Exam 1 October 9th 2017 MTH 234 Name Section Recitation Instructor INSTRUCTIONS Fill in your name etc on this rst page Without fully opening the exam check that you have pages 1 through 11 Show all your work on the standard response questions 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 You will be given exactly 90 minutes for this exam Remove and utilize the formula sheet provided to you at the end of this exam ACADEMIC HONESTY Do not open the exam booklet until you are instructed to do so Do not seek or obtain any kind of help from anyone to answer questions on this exam If you have questions consult only the proctor s Books notes calculators phones or any other electronic devices are not allowed on the exam Students should store them in their backpacks No scratch paper is permitted If you need more room use the back of a page Anyone who violates these instructions will have committed an act of academic dishonesty Penalties for academic dishonesty can be very severe All cases of academic dishonesty will be reported immediately to the Dean of Undergraduate Studies and added to the student s academic record I have read and understand the above instructions and statements regarding academic honesty SIGNATURE cid 63 Page 1 of 11 MTH 234 Exam 1 October 9th 2017 Standard Response Questions Show all work to receive credit Please BOX your nal answer 1 7 points Find a parametrization for line of intersection between the planes x y z 1 and 2x z 3 2 7 points What is the distance between the origin and the plane x y 3z 2 Page 2 of 11 MTH 234 Exam 1 October 9th 2017 3 An object moves along the curve r t 3 1 cid 104 t2 5 t3 for time t cid 105 0 a 5 points What is the speed of the object at time t 2 b 9 points What is the length of the curve from t 0 to t 2 Page 3 of 11 MTH 234 Exam 1 October 9th 2017 4 Consider the function f x y x y2 a 5 points Sketch the domain of f cid 112 b 6 points Sketch the level curves of f for k 0 k 1 and k 2 c 3 points What is the range of f y y x x Page 4 of 11 MTH 234 Exam 1 October 9th 2017 5 7 points Evaluate the limit or show that it does not exist y2 x2 x y lim 3 x 3 y 6 7 points Evaluate the limit or show that it does not exist lim 1 0 x y xy x y 1 Page 5 of 11 MTH 234 Exam 1 October 9th 2017 7 Consider the function f x y 4x ln xy 1 3 a 5 points Calculate the partial derivatives fx and fy b 5 points Use your answer in part a to nd the linearization of f at 1 2 c 4 points Use your answer in part b to approximate f 1 2 1 9 Page 6 of 11 MTH 234 Exam 1 October 9th 2017 Multiple Choice Circle the best answer No work needed No partial credit available 8 4 points Find the radius and center for the sphere x2 y 1 2 z2 6z 7 A center 0 B center 0 1 3 radius 7 1 6 radius 7 C center 0 3 radius 7 D center 0 3 radius 4 E center 0 1 3 radius 4 1 1 A B C D E 2 cid 104 2 1 cid 105 cid 104 2 1 cid 105 1 cid 105 1 cid 105 cid 104 2 cid 104 0 0 cid 105 cid 104 9 4 points Consider the vectors a and b shown to the right in R2 Which of the following vectors could be projba y a b x 10 4 points Determine what quadric surface this equation represents y2 z x2 A Hyperboloid of One Sheet B Elliptic Paraboloid C Hyperbolic Paraboloid D Cone E Hyperboloid of Two Sheets Page 7 of 11 MTH 234 Exam 1 October 9th 2017 11 4 points Find the area of the parallelogram determined by i 2k and 2i j k A 4 B 14 C 11 D 10 E 3 A r t t 1 B r t C r t D r t E r t t2 2 t2 t 2 cid 11 with t 0 2 0 2 1 with t with t cid 10 cos t sin t 1 cid 10 cid 11 cid 105 cid 104 cos t sin t 2 cid 105 with t cos t sin t 0 cid 105 cid 104 cid 104 with t 0 2 0 2 0 2 A r t B r t C r t D r t t2 3t cos t cid 105 t2 1 3t 2 cos t 3 t2 1 3t 2 t2 1 3t 2 cos t 2 cos t 3 cid 105 cid 105 cid 105 E r t 2 0 cos t cid 105 cid 104 cid 104 cid 104 cid 104 cid 104 12 4 points Which of the following is a parametrization for the full curve of intersection between x2 y2 z2 2 and z x2 y2 13 4 points Which of the following satisfy r cid 48 t 2t 3 cid 104 sin t cid 105 and r 0 1 2 3 cid 105 cid 104 Page 8 of 11 MTH 234 Exam 1 October 9th 2017 14 4 points Consider the function f x y Calculate fxy 2x y A fxy 2 y 2 B fxy y2 C fxy 2x y2 D fxy 2 E fxy 0 A 6 B C D E 14 15 3 84 A B C D E 0 3 cid 104 0 1 cid 105 3 10 1 10 cid 68 2 0 sin t cid 104 2 0 0 cid 104 cid 105 1 0 0 cid 105 cid 104 cid 69 cid 105 15 4 points Suppose z x2y where x and y are di erentiable functions of t with x 1 3 x cid 48 1 2 y 1 4 y cid 48 1 5 Which of the following is equivalent to dz dt t 1 cid 12 cid 12 cid 12 16 4 points Find the unit tangent vector of r t 2ti 3j cos t k at t 0 Page 9 of 11 MTH 234 Exam 1 October 9th 2017 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 …