Limits and Properties of Step Functions

The video tutorial introduces step functions, focusing on the greatest integer function. It explains how to graph these functions and explores the concept of limits, particularly when they exist or do not exist for step functions. The tutorial includes solving various limit problems and concludes with tips for evaluating limits of step functions.

What is the primary focus of the video tutorial?

• Probability theory

• Integration techniques

• Limits of step functions

• Derivatives of functions

What is another name for the step function?

• Median integer function

• Greatest integer function

• Least integer function

• Average integer function

What does the step function return for a value of 1.2?

• 1

• 2

• 0

• 1.2

What is the range of the step function?

• Rational numbers

• Integers

• Real numbers

• Complex numbers

What is the step function value for x between 0 and 1?

• x+1

• x

• 0

• 1

What is the step function value for x between 1 and 2?

• 1

• 2

• 0

• x

What is the right limit of step function as x approaches 1 from the right?

• 2

• 1

• Does not exist

• 0

What is the left limit of step function as x approaches 1 from the left?

• 2

• Does not exist

• 1

• 0

Does the limit of step function exist at x = 1?

• Yes

• No

• Only from the right

• Only from the left

What is the limit of step function as x approaches 1.5?

• Does not exist

• 2

• 1.5

• 1