Show that f(x) = sinx is continuous on R .

Assertion (A) : f(x) sinx is continuous on R . Reason (R) : f(x) = sinx is defind AA x in R . The correct answer is

Show that f(x) = [x] (x in R) is continuous at only those real numbers that are not integers.

f: N to R be any function then show that f is continuous on N .

Let f be a function defined on R such that f(x + y) = f (x) + f(y) AA x,y in R . If is continuous at x = 0 , Prove that it is continuous on R .

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

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

Show that g (x) = {{:( x^(2) " if " x le 1), ( x " if " x gt 1):} is continuous or R .