Exam 1 Oct 12 2015 MTH 234 Name Section Recitation Instructor READ THE FOLLOWING INSTRUCTIONS Do not open your exam until told to do so No calculators cell phones or any other electronic devices can be used on this exam Clear your desk of everything excepts pens pencils and erasers If you need scratch paper use the back of the previous page Without fully opening the exam check that you have pages 1 through 9 Fill in your name etc on this rst page Show all your work Write your answers clearly Include enough steps for the grader to be able to follow your work Don t skip limits or equal signs etc Include words to clarify your reasoning Do rst all of the problems you know how to do immediately Do not spend too much time on any particular problem Return to di cult problems later If you have any questions please raise your hand and a proctor will come to you There is no talking allowed during the exam You will be given exactly 90 minutes for this exam I have read and understand the above instructions SIGNATURE Page 1 of 9 MTH 234 Exam 1 Oct 12 2015 Multiple Choice Circle the best answer No work needed No partial credit available 1 8 points Consider the surface given by equation below and answer the questions that follow a Horizontal traces or cross sections i e planes parallel to z k 1 of the surface 3z x2 2 y2 9 1 b Vertical traces or cross sections i e planes parallel to either x k or y k of the surface 2 4 points The contour plot level curves to the right could be from which function de ned by 1 are A Circles B Parabolas C Ellipses D Hyperbolas E None of the above de ned by 1 are A Circles B Parabolas C Ellipses D Hyperbolas E None of the above A f x y x sin y B f x y x sin y C f x y y sin x D f x y x cos y E f x y y sin x F None of the above Extra Work Space Page 2 of 9 xy MTH 234 Exam 1 Oct 12 2015 Fill in the Blanks No work needed No partial credit available 3 10 points Find the velocity and position functions of a particle that satis es the following conditions a t sin t i 12e 2t j 8 k v 0 i 6 j r 0 3 j k 4 8 points Let u 3 i 2 j k and v i 5 j 2 k Find each of the following b Let be the angle between u and v Then cos 5 6 points The line segment from 3 7 5 to 2 4 1 is given by the parametric equations a v t b r t a 2u 3v x t y t z t t 0 1 Extra Work Space Page 3 of 9 MTH 234 Exam 1 Oct 12 2015 Standard Response Questions Show all work to receive credit Please BOX your nal answer 6 12 points Find the length of the curve below r t i 4t j t2 k 0 t 1 8t3 2 3 7 Let f x y 1 cid 112 2x2 1 y a 8 points Sketch the domain of f y b 4 points Give the range of f Express your answer using interval notation x Page 4 of 9 MTH 234 Exam 1 Oct 12 2015 8 14 points Find the following limits or show that they do not exist a lim x y 0 0 x2 sin2 y 2x2 y2 b lim x y 0 0 xy2 8x2 3y4 9 Let f x y x2 ey 6y x a 12 points Find the linearization of f x y at the point 4 0 b 6 points Use the linearization from part a to approximate f 3 9 0 2 Page 5 of 9 MTH 234 Exam 1 Oct 12 2015 10 12 points Find the equation of the plane containing the points A B and C if A 3 0 1 B 1 2 2 C 6 1 3 11 10 points Let w xy2 yex 2 where x x s t and y y s t are di erentiable Suppose also that x 1 3 2 xt 1 3 4 xs 1 3 5 y 1 3 3 yt 1 3 6 ys 1 3 0 Find wt 1 3 Page 6 of 9 MTH 234 Exam 1 Oct 12 2015 12 10 points Let g x y 5x2y3 Find gxy and gyy ln 2y x 13 12 points Find the parametric equations for the line tangent to the curve r t cid 104 2 ln t t2 3 1 4t3 cid 105 at the point 2 4 3 gxy gyy x t y t z t Page 7 of 9 MTH 234 Exam 1 Oct 12 2015 14 14 points Let f x y 3xy2 2y and answer the questions below a Find the equation of the plane tangent to surface z f x y at the point P 2 1 4 b Find the distance from the point Q 2 4 5 to the tangent plane from part a Page 8 of 9 MTH 234 Exam 1 Oct 12 2015 Congratulations you are now done with the exam Go back and check your solutions for accuracy and clarity Make sure your nal answers are BOXED When you are completely happy with your work please bring your exam to the front to be handed in Please have your MSU student ID ready so that is can be checked DO NOT WRITE BELOW THIS LINE Page Points Score 2 3 4 5 6 7 8 12 24 24 32 22 22 14 Total 150 Page 9 of 9