Please answer each step thoroughly for a like.

Question 1. Let F(x) = / f(t) dt and G(x) = / g(t) dt, where the graphs of f(x) and g(x) on [-2, 4] are below. 2 y - f(x) -2 2 V - g(x) Evaluate the following integrals. 1. (2 points) (F) - 9()] dx 2. (3 points) (8()5(2) - G()9(2)] dx 3. (5 points) / S'(F(x))F(2)f(2) da Numeracy 2. A function of n variables f(x), where x = (21, . .., In), is said to be homogeneous of degree ke N if f(tx) = t* f(x) for all & E R. For each function below, show it is homogeneous (of some degree k) or give an example to show it is not homogeneous. 1. (2 points) f(x, y, 2) = Vx' ty + 29 2. (2 points) f(x, y, 2, w) = xy' + 2 w' + ryzu 3. (2 points) f(x, y) = Vx2 ty. 4. (4 points) f(x, y) = /(x34x2+7)ds Numeracy 3. (10 points) Solve the following non-linear system of equations: 12 -12 +222 =2 22 =3Numeracy 4. Some regions ? in IR3 can be written down by describing the functions which form their boundaries. For example, the set 0 = ((x, y) : -1