MATH 151 FALL 2005 COMMON EXAM II VERSION A NAME print INSTRUCTOR SECTION NUMBER UIN DIRECTIONS 1 The use of a calculator laptop or computer is prohibited 2 In Part 1 Problems 1 13 mark the correct choice on your ScanTron form No 815 E using a No 2 pencil For your own records also record your choices on your exam ScanTrons will be collected from all examinees after 90 minutes and will not be returned 3 In Part 2 Problems 14 18 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 13 52 14 14 15 8 16 8 17 8 18 10 100 1 PART I 1 4 pts If f x e4x 5e3x 3ex sin x then f 0 0 a 1 b 0 c 6 d 7 e 8 2 4 pts If F x f g x where f 2 3 g 2 5 g 0 2 4 f 0 2 2 g 0 3 7 and f 0 5 11 then F 0 2 a 72 b 44 c 2 d 8 e 14 Exam continues on next page 2 3 4 pts Find lim x 0 3x 1 cos x sin 4x 3 2 3 b 4 c 0 a 3 4 3 e 2 d 4 4 pts Find d x cos 2x dx a sin 2x 2x cos 2x b sin 2x 2x cos 2x c cos 2x 2x sin 2x d cos 2x 2x sin 2x e 2x sin 2x Exam continues on next page 3 5 4 pts Find d 2 x y when x 2 and y 3 given that dx dt 2 and dy dt 4 dt a 28 b 16 c 4 d 8 e 12 6 4 pts If f x a b c d e 2x 1 then the inverse function of f x is x 5 x 5 2x 1 1 5x x 2 1 5x x 2 1 5x x 2 2x 1 x 5 Exam continues on next page 4 7 4 pts If h t t3 t2 t 1 3 then h 0 1 a 216 b 108 c 72 d 12 e 6 8 4 pts Find lim ex 1 x a b e c 1 1 d e e 0 Exam continues on next page 5 9 4 pts If log4 x log4 x2 6 then x a 16 b 8 c 4 d 2 e 0 10 4 pts If f x x5 2x 1 and g x denotes the inverse function of f x then g 0 4 a 4 b 1 1 c 7 1 d 8 1 e 12 Exam continues on next page 6 For problems 11 13 let the time t position of a particle be given by the vector function r t ht3 4t2 2 2t2 3ti 11 4 pts Find the position vector of the particle at time t 2 a h 6 2i b h 4 2i c h 2 4i d h0 0i e h2 4i 12 4 pts Find the speed of the particle at time t 2 a h 2 6i b h 4 5i c h0 8i d 41 41 e 13 4 pts Find the acceleration of the particle at time t 2 a h1 2i b h4 4i c h4 2i d h 4 4i e h8 6i Exam continues on next page 7 PART II 14 Find f 0 x for the following functions Don0 t simplify a 7 pts f x cos 2x sin 3x tan 4x b 7 pts f x e x2 3x 4 Exam continues on next page 8 15 8 pts Find the equation of the tangent line to the curve y 5 3x2 y 3 x3 5 0 at the point 2 1 Exam continues on next page 9 16 8 pts Starting with x1 1 use Newton s method to find the approximation x2 to the solution of the equation x5 x3 1 0 Exam continues on next page 10 17 8 pts Find the quadratic approximation of 4 x for x near 16 Exam continues on next page 11 18 10 pts A balloon is rising at a constant speed of 5 ft sec A boy is cycling along a straight road at a speed of 15 ft sec When he passes under the balloon it is 45 ft above him How fast is the distance between the boy and the balloon increasing 3 seconds later End of exam 12
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