Let V be the subspace of the vector space of continuous functions on R spanned by the functions cos(t) and sin(t). Consider the linear transformation T: V→ V given by for f € V. Find the matrix A associated to Twith respect to the basis (cos(t), sin(t)). (T(f))(t) = f"(t) +8f' (t) + 2f(t),

(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.

Find the derivative of the vector function r(t) = In(4 – t²) i+ v6+ij+7e¬6 k -6t r'(t) = (