an introduction to limits and their notation, followed by a detailed examination of one-sided limits as x approaches 2 from both the left and right sides. The tutorial highlights that these limits approach negative and positive infinity, respectively, and thus do not exist. It then discusses regular limits, emphasizing that if one-sided limits approach different infinities, the regular limit does not exist. The video also covers the limit at x=1, demonstrating that a hole in the graph does not affect the limit's existence, which is determined to be -1. The tutorial concludes with a preview of the next video on limits at infinity.

What does the notation for a one-sided limit indicate?

• Approaching a value from the right side only

• Approaching a value from the left side only

• Approaching a value from both sides

• Approaching a value from above

As x approaches 2 from the left, what happens to the function's y-values?

• They approach negative infinity

• They approach positive infinity

• They approach zero

• They remain constant

What is the left-sided limit of the function as x approaches 2?

• One

• Negative infinity

• Positive infinity

• Zero

As x approaches 2 from the right, what happens to the function's y-values?

• They approach zero

• They approach positive infinity

• They approach negative infinity

• They remain constant

What is the right-sided limit of the function as x approaches 2?

• Positive infinity

• Zero

• Negative infinity

• One

Why does the overall limit as x approaches 2 not exist?

• The function is continuous

• The left and right limits are equal

• The function has a hole

• The left and right limits are not equal

What is the overall limit of the function as x approaches 2?

• Zero

• Positive infinity

• Negative infinity

• Does not exist

What is the significance of a hole in the graph when determining limits?

• It means the limit is infinite

• It means the limit is zero

• It always means the limit does not exist

• It affects the function value but not the limit

What is the limit of the function as x approaches 1?

• -1

• Positive infinity

• Zero

• Negative infinity

How does the presence of a hole at x = 1 affect the limit?

• The limit is zero

• The limit is determined by the approaching values

• The limit does not exist

• The limit is affected by the hole