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# Calculus III MATH 2210

The U

GPA 3.95

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This 3 page Study Guide was uploaded by Miss Noel Mertz on Monday October 26, 2015. The Study Guide belongs to MATH 2210 at University of Utah taught by Staff in Fall. Since its upload, it has received 23 views. For similar materials see /class/229950/math-2210-university-of-utah in Mathematics (M) at University of Utah.

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Date Created: 10/26/15

MIDTERM I INFORMATION Our first midterm will be held in class this Friday February 15 Listed below are the topics which you will be expected to know along with sample problems representing the types of questions which might appear Also listed are the formulae you are expected to memorize as well as those which will be provided for you Calculators and cell phones will not be allowed on the test Chapter 11 Topics 0 Dot Products Know the definition and how to compute Remember the formula 11 V Hull HVH COS97 and its important consequence u v 0 ltgt uv orthogonal Sample problems Chapter 11 Concept Test 9 40 Chapter 11 Sample Test 3 6 0 Cross Products Know the definition and how to compute it Remember the fact u gtlt v is orthogonal to both u v Sample problems Chapter 11 Sample Test 5 9 0 Lines and Planes Know how to find the Cartesian equations and parametric equations for lines and planes Sample problems Chapter 11 Sample Test 13 14 15 19 o Curvature and Components of Acceleration Know the concept of curvature and the original definition 7 H T H Is 7 Hr H Know how to find unit tangent vector T and the principal unit normal N Understand the decomposition a aTT aNN Date February 9 2008 You will not be required to remember the following formulae They will be given to you if needed H m 711 WHr XMl W llgt213 Hr HS dzs r r 0T 0FW 2 a e K a N dt N M 39 Sample Problems Chapter 11 Concept Test 33 36 45 Chapter 11 Sample Test 29 117 34 47 Chapter 12 Topics 0 Partial Derivatives Know how to compute partial derivatives of any order Sample Problems Chapter 12 Sample Test 3 6 7 o Gradient and Directional Derivative Know how to compute the gradient V f of a function f Remember the formula for computing the derivative of f at the point a in the direction of the unit vector u Dufa Vfa u Remember the important consequence of the above formula V f a points in the direction f increases most rapidly at a Sample Problems Chapter 12 Sample Test 13 14 16 0 Chain Rule Know how to use the chain rule to compute various derivatives Sample Problems Chapter 12 Sample Test 19 20 o Tangent Planes Know how to find the equation of the tangent plane to a surface defined by an equation 9672172 0 at a point a b c on the surface Sample Problems Chapter 12 Sample Test 23 127 17 o Differentials and Approximation Know the definition of the differential df of a function f and how to use it to approximate values of f Sample Problems Chapter 12 Sample Test 24 25 0 Local Extrema Know how to find the critical points of a function f ie the singular points where f is not differentiable and the stationary points where V f a 0 Remember the matrix of second derivatives fma 5 fez17 H 17 b 7 lt Ma M Ma b and how to use it to test a stationary point in order to determine if it39s a local max local min or saddle point Sample Problems 128 2 3 6 o Constrained Optimization Lagrange Multipliers Know how to find the critical points of a constrained system Remember how to find the global max min of a function f defined on a closed bounded set S 1 Find all of the critical points of f but keep only those contained in S 2 Find the critical points of f constrained to the boundary of S 3 Compare the values of f at all of the critical points found in the previous two steps Sample Problems Chapter 12 Sample Test 28 29 129 23

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