Understanding Limits That Fail to Exist

Mr. Baker explains limits that fail to exist, covering three scenarios: differing left and right approaches, unbounded growth, and oscillation. He provides examples for each case, demonstrating how limits can fail to exist when approaching a specific constant. The video includes practical examples and graphical representations to illustrate these concepts.

What is one condition that can cause a limit to not exist?

• The function is differentiable at the point.

• The function is continuous at the point.

• The function approaches the same value from both sides.

• The function approaches different values from the left and right.

Which of the following is NOT a reason for a limit to fail to exist?

• The function is continuous at the point.

• The function oscillates between two values.

• The function approaches different values from the left and right.

• The function grows without bound.

In the first example, what happens to the limit of the absolute value of x divided by x as x approaches 0?

• The limit exists and equals 0.

• The limit does not exist because the function is continuous.

• The limit does not exist because the function approaches different values from each side.

• The limit exists and equals 1.

In the first example, what value does the function approach from the left as x approaches 0?

• -1

• 1

• 0

• Infinity

Why does the limit of the function in the second example not exist?

• The function grows without bound as x approaches 0.

• The function approaches the same value from both sides.

• The function is continuous at the point.

• The function is differentiable at the point.

In the second example, what happens to the function values as x approaches 0?

• They approach a finite number.

• They remain constant.

• They oscillate between two values.

• They grow larger without bound.

In the second example, what is the result when plugging in smaller and smaller values for x?

• The function values grow larger.

• The function values decrease.

• The function values oscillate.

• The function values remain constant.

What behavior is observed in the third example that causes the limit to not exist?

• The function approaches the same value from both sides.

• The function oscillates between two values as x approaches 0.

• The function is continuous at the point.

• The function grows without bound.

What is the behavior of the sine of 1/x as x approaches 0 in the third example?

• It oscillates between positive and negative values.

• It remains constant.

• It approaches a single value.

• It grows without bound.

Which example demonstrates a limit that does not exist due to oscillation?

• None of the examples

• Example 3

• Example 2

• Example 1