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# Calculus III MTH 203

GVSU

GPA 3.58

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This 2 page Class Notes was uploaded by Cristal Erdman on Saturday September 26, 2015. The Class Notes belongs to MTH 203 at Grand Valley State University taught by Brian Drake in Fall. Since its upload, it has received 20 views. For similar materials see /class/214359/mth-203-grand-valley-state-university in Mathematics (M) at Grand Valley State University.

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Date Created: 09/26/15

Math 203 Fall 2010 Drake Final Exam Review The textbook sections that will be on the nal exam are 91 95 97 101 104 111 118 121 125 127 128 Approximately half of the exam will be on material since the last test 118 128 and the other half will be on chapters 9 11 Suggested Review I wont be posting answers you could just do odd problems or nd a way to check for yourself 0 Chapter 9 Review pp 687 690 7 Concept check 1 131516 7 True False Quiz 1 18 7 Exercises 1 3 4a j 10 12 15 17 18 20 0 Chapter 10 Review pp 733 734 7 Concept check 1 5 7 True False Quiz 1 5 7 Exercises 138 9 11 16 0 Chapter 11 Review pp 822 826 7 Concept Check 1 6 8 11 13 17 19 7 True False Quiz 134579 7 Exercises 345 7 14 19 25 33 43 45 47 49 51 54 59 62 0 Chapter 12 Review pp 899 902 7 Concept Check 1234ac 7 8ac 9 7 True False Quiz 179 7 Exercises 1 3 5 9 10 11 12 13 15 17 19 23 27 29 31 41 42 47 Additional problems 1 Find a point on the y axis equidistant from 25 73 and 73 6 1 2 Find a unit vector in the same direction as 723 6 3 Find the angle between the vectors 123 and 27371 4 Find a vector which is normal to the plane containing the points 1714 201 and 023 5 Find the volume of the tetrahedron with corners 001 124 113 and 212 6 Find paramentric equations for the line through the points 321 and 71 24 7 Sketch contour diagrams for the function fzy y 7 z3 00 3 H H 2 Show that yz does not exist 2 7 lim 7 mapm z y A right circular cone is changing its height h is decreasing at a rate of 3 cm per second7 while the radius is increasing at a rate of 2 cm per second Recall that the volume is V wrzh ls the volume increasing or decreasing when r 5 and h 6 The production capacity P is a function of capital K and labor L and is modeled by PK L 12K03921L03979 Suppose that capital increases by 1 while labor remains unchanged Use the differential to estimate the percentage increase in production Suppose ay y and V 4i 7 3j Find the directional derivative at the point 26 in the direction of V The temperature at any point in the plane is given by the function 100 T MI 1 952 112 a Where on the plane is it hottest What is the temperature at that point b Find the direction of the greatest increase in temperature from the point 32 What is the magnitude of that greatest increase in degrees per unit of distance A student was asked to use the gradient to nd the directional derivative of ay Hey at the point 17 0 in the direction of V 4i 3j His answer was 8 3 Duf170 f170 11 51 3 How can you tell this is wrong at a glance What is the correct answer Find the critical points of the function ay 8y3 12 7 24xy and classify each critical point A company produces two items7 sold in separate markets If qi items are to be sold7 the price should be pi where Notice that if we want to sell more items7 we need to lower the price The production costs for the two items are related the total production cost is C 16 1211 15QZ 02q1q2 Find the production levels to maximize pro t Recall that pro t revenue gtlt cost7 while revenue price gtlt quantity Use the method of Lagrange multipliers to nd the maximum value of ay z y on the circle 2 y2 4 lllustrate geometrically

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