Understanding Limits in Calculus

The video tutorial explains the concept of limits in calculus, focusing on how to determine the limit of a function as x approaches a specific value from both the left and right. It discusses the conditions under which a limit exists, using examples to illustrate one-sided limits and the importance of their equality for the overall limit to exist. The tutorial also covers scenarios where limits do not exist due to differing one-sided limits.

What value does f(x) approach as x gets closer to 2 from values less than 2?

• 3

• 1

• 5

• 7

When approaching x equals 2 from values greater than 2, what value does f(x) approach?

• 1

• 7

• 3

• 5

For a limit to exist at a point, what must be true about the one-sided limits?

• They must be different

• They must be equal

• One must be zero

• They must be undefined

As x approaches 4 from both sides, what is the limit of f(x)?

• -5

• 0

• 5

• 10

What happens to the limit of f(x) as x approaches 8 from the left?

• It approaches 1

• It approaches 3

• It does not exist

• It approaches 5

What is the limit of f(x) as x approaches 8 from the right?

• 3

• 1

• 5

• Does not exist

Why does the limit of f(x) not exist as x approaches 8?

• The function is linear

• The one-sided limits are different

• The function is continuous

• The function is undefined

As x approaches -2 from the left, what value does f(x) seem to approach?

• 2

• 3

• 5

• 4

What is the significance of one-sided limits being equal?

• The function is undefined

• The limit exists

• The limit does not exist

• The function is discontinuous

What is the limit of f(x) as x approaches -2 from both directions?

• 4

• 3

• 5

• 2