Understanding Limits from Graphs

The video tutorial explains how to determine limits from a graph. It covers one-sided limits as x approaches zero from both the left and right, showing that the left-hand limit is 3 and the right-hand limit is approximately 3.8. The general limit at zero does not exist due to differing one-sided limits. The tutorial then examines limits as x approaches four, where the left-hand limit does not exist due to oscillation, and the right-hand limit is 3. The general limit at four also does not exist. The video concludes with a summary of these findings.

What is the limit of f(x) as x approaches zero from the left?

• Does not exist

• 3.8

• 3

• 4

How does the function value at x = 0 compare to the limit from the left?

• They are the same

• Function value is higher

• Function value does not exist

• Function value is lower

What is the function value at x = 0?

• 4

• 3

• 3.8

• Does not exist

What is the limit of f(x) as x approaches zero from the right?

• 3

• 3.8

• Does not exist

• 4

Does the general limit of f(x) as x approaches zero exist?

• No, it does not exist

• Yes, it is 3.8

• Yes, it is 3

• Yes, it is 4

What happens to the function values as x approaches four from the left?

• They oscillate between 2 and 4

• They stabilize at 3

• They decrease steadily

• They stabilize at 4

Does the limit of f(x) as x approaches four from the left exist?

• Yes, it is 2

• Yes, it is 3

• Yes, it is 4

• No, it does not exist

What is the limit of f(x) as x approaches four from the right?

• 3

• Does not exist

• 2

• 4

What must be true for the general limit of f(x) as x approaches four to exist?

• Left and right limits must be equal

• Left limit must be greater

• Right limit must be greater

• Function must be continuous

Does the general limit of f(x) as x approaches four exist?

• Yes, it is 2

• Yes, it is 4

• No, it does not exist

• Yes, it is 3