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.

Find the intervals in which the function f(x)=sin x-cos x where 0 lt x lt 2pi is decreasing.

Prove that the function f(x)=|x| is not differentiable there at x=0.

Find the intervals in which the function f(x)=sin x-cos x where 0 lt x lt 2pi is increasing.

If [x+[2x]] lt3 , where [.] denotes the greatest integer function, then x is

If 0 lt x lt pi/2 , show that, sin x lt x lt tan x

Find by the definition the differential coefficient of the following: Let the function f(x) is differentiable at x=1 f(1)=0 and underset(hrarr0)Lt f(1+h)/h=5 find f'(1)

If f(x) = 0 for x lt 0 and f(x) is differentiable at x = 0 then for xgt 0 , f(x) may be

Discuss the continuity of the function defined by {{:(x+2," if "x lt 0),(-x+2," if "x gt 0):}

A function f(x) is defined as follows : f(x)=-x," when "x lt0 =2," when "0 lex lt2 =4-x," when "x ge2 Draw the graph of the function and from the graph examine whether f(x) is continuous at x = 0 and x = 2 or not.