Prove that the greatest integer function `[x]` is continuous at all points except at integer points.

Is greatest integer function [x] is continuous everywhere ?

Consider the following statements: 1. The function f(x)=[x] where [.] is the greatest integer function defined on R, is continuous at all points except at x=0. 2. The function f(x)=sin|x| is continuous for all x""inR . Which of the above statements is/are correct?

Consider the following statements: I. The function f(x)=[x] . Where [.] is the greatest integer function defined on R. is continuous at all points except at x = 0. II. The function f(x)=sin|x| is continuous for all x inR . Which of the above statements is/are correct?

The function f(x)=x-[x], where | denotes the greatest integer function is (a) continuous everywhere (b) continuous at integer points only ( continuous at non- integer points only (d) differentiable everywhere

Greatest integer function and properties

f(x)=[sinx] where [.] denotest the greatest integer function is continuous at:

Let f(x)={{:(,1+x,"if "x lt 0),(,1+[x]+sin x,0 le x lt pi//2),(,3,x ge pi//2):} Statement-1: F is a continuous on R-[1] Statement-2: The greatest integer function is discontinuous at every integer point.

f(x) = [x] (greatest integer function ) is continuous at x = 0 then f(0) = ?

Explain Greatest integer function with graph