Understanding Limits and Infinity

The video tutorial explores the concept of limits, focusing on scenarios where limits become unbounded. It introduces new notation for expressing limits that approach infinity and discusses the implications of one-sided limits. An example problem is presented, analyzing graphs to determine the behavior of limits as they approach specific points. The tutorial emphasizes understanding the direction of limits and the use of appropriate notation.

What happens to the value of 1/x^2 as x approaches zero from either side?

• It becomes unbounded in the positive direction.

• It remains constant.

• It becomes unbounded in the negative direction.

• It approaches zero.

What is the new notation introduced for limits that go to infinity?

• The limit is infinity.

• The limit is undefined.

• The limit is negative infinity.

• The limit is zero.

Why can't we say the limit of 1/x as x approaches zero exists?

• Because it approaches a finite value.

• Because it approaches different infinities from each side.

• Because it approaches zero.

• Because it remains constant.

What is the limit of 1/x as x approaches zero from the left?

• Undefined

• Positive infinity

• Zero

• Negative infinity

What is the limit of 1/x as x approaches zero from the right?

• Negative infinity

• Positive infinity

• Zero

• Undefined

In the example problem, what is the behavior of the limit as x approaches 1 in graph A?

• It goes to positive infinity from the left and negative infinity from the right.

• It goes to negative infinity from both sides.

• It goes to positive infinity from both sides.

• It remains constant.

Which graph satisfies the condition that the limit as x approaches 1 is infinity?

• None of the graphs

• Graph C

• Graph B

• Graph A

What is the behavior of the limit in graph C as x approaches 1?

• It remains constant.

• It goes to negative infinity from the left and positive infinity from the right.

• It goes to negative infinity from both sides.

• It goes to positive infinity from both sides.

What is the significance of dashed lines in the graphs discussed?

• They represent asymptotes.

• They represent the y-axis.

• They represent the origin.

• They represent the x-axis.

Why is graph B the correct choice for the example problem?

• Because it approaches negative infinity from both sides.

• Because it remains constant.

• Because it approaches infinity from both sides.

• Because it approaches zero from both sides.