Show that `f(x)= [x] + [-x], x in R-` {integer} is a continuous function. Where [ ] is a greatest integer function

Range of greatest integer function is…….

The right hand derivative of f(x)= [x] tan (pi x) at a point x=7 is k pi then find the value of k. where [.] is the greatest integer function.

Sketch the curves (iii) y=|[x]+sqrt(x-[x])| (where [.] denotes the greatest integer function). (where [.] denotes the greatest integer function).

Show that the function defined by f(x)= |cos x| is a continuous function.

Find the left hand derivative of f(x)= [x] sin (pi x) at x=k. where k is an integer and [.] denotes the greatest integer function.

The period of the function f(x)=Sin(x +3-[x+3]) where [] denotes the greatest integer function

Show that the function defined by f(x)= sin (x^(2)) is a continuous function

Show that the function defined by f(x)= sin (x^(2)) is a continuous function

f (x)= {x} and g(x)= [x]. Where { } is a fractional part and [ ] is a greatest integer function. Prove that f(x)+ g(x) is a continuous function at x= 1.