Understanding the Greatest Integer Function and Limits

The video tutorial explains how to determine limits involving the greatest integer function, also known as the step function. It begins by introducing the concept and analyzing the function using a table of values. The tutorial then demonstrates how to determine limits as x approaches specific values, including one-sided limits. The video concludes with examples to illustrate these concepts, emphasizing the behavior of the function at different points.

What is the definition of the greatest integer function?

• The smallest integer greater than or equal to x

• The largest integer less than or equal to x

• The integer closest to x

• The fractional part of x

What is the function value of f(x) = greatest integer of (x + 1) when x = 1?

• 1

• 2

• 4

• 3

How does the function value change as x increases from 1.2 to 1.8?

• It oscillates

• It increases

• It decreases

• It remains constant

What happens to the function value at integer points?

• It remains constant

• It jumps to the next integer

• It becomes undefined

• It decreases

What is the limit of the greatest integer function as x approaches 1.2?

• 3

• 1

• 2

• Does not exist

What is the function value as x approaches 3 from the right?

• 3

• 4

• 2

• Does not exist

Why does the limit not exist as x approaches 3?

• The one-sided limits are equal

• The function is undefined at x = 3

• The function value is constant

• The one-sided limits are not equal

What is the one-sided limit as x approaches 2 from the positive side?

• 4

• 3

• 2

• 1

What is the one-sided limit as x approaches 2 from the negative side?

• 3

• 2

• 4

• 1

What is the significance of one-sided limits in this context?

• They help in understanding the function's jumps

• They are irrelevant to the function's behavior

• They show the function's behavior at non-integer points

• They determine the continuity of the function