Examples of functions satisfying each of the following conditions

(a) lim as x goes to zero of f of x^2 exists, but the lim as x goes to zero of f of x does not.

(b) lim as x goes to zero of f of 1/x exist, but the lim as x goes to zero of f of x does not.

(c) f(x) is not continuous at 1, but g(x) = |f(x)| is continuous at 1.

(d) f(x) is nto continuous anywhere, but g(x) = |f(x)| is continuous everywhere.

For each condition provide one function.