Prove theat the greatest interger function defined by `f(x)= |x|, 0 lt x lt 3` is not differentiable at x=1 and x= 2.

Find all the points of discontinuity of the greatest interger function defined by f(x)= [x] , where [x] denote the greatest integer less than or equal to x.

Check whether the function f (x) = {{:(3 + x if x ge 0), ( 3-x if x lt 0):} is differentiable at x =0.

The range of the function f(x) = cos[x] where -pi/2 lt x lt pi/2 is

Show that the function f (x) = x ^(p) sin ((1)/(x)) x , ne 0, f (0) =0 is continuous but not differentiable at x=0 if 0 lt p le 1.

If f(x)=(x^(2)+1)/([x]) , ([.] denotes the greatest integer function), 1 le x lt 4 , then

Check the continuity of the function f defined by f(x)={{:(x+1,if xle1),(2x,if 1 lt x lt 2x),(1+xA^(2),if x ge 2):} at x=1 and 2

If f(x)=|x-1|+|x-2|+|x-3|,2 lt x lt 3 , then f is

Define f(x) = (1)/(2)[|sinx|+sin x], 0 lt x le 2pi . Then f is

If f(x)=|x-1|+|x-2|+|x-3| when 2 lt x lt 3 is

Discuss Lt_(xtoa)[x] where [x] is the greatest integer function and ainR