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

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.

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

Prove that the function f(x)= 5x- 3 is continuous at x=0, at x= -3 and at x= 5

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

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

If function f(x) = (sqrt(1+x) - root(3)(1+x))/(x) is continuous function at x = 0, then f(0) is equal to

Prove that the function f(x)= x^(n) is continuous at x= n, where n is a positive integer

Prove that f(x)= {((sin x)/(x)+ cos x ",",x ne 0),(2",",x=0):} is a continuous function at x= 0