Problem #6: Let f(x) = sinx. Which of the following would you use to calculate f'(/2) using the definition of derivative (i.e., first principles)? COS( TT/2 + h) sin(7/2 + h) -1 (C) lim COs(7/2 + h) + 1 (D) lim sin(-7/2 + h) + 1 (A) lim (B) lim h- 0 h h h-0 h h (E) lim Cos(-7/2 + h) - 1 (F) lim sin(7/2 + h) (G) lim COS(-7/2 + h) (H) lim Sin(7/2 + h) h- 0 h h-0 h ho h h- 0 h Problem #6: Select vProblem #4: Suppose that f is continuous on [0, 6] and that the only solutions of the equation f (x) = 3 are .T = l and x = 5. If f (4) = 2, then which of the following statements must be true'? (i)f(2) > 3 (ii)f(0) 3 (A) (i) only (B) (i) and (ii) (C) (iii) only (D) none of them (E) (i) and (iii) (F) all of them (G) (ii) and (iii) (H) (ii) only Problem #4: Problem #7: The following limit represents the derivative of some function fat some number a. Find such an fand a. lim V36 + h - 6 h-0 h (A) f (x) = Vx, a = 6 (B) f (x) = Vxth, a = 36 ( C)f (x) = Vxth, a = 6 (D) f(x) = Vx, a=6+h (E) f (x) = Vx, a= 36 +h (F)f(x) = Vxth - 6, a =36 ( G) f(x) = Vx - 6, a =6 (H) f (x) = Vx, a=36 Problem #7: Select