QUESTION FOUR (a) Find the maximal solutions for the following initial value problems dx (i) (ii) = x dt x(0) = < dx =cos dt (X(to) = C, to # 0 [0, {2(1xXx),xe (1/2, 1) (b) Verify whether the tent map f(x) = extended to a map g: [1,1] [1,1] defined by g(x) = Where the function is a le-limit set. (-f(x),x [-1,0] -f(x),x [0, 1] [5 Marks] [5 Marks] [5 Marks]