Prove that the functions sin x, cos x are continuous on R

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^(n) is continuous at x= n, where n is a positive integer.

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

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

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

Integrate the functions sqrt(sin2x)cos2x

The function sin (x^2) + cos sqrt(x) is

Assertion (A): f(x) = (sin {[ x] pi})/(1 + x^(2)) here [x] denotes greastest integer function, is continuous on R Reason (R) : Every constant function is continuous on R

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

Examine that sin |x| is a continuous function.