Instruction: Identify if the following statement is true or false. If the statement is true, then prove. Otherwise, if the statement is false, then give a counterexample. (2 points each) 1. We say that the vector field F is conservative if and only if V X F = 0. 2. If F = (6x - 4y, z - 4x, y - 8z), then V X F = 0. 3. Let {an } be a sequence of real number. Suppose that the power series on R below E an (x - a)" n=0 is converge absolutely on some set / C R. Suppose that the sequence , anti converge to 0. Then, an n=0 I = R. 4. For n E N, suppose f,: X - Y where X and Y are metric spaces. Suppose f - f on X and set My = sup dy (fn (x), f(x)). If fn converges uniformly to f on X, then there is a natural number N such that XEX Mn