2.a Given f(x) = x2 - 4x + 4. Compute the first and second derivatives of f (x), and evaluate f(x0) and the first two derivatives at x0 = 3. = d' f dx da. 2 = f(xo) x0=3 = df dx x0=3 = dx2 x0=3 = 2.b By Taylor's theorem, f(x) = f(x0) + x da z=xo (x - x0) + d 2 dx2 x =x0 (2 - x0)2+ .... Given the function and your work in part (a), fill in the blanks below to write the Taylor expansion of f(x) about reference point To = 3. Hint: Look at the Taylor series expansion formula carefully. f (a) = + (2 - 3) + (2 - 3)2 3. Use e = cos + j sin 0 to show that cos(a - B) = cosa cos B + sin a sin S and sin(a - B) = sin a cos B - cos a sin B. Hint: cos(-0) = cos 0, and sin(-0) = - sin 0. Answer: cos(a - B) + j sin(a - B) = ej(a-B) = 4. Given cos(a + 3) = cos a cos B - sin a sin S and sin(a + 3) = sin a cos B + cos a sin 3, show that cos 20 = cos2 0 - sin 0 and sin 20 = 2 sin 0 cos . cos 20 = sin 20 =