Let A := (0, 1] and let f: A R be defined by f(x) = !. Prove that f is continuous on A. Let D := [0, 1] and let f : D→ R be the function defined by f(x) = VT. Show that f is uniformly continuous on D...

Extracted text: Let A := (0, 1] and let f: A R be defined by f(x) = !. Prove that f is continuous on A. Let D := [0, 1] and let f : D→ R be the function defined by f(x) = VT. Show that f is uniformly continuous on D but not Lipschitz there. Determine whether the given function is differentiable at the indicated point(s). (a) h(x) = x|x| at c = 0. (b) k(x) = |r| + |x – 1| at c = 0 and c2 = 1.