1.) Use the ed definition of limits to prove that the function f(x) = x/x^(〖2 〗_(+ 1) ) is continuous at x = 0. (3 marks).
2.) Consider the function f(x) = {_0^(x^3 cos⁡〖(1/x^2 )〗 ), x ≠ 0
x = 0.
(a) Use the Squeeze theorem to show that lim┬(x→0 )⁡〖f (x)〗= 0
(b) Is f(x) continuous at x = 0? Explain.
(c) Show that f(x) differentiable at x = 0?
(d) Find f'(x).