Understanding Limits from a Graph

The video tutorial explains the concept of limits using a graph of a function. It examines the behavior of the function as x approaches 3 from both the left and right sides. The left-handed limit approaches 4, while the right-handed limit approaches 1. Since the limits from both sides are not equal, the overall limit at x=3 does not exist. The tutorial emphasizes that for a limit to exist, the values from both sides must converge to the same point.

What is the main focus of the video tutorial?

• Finding the derivative of a function

• Understanding the concept of limits

• Graphing linear functions

• Solving algebraic equations

What does the negative superscript indicate when finding the limit?

• Approaching from values not equal to 3

• Approaching from values equal to 3

• Approaching from values less than 3

• Approaching from values greater than 3

Tags

CCSS.HSF-IF.C.7B

As x approaches 3 from the left, what value does f(x) seem to approach?

• 1

• 2

• 3

• 4

What is the left-sided limit of f(x) as x approaches 3?

• 2

• 1

• 3

• 4

As x approaches 3 from the right, what value does f(x) seem to approach?

• 1

• 2

• 4

• 3

What is the right-sided limit of f(x) as x approaches 3?

• 4

• 2

• 3

• 1

Why does the limit of f(x) as x approaches 3 not exist?

• The function is not defined at x = 3

• The function has a vertical asymptote

• The left and right-sided limits are different

• The graph is not continuous

What condition must be met for a limit to exist at a point?

• The function must be continuous

• The left and right-sided limits must be equal

• The function must be differentiable

• The function must have a horizontal asymptote

What happens if the left and right-sided limits are not equal?

• The function is differentiable

• The function is continuous

• The limit does not exist

• The limit exists

What would make the limit of f(x) as x approaches 3 exist?

• If the function is differentiable at x = 3

• If the left and right-sided limits are equal

• If the function is continuous at x = 3

• If the function has a horizontal asymptote at x = 3