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.

Prove that f(x)= 2x-|x| is a continuous function at x= 0.

Prove that the function defined by f(x)= tan x is a continuous function

Is the function defined by f(x)= |x|, a continuous function

Prove that the function f(x)= x^(2) is continuous at x=0.

If f(x)=cos[pi/x] cos(pi/2(x-1)) ; where [x] is the greatest integer function of x ,then f(x) is continuous at :

Let [x] be the greatest integer function f(x)=(sin(1/4(pi[x]))/([x])) is

Let [.] represent the greatest integer function and f (x)=[tan^2 x] then :

f(x) {(|x-(1)/(2)|",",0 le x lt 1),(x[x]",",1 le x lt 2):} where [.] denotes the greatest integer function. Show that f(x) is continuous at x=1 but not differentiable at x=1.

f(x)= [x] + sqrt(x -[x]) , where [.] is a greatest integer function then …….. (a) f(x) is continuous in R+ (b) f(x) is continuous in R (C) f(x) is continuous in R - 1 (d) None of these