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# Calculus MATH 234

UW

GPA 3.8

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This 3 page Class Notes was uploaded by Zechariah Hilpert on Thursday September 17, 2015. The Class Notes belongs to MATH 234 at University of Wisconsin - Madison taught by Staff in Fall. Since its upload, it has received 58 views. For similar materials see /class/205288/math-234-university-of-wisconsin-madison in Mathematics (M) at University of Wisconsin - Madison.

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Date Created: 09/17/15

MBA Eamwm Topics and Rules for Exam 1 For our rst exam October 9 Unless we have made special arrangements for something like a con ict your exam is 5304 700 PM If your TA is Nicos Georgiou or Christelle V incent you take the exam in B130 Vanl Vleck If your TA is Achilles Beros or Ben Otto you take the exam in B102 Van Vleck b You are allowed to use a calculator including graphing calculators but the problems will bd such that a calculator will not help much Kc You are allowed to bring in notes on one piece of paper not larger than 85quot by 55quot one half of a sheet of notebook paper You are allowed to use both sides and to write however small you want d Bring a picture ID card to the exam The exam problems will mostly resemble problems that were suggested in the syllabus for the course from the sections we have covered through 144 Clearly there cannot be problems on all of thatl material thou 11 Here are some comments 011 to ics sections and exam roblems o 13l introduced various terms and operations for vector functions They were described int terms of an object moving in the plane or in space There will M be an emphasis on physicsl or story problemsquot but vou may well find it easiest to think about these things in terms of motion and uestions ma r39 well use terms like osition velocit r39 and acceleration You wil not be asked to use and 3 to verify a limitl lications in 132 will not a ear on the exam You should be able to calculate arc length the local unit vectors T I speed curvature KH and torsion and the normal and tangential components of acceleration 11 and 1N for a 039iven parametrized path as derived in 1337 135 You will not be asked to solve fort parametrization in terms of arc length Note That does rule out calculating arc length 136 will not be 011 the exam l4l introduces terms and ways to picture functions of several variables You should be abld to use the terms an open region in the plane You will not be asked to draw graphs level curves or surfaces or contours but on rnav be asked uestions about ictures that present them From 142 you should be able to nd paths showing that a function is not continuous at a point probably the originl You certainly need to be able both to use the notation and to calculate partial derivatives foil functions of two or more variables de ned in l43 including higher derivatives You shouh be able to calculate the partials as functions as well as their values at specific points This tool set is developed further in 144 using the chain rule where vour under tandino39 of thd notation for partial derivatives is even more critical Math 234 Worksheet 1 Additional Book Problems in case you can7t get enough of them 0 Chapter 12 Review 15237455375575159 0 Section 131 1113715725729735737741 0 Section 133 3717except part e 0 Section 134 16711719721 0 Chapter 13 Review 23 without nding B3133 0 Section 141 97217252731745 0 Section 142 7 173745505 0 Section 143 1973174957765 More Challenging Problems guaranteed to keep you busy for a While H Find the equation ofthe plane passing through the points Px0y07 20 and Qx1y1 21 and is parallel to the vector V lt 111112113 gt D Find the equation of the line that is parallel to the intersection of the planes z y 32 2 and z 7 y 7 22 37 if you know that this line also passes from the common point of intersection of the lines r1t lt 2 123 2t7 71 7 t gt and r2s lt 72 2517 s1gt 242 t t 17 t 3 If rt lt 5 7 gt7 nd lgr rt 17cost2 r If the acceleration of a particle in time t is given by 1 1 a t lt 12277 gt7 t t2 1 and at time t 1 the position and velocity vector are equal to lt 1172log2 gt and lt 107 7 log2 gt7 respectively7 nd the position vector rt in time t CH If the velocity vector of a particle at time t is given by Vt lt cosz t sin 5t cos 5t7 2t 1 sint t2 gt7 nd the position vector and the acceleration vector at time t 0 03 Here is the position vector as a function of time of a particle moving in 3 dimensional space rt 0052ti x2costsin tj sinZ tk7 t2 0 i Find the velocity vector ii Find the acceleration vector iii ls it true that the velocity vector at time 7139 is perpendicular to the acceleration vector at that particular time iv Show that the particle is only moving on the surface of a sphere7 and nd the radius of that sphere 5 If a particle leaves the origin at time t 0 and the velocity vector at time t is given by Vt lt 6t cos t7 etsin t7 6t gt Find the following the position vector I39t7 ii the acceleration vector at7 iii the arc length pararneter 5t iv the arc length L from the point where t g to the point with t 7T v the curvature st7 vi the equation of the circle of curvature at the origin7 vii the unit tangent vector Tt7 viii the unit normal vector Nt7 ix the speed at time t log 2 00 Find the domain of the function 16 7 2 7 y2 f 9671 we 7 allow Check whether it is open7 closed7 bounded or unbounded Do the same for the function 1 9 2 2 2 2 OE 9 WM x2 y 7 4 Find the value of the following lirnits if they exist7 or explain why they do not exist 3 i 4 4 1 yllglob W7 ii Wyliglon 7 10 If fxyz 6w cosz tanz y 7 log3 23 nd fmy ii 7 iii fym 11 If the function Fzy7 2 satis es F07 1 el2 g and has partial derivatives 7 yz coszyz em z 22 4x 67 x2 coszyz z em 7 siny7 3F 22 a zycosxyz y m 17 nd the equation of Fxyz

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