Determine the points of continuity of the following functions and state which theorems are used in each

Question:

Determine the points of continuity of the following functions and state which theorems are used in each case.
(a) f(x) := x2 + 2x + 1/x2 + 1 (x ∈ R),
(b) g(x) := √x + √x (x > 0),
(c) h(x) := √1 + |sin x|/x (x ≠ 0),
(d) k(x) := cos √1 + x2 (x ∈ R):