Understanding Limits Graphically

The video tutorial explains how to determine limits graphically using a function's graph. It covers the concept of approaching a specific X value from both sides to find the corresponding Y value, which represents the limit. The tutorial provides examples of finding limits as X approaches 2, 0, and -1, and discusses the existence of limits even when there is a hole in the graph. The video concludes with a preview of future topics, including one-sided limits and limits at infinity.

What is the limit of f(x) as x approaches 2?

• 3

• 0

• -3

• 2

Tags

CCSS.8.EE.B.5

Why is it important to sketch a vertical line at x = 2?

• To identify the y-intercept

• To find the x-intercept

• To know where we are approaching

• To determine the slope

What does the concept of a limit focus on?

• The derivative at the point

• The integral of the function

• The exact value at the point

• The value as we approach from both sides

What is the limit of f(x) as x approaches 0?

• 0

• -1

• 2

• 1

When approaching x = 0, what are we trying to determine?

• The y-intercept

• The slope of the tangent

• If we approach the same function value from both sides

• The maximum value of the function

Tags

CCSS.HSF.IF.A.2

What is the limit of f(x) as x approaches -1?

• -2

• 0

• 2

• 1

Tags

CCSS.HSF.IF.A.2

What is the function value at x = -1?

• -3

• -2

• 1

• 0

What happens to the limit if there is a hole at x = 2?

• The limit is undefined

• The limit still exists

• The limit is zero

• The limit does not exist

What is the limit of f(x) as x approaches 2, despite the hole?

• 0

• 1

• 2

• -3

Tags

CCSS.HSF.TF.A.4

What will be covered in the next videos?

• One-sided limits and limits at infinity

• Trigonometric functions

• Graph transformations

• Derivatives and integrals

Tags

CCSS.HSF.TF.A.4