MATH 152 FALL 2011 COMMON EXAM III VERSION A PRINT LAST NAME FIRST NAME INSTRUCTOR SECTION NUMBER UIN SEAT NUMBER Directions 1 The use of all electronic devices is prohibited 2 In Part 1 Problems 1 12 mark the correct choice on your Scantron using a No 2 pencil Record your choices on your exam Scantrons will not be returned 3 In Part 2 Problems 13 17 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 and version letter of the exam on the Scantron form 5 Any scratch paper used must be handed in with the exam 6 Good Luck THE AGGIE CODE OF HONOR An Aggie does not lie cheat or steal or tolerate those who do Signature http foxtrot com Question 1 12 13 14 15 16 17 TOTAL 48 10 14 7 11 10 100 Points Awarded Points Possible 1 MATH 152 FALL 2011 COMMON EXAM III 1 Find a unit vector in the direction of the vector h 3 3 2i a 4h 3 3 2i 1 b h 3 3 2i 16 c 16h 3 3 2i 1 d h 3 3 2i 16 1 e h 3 3 2i 4 2 What is the distance between points 2 1 4 and 1 3 2 a 3 b 29 c 7 d 61 e 49 3 What is the Maclaurin series for e a b c d e x2 2 X xn 2 2 n n 0 X n 0 X n 0 X n 0 X n 0 xn 2 n xn 2n n x2n 2n n x2n 2n 2n 2 VERSION A MATH 152 FALL 2011 COMMON EXAM III 4 Which series diverges a b c d e X n2 2n 1 n 2 X n 0 X n 1 X n 1 X n 1 n3 4n 1 n2 2n 4 2 ne n 1 n 1 n n 5 Which series converges absolutely a b c d e X 1 n n n 1 X 1 n en n 1 X n 1 X n 1 X n 1 en 1 n 2 n 1 n n 2 n n 6 What is the power series representation of f x a b c d e X n 0 X n 0 X n 0 X n 0 X n 1 1 n 4n x2n 9n 1 4n x2n 9n 1 9n x2n 4n 1 1 n 9n x2n 4n 1 4n x2n 9 3 1 at x 0 9 4x2 VERSION A MATH 152 FALL 2011 7 Given that the power series X COMMON EXAM III cn xn converges when x 3 and diverges when x 6 which of the n 0 statements is certain to be true a b c d X n 0 X n 0 X n 0 X VERSION A cn 6 n is divergent cn 4 n is convergent cn 3 n is convergent cn 2 n is convergent n 0 e None of these statements is certain to be true 8 What is the cosine of the angle between the vectors h 1 2 3i and h3 2 1i 5 a 7 5 b 7 5 c 7 2 d 7 2 e 7 9 Let a b c and d be nonzero vectors where kak is the length of a Given a b kakkbk and 0 c d kckkdk Which of these statements is true a a and b are parallel c and d are neither orthogonal nor parallel b a and b are orthogonal c and d are neither orthogonal nor parallel c a and b are neither orthogonal nor parallel c and d are orthogonal d a and b are neither orthogonal nor parallel c and d are parallel e None of the above statements is true 4 MATH 152 FALL 2011 COMMON EXAM III 10 Find the vector projection of the vector h3 2 1i onto the vector h1 2 3i a b c d e 5 7 10 14 1 h30 20 10i 14 1 h10 20 30i 14 1 h30 20 10i 14 11 Find the radius of convergence of the power series X 3n x 5 n n 1 n a 0 1 b 3 c 3 16 d 3 e 12 The equation of the sphere passing through the point 1 2 3 with center 2 1 3 is a x 1 2 y 2 2 z 3 2 10 b x 2 2 y 1 2 z 3 2 10 c x 1 2 y 2 2 z 3 2 10 d x 2 2 y 1 2 z 3 2 10 e x 1 2 y 2 2 z 3 2 100 5 VERSION A MATH 152 FALL 2011 COMMON EXAM III VERSION A 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 13 10 points Find the radius and center of the sphere x2 y 2 z 2 4x 2y 6z 11 6 MATH 152 FALL 2011 COMMON EXAM III VERSION A 3 14 8 points Find the first four terms of the Taylor series for f x x 2 centered at a 4 6 points Use Taylor s Inequality to give a bound for the error for when using T1 x the first degree 3 Taylor polynomial centered at a 4 to approximate f x x 2 on 3 5 Taylor s Inequality Rn x M x a n 1 on the interval 3 5 where M max f n 1 x n 1 on 3 5 7 MATH 152 FALL 2011 15 7 points Compute the Maclaurin series for COMMON EXAM III cos x 1 x2 8 VERSION A MATH 152 16 6 points The series FALL 2011 X 1 n COMMON EXAM III n VERSION A converges conditionally Determine whether this series n also converges absolutely Clearly explain your reasoning n 1 3n 2n2 5 points What is a bound on the error if we sum the first 3 terms of the series 9 MATH 152 FALL 2011 COMMON EXAM III 17 10 points Find the interval of convergence for the power series X x 5 n 3n n2 2 n 0 10 VERSION A
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