Question

Let f :D→R be a function and let c be a limit point of D.

Answer 1

Assume f(x)→L as x→c：

(a) Prove that |f(x)| → |L| as x → c

(b) If f(x)>= 0 for all x ∈ D,prove that square root of f(x) →square root of L as x → c