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

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

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

Show that the function f(x)= |sinx + cos x| is continuous at x= pi

Let f(x+y)=f(x)+f(y) for all xa n dydot If the function f(x) is continuous at x=0, show that f(x) is continuous for all xdot

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

If f(x)={{:(,x[x], 0 le x lt 2),(,(x-1)[x], 2 le x lt 3):} where [.] denotes the greatest integer function, then (x) is continuous at x=2

f(x)= {((1- cos 4x)/(8x^(2))",",x ne 0),(k",",x= 0):} . If the function f(x) is continuous at x= 0, then find k.

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