1.T.2 Let V be the set of all twice-differentiable functions f : R → R satisfying f"(x) = f(x) – 5. Is V a vector space? Why or why not?

State whether this is true or false. If true, give an explanation. If false, give a counterexample.

(1) Give an example of a function z = f(x, y) and a unit vector i such that f.(0,0) = 2, fy(0,0) = 1 and fã(0,0) is negative.

Let x, y, z be vectors. Let f : R^2 → R be a function. Letr(t) be a vector-valued function. Determine if each of the following is a scalar, vector, or nonsense. No explanation is needed.a. x · yb. (x · y) × zc. [(x · y)z] × yd. r′(t)e. Duf(x, y)f. ∇x