LIMITS AND THE GREATEST INTEGER FUNCTION

Front

What is the Greatest Integer Function?

Back

The Greatest Integer Function, also known as the floor function, is a mathematical function that takes a real number and gives the largest integer less than or equal to that number.

Front

What is the notation for the Greatest Integer Function?

Back

The notation for the Greatest Integer Function is ⌊x⌋, where x is the input value.

Front

What is the value of ⌊3.7⌋?

Back

The value of ⌊3.7⌋ is 3.

Front

What is the value of ⌊-2.3⌋?

Back

The value of ⌊-2.3⌋ is -3.

Front

How does the Greatest Integer Function behave at integer values?

Back

At integer values, the Greatest Integer Function returns the integer itself. For example, ⌊5⌋ = 5.

Front

What is the limit of the Greatest Integer Function as x approaches 2 from the left?

Back

The limit of the Greatest Integer Function as x approaches 2 from the left is 1, since values just below 2 will round down to 1.

Front

What is the limit of the Greatest Integer Function as x approaches 2 from the right?

Back

The limit of the Greatest Integer Function as x approaches 2 from the right is 2, since values just above 2 will round down to 2.

Front

What is the discontinuity in the Greatest Integer Function?

Back

The Greatest Integer Function has jump discontinuities at every integer value.

Front

Provide an example of a piecewise function that includes the Greatest Integer Function.

Back

f(x) = { ⌊x⌋ for x < 0; x^2 for x >= 0 }.

Front

What is the graphical representation of the Greatest Integer Function?

Back

The graph of the Greatest Integer Function consists of horizontal line segments at each integer value, with open circles at the right endpoints.