Sage-Tips

Is the greatest integer function continuous at 0?

The greatest integer function, [ x], is defined to be the largest integer less than or equal to x (see Figure 1 ). Figure 1 The graph of the greatest integer function y = [ x]. hence, and f( x) is not continuous at n from the left. hence, f is continuous at x = 0 from the right only.

Do greatest integer functions have zeros?

Starts here16:10Greatest Integer Function With Limits & Graphs – YouTubeYouTubeStart of suggested clipEnd of suggested clip58 second suggested clipAll of these integers are less than point seven but the greatest of these is zero. So the greatestMoreAll of these integers are less than point seven but the greatest of these is zero. So the greatest integer of point seven is zero.

How can you prove a function is not differentiable?

We can say that f is not differentiable for any value of x where a tangent cannot ‘exist’ or the tangent exists but is vertical (vertical line has undefined slope, hence undefined derivative).

Is greatest integer function continuous at?

[Since (2+h) lies between 2 and 3 and the least being 2]

(iii) Thus from above 3 equations left side limit is not equal to right side limit.

So, limit of function does not exist.

Hence, it is discontinuous at x=2.

So, greatest integer function is not constant at all points.

Are greatest integer functions discontinuous?

 Continuous from the left and from the right. discontinuous at n. Hence, the greatest integer function is discontinuous at ALL INTEGERS.

What is the difference between greatest integer function and least integer function?

We have seen that greatest integer function represents the integer, which can be considered to be the floor integral value of a real number. Correspondingly, we define a ceiling function called “least integer function (LIF)”, which returns the least integer greater than or equal to the number (x).

Which of the following function is not differentiable?

Discontinuous function is always non differentiable.