MATH 151 FALL 2008 COMMON EXAM II VERSION A LAST NAME First name print INSTRUCTOR SECTION NUMBER UIN SEAT NUMBER DIRECTIONS 1 The use of a calculator laptop or computer is prohibited 2 In Part 1 Problems 1 10 mark the correct choice on your ScanTron using a No 2 pencil For your own records also record your choices on your exam 3 In Part 2 Problems 11 16 present your solutions in the space provided Show all your work neatly and concisely and clearly indicate your final answer You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it 4 Be sure to write your name section number and version letter of the exam on the ScanTron form THE AGGIE CODE OF HONOR An Aggie does not lie cheat or steal or tolerate those who do Signature DO NOT WRITE BELOW Question Points Awarded Points 1 10 40 11 12 12 10 13 10 14 12 15 8 16 8 100 1 PART I Multiple Choice 1 4 pts In order to solve the equation x5 2x 5 0 we apply Newton s Method with an initial guess x1 1 What value does Newton s Method give for x2 the second approximation 7 3 1 b 4 a c d 1 3 7 4 e 1 4 sin2 3 0 2 2 4 pts lim a 9 b 3 1 c 9 1 d 3 e The limit does not exist 2 3 4 pts Find the tangent vector of unit length for r t e2t t cos t at t 0 1 1 a 2 2 b h2 1i c h1 0i 2 1 d 5 5 e h1 1i 4 4 pts Solve the equation ln x e ln x e 2 ln 3 a x 3e only b x 1 and x 3e c x 2e only d x 2e and x 2e e No solution 3 5 4 pts If g is the inverse of f find g 2 if it is known that f 3 2 f 3 7 f 2 11 and f 11 8 Assume g to be differentiable a b c d e 1 7 1 11 1 8 1 2 1 5 6 4 pts If h x f g f g x find h 3 given that g 3 4 f 3 7 g 3 2 f 2 11 and f 4 3 a 28 b 44 c 14 d 6 e 3 4 7 4 pts An object is moving with position function f t 2 sin t 3 cos t Find the velocity v t and the acceleration a t at t 6 3 3 a v 3 1 a 6 2 6 2 3 3 3 3 1 a b v 6 2 6 2 3 3 3 c v 3 1 a 6 2 6 2 3 3 3 3 1 a d v 6 2 6 2 3 3 3 1 3 a e v 6 2 6 2 8 4 pts If Q x is the quadratic approximation for f x a 3 5 b 2 3 c 2 7 d 2 9 e 2 5 2 at x 1 then Q x 1 2 9 4 pts Evaluate lim e1 x x 0 a 1 b 0 c d e e 10 4 pts Find the inverse function of f x a f 1 x b f 1 x c f 1 x d f 1 x e f 1 x 1 x 4x 3 1 3x 4x 1 3x 1 4x 1 4x 3 1 x 1 3x 4x 3x 1 4x 6 PART II WORK OUT Directions Present your solutions in the space provided Show all your work neatly and concisely and Box your final answer You will be graded not merely on the final answer but also on the quality and correctness of the work leading up to it 11 Find the derivative of i 6 pts f x tan3 x tan x3 ii 6 pts g t p 1 t 7 3 12 10 pts Water is poured into a conical cup at the rate of cubic inches per second If the cup is 6 inches tall and 2 the top of the cup has a radius of 2 inches how fast does the water level rise when the water is 4 inches deep Be 1 sure to include units with your answer NOTE The volume of a cone is V r2 h 3 8 13 10 pts Find the equation of the tangent line to the curve y 2 sin 2x 8 2y at the point 9 4 2 14 Consider the curve given by parametric equations x t2 10t y t3 3t2 i 6 pts Find the equation of the tangent line at t 1 ii 6 pts Find all points on the curve where the tangent line is a vertical b horizontal Exam continues on next page 10 15 8 pts Use differentials or a linear approximation to approximate 16 03 16 8 pts Find all value s of x 0 x 2 where f x x 2 sin x has a horizontal tangent End of Exam 11
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