Understanding Limits from Graphs

The video tutorial explores the concept of limits using graphical representations of functions f(x) and g(x). It examines the limits of f(x) as x approaches 6, 4, and 2, highlighting different scenarios where limits exist or do not exist. The tutorial also analyzes the limits of g(x) as x approaches 5, 7, and 1, emphasizing the importance of approaching the same value from both sides for a limit to exist. The video provides a comprehensive understanding of limits through visual examples.

What is the limit of f(x) as x approaches 6?

• Does not exist

• 2

• 1

• 0

When x approaches 4, what is the limit of f(x)?

• Does not exist

• 5

• 4

• 3

What is the significance of a limit existing at a point where the function is not defined?

• It indicates a removable discontinuity

• It shows the function is undefined everywhere

• It means the function is continuous

• It implies the function is differentiable

Why does the limit of f(x) not exist as x approaches 2?

• The function is not defined at x = 2

• The function is constant

• The function approaches different values from the left and right

• The function is unbounded

What is the value of f(2) given in the video?

• 5

• 4

• 3

• 2

What is the approximate limit of g(x) as x approaches 5?

• 0.2

• 0.3

• 0.4

• 0.5

As x approaches 7, what is the limit of g(x)?

• 2

• 5

• 3

• 1

What happens to g(x) as x approaches 1?

• It becomes unbounded

• It approaches 1

• It approaches 2

• It approaches 0

What is the value of g(7) as defined in the video?

• 4

• 2

• 5

• 3

What does it mean when a limit is said to be unbounded?

• The limit is constant

• The limit approaches zero

• The limit does not exist

• The limit approaches a finite value