Exploring Limits that Fail to Exist

Mr. Baker explains limits that fail to exist, covering three scenarios: when a function approaches different values from the left and right, when it grows without bound, and when it oscillates between values. He provides examples for each case, demonstrating how to analyze limits using calculations and graphs.

What can cause a limit to not exist?

• Function approaches the same number from both sides

• Function approaches different numbers from each side

• Function remains constant as it approaches a point

• Function has a defined value at the point of interest

What happens to the limit of a function as it approaches infinity?

• The limit always exists

• The limit does not exist if the function decreases without bound

• The limit is always zero

• The limit does not exist if the function increases without bound

What is observed when approaching zero from the left side of the absolute value of x divided by x?

• The function approaches 0

• The function approaches -1

• The function approaches 1

• The function remains constant

What is observed when approaching zero from the right side of the absolute value of x divided by x?

• The function approaches 1

• The function remains constant

• The function approaches -1

• The function approaches 0

What is the result of approaching zero from both sides for the absolute value of x divided by x?

• The function oscillates

• The function approaches different values from each side

• The function approaches the same value from both sides

• The function remains constant

What does it mean for a function to increase without bound?

• The function approaches a finite limit

• The function decreases to negative infinity

• The function increases towards infinity

• The function oscillates between two values

What pattern is observed in the function values as they get infinitely closer to zero?

• The values decrease steadily

• The values oscillate between two numbers

• The values remain constant

• The values increase without limit

What behavior is exhibited by the sine of one over x as x approaches zero?

• It decreases without bound

• It remains constant

• It oscillates between positive one and negative one

• It approaches a finite limit

Why does the limit of the sine of one over x as x approaches zero not exist?

• Because it approaches a single value

• Because it decreases without bound

• Because it oscillates between two values

• Because it increases without bound

In the context of limits, what does it mean if a function oscillates as it approaches a point?

• It approaches a finite limit

• It decreases steadily

• It increases steadily

• It bounces between two or more values