Defining Limits and Limit Notation in Calculus

What is the main focus of this lesson?

• Derivatives

• Integrals

• Sequences

• Limits

What does the limit of a function describe?

• The exact value of the function at a point

• The area under the curve

• The slope of the function

• The value the function approaches as the input approaches a certain point

In the first example, what is the limit of f(x) as x approaches 2?

• 0

• 1

• 2

• 3

What is the value of f(2) in the second example?

• 0

• 1

• Undefined

• 3

In the third example, what is the limit of f(x) as x approaches 2?

• 1

• 0

• 2

• 3

What is the value of the function at x = 2 in the third example?

• 0

• 1

• 2

• 3

What is the limit of f(x) as x approaches 1 in the practice problem?

• 2

• -1

• 0

• 1

What is the value of the function at x = -3 in the practice problem?

• 0

• 2

• 1

• -1

What does the limit as x approaches 7 of f(x) = 10 mean?

• As x equals 7, f(x) is undefined

• As x approaches 7, f(x) equals 10

• As x approaches 7, f(x) approaches 10

• As x equals 7, f(x) is 10

True or False: The value of f(1) is always equal to the limit of f(x) as x approaches 1.

• True

• False