1. Suppose f(x) > 0 for all x and f(x) is differentiable everywhere. If q(x) _ sin (x) + 2 f (x)]2 , which of the following is true? J4 + f ( I ) (a) g'(x) = [x +f(x)] . 2 sin (x) + x2 f(x)] . [cos (x) + x2 f'(x) + 2xf(x)]] - [sin (x) + 12 f(x)]2 . [Ax' + f'(x) [204 + f (20 ) 12 (b) g'(z) = 12 sin (3) + x2 f (x)] . [cos (x) + x2 f'(x) + 2xf(x)11 [4203 + f' (20) ] (c) g'(x) = [+f(x)] . [2 sin (x) + x2f(x)] . [cos (x) + 2xf'(x)]] - [sin (x) + x2 f(x) ]2 . [4x3 + f'(x) ] [ac4 + f (20 ) 12 (d) g'(2) = [2 sin (x) + x2 f(x)] . [cos (x) + x2 f'(x) + 2xf (x)] [+ + f (2) 12 2. If f(2) = 2, f'(2) = -1,g(2) = 0, g'(2) = 2 and h(x) = - f (2) + g(), which of the following is true? (a) h'(x) = f(x) + 9(x)] . [f'(x)9'(x) ] - If(x)9(2)] . [f(2) +9(2)1 h(2) =-1. If (z) + g(x)] (b) h' (z) = If(2) + 9(20)] . If'(2.)g(2) + f (z)g' (20) ] - If(2) 9(20) ] . [f'(2) +9(20)1 h(2) =2. If (z) + 9(20) 12 f' (x)g'(2 ) ( c) h(z) = fi(x) + g'(I)' h' ( 2 ) = -2 (d) h'(a) = 1 [f (x)9(x)] . [f'(x) + 9'(x)] - If(x) + 9(x)] . [f'(x)9(x) +f(x)9()] h' ( 2 ) = - 2 If (20) + 9() 123. Let f(x) be a continuous function such that f(x) 0 for x > 0. Which of the following claims must be true? Check all that apply. (a) lim f(x)