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Course: MATH 160, Fall 2008
School: Boise State
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Word Count: 317

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APPLICAnONS 8.2 TO GEOMETRY 435 14. Rotate the bell-shaped curve y = e-xz/2 shown in Figure 8.21 around the y-axis, forming a hill-shaped solid of revolution. By slicing horizontally, find the volume of this hill. y 1 Y = e-xzJ2 x Figure 8.21 15. The circumference of the trunk of a certain tree at different heights above the ground is given in the following table. Height (feet) 120&quot; Circumference (feet)...

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APPLICAnONS 8.2 TO GEOMETRY 435 14. Rotate the bell-shaped curve y = e-xz/2 shown in Figure 8.21 around the y-axis, forming a hill-shaped solid of revolution. By slicing horizontally, find the volume of this hill. y 1 Y = e-xzJ2 x Figure 8.21 15. The circumference of the trunk of a certain tree at different heights above the ground is given in the following table. Height (feet) 120" Circumference (feet) 1 . I Assume all horizontal cross-sections of the trunk are circles. Estimate the volume of the tree trunk using the trapezoid rule. 16. Most states expect to run out of space for their garbage soon. In New York, solid garbage is packed into pyramid-shaped dumps with square bases. (The largest such dump is on Staten Island.) A small community has a dump with a base length of 100 yards. One yard vertically above the base, the length of the side parallel to the base is 99 yards; the dump can be built up to a vertical height of 20 yards. (The top of the pyramid is never reached.) 65 If cubic yards of garbage arrive at the dump every day, how long will it be before the dump is full? 17. The hull of a certain boat has widths given by the following table. Reading across a row of the table gives widths at points 0, 10, . . . , 60 feet from the front to the back at a certain level below waterline. Reading down a column of the table gives widths at levels 0, 2, 4, 6, 8 feet below waterline at a certain point from the front to the back. Use the trapezoidal rule to estimate the volume of the hull below waterline. Front of boat ---+ Back of boat 0 10 20 30 40 50 60 0 2 8 13 16 17 16 10 Depth 2 1 4 8 10 11 10 8 below 4 0 3 4 6 7 6 4 waterline 6 0 1 2 3 4 3 2 (in feet) 8 0 0 1 1 1 1 1 For Problems 18 and 19, find the arc length of the given function from x = 0 to x = 2. 18. f(x) = ~ 19. f(x) = R 20. (a) Write an integral which represents the circumference of a circle of radius r. (b) Evaluate the integral, and show that you get the answer you expect. .
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Boise State - MATH - 160
21. Figure 8.22 is a graph of the function1(X-X)Y~2e +e .It is called a catenary and represents the shape in which a cable hangs. Find the length of thiscatenary between x = -1 and x = 1.y 1Y = -(eX +e-X)2x1Figure 8.22.22. , Compute the p
Boise State - MATH - 160
Problems for Section 8.3I. A water tank is in the fonn of a right circular cylinder with height 20 ft and radius 6 ft. If tIJtank is half full of water, find the work required to pump all of it over the top rim. (NoteI cubic foot of water weighs 6
Boise State - MATH - 160
9. Show that the escape velocity needed by an object to escape the gravitational influence of aspherical planetof density p and radius R is proportional to R and to ~.10. Calculate the escape velocity of an object from the moon. The acceleration du
Boise State - MATH - 160
ems for Section 8.6..1. Consider the fishing data given in Example 1 on page 463. Show that the area under thedensity function in Figure 8.44 is 1. Why is this to be expected?2. Find the mean daily catch for the fishing data in Figure 8.44, page
Boise State - MATH - 160
(b) What was the median income?(c) Sketch a density function for this distribution. Where, approximately, does your densityfunction have a maximum? What is the significance of this point, in terms of incomedistribution? How can you recognize this
Boise State - MATH - 160
REVIEW PROBLEMS FOR CHAPTER EIGHT1. (a) Sketch the solid obtained by rotating the region bounded by y = yf&quot;i, x = 1, and y = 0around the line y = O. -(b) Approximate its volume by Riemann sums, showing the volume represented by eachterm in your s
Boise State - MATH - 160
Antiderivatives and Indefinite Integrals Worksheet Evaluate the following indefinite integrals 1.-2 dx =2.2x 5dx =3.3t - 7dt =34.2u 4 du =5.3x-2 3dx =6.1 dx = 3x 5 3 dt = t7.8.- ( 1+ u + u ) du =29.- ( 0.3t
Boise State - MATH - 160
Antiderivatives and Indefinite Integrals Worksheet Evaluate the following indefinite integrals 1.-2 dx =2.2x 5dx =3.3t - 7dt =34.2u 4 du =5.3x-2 3dx =6.1 dx = 3x 5 3 dt = t7.8.- ( 1+ u + u ) du =29.- ( 0.3t
Boise State - MATH - 160
Area Between Curves Worksheet1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30.31.32.33.34.35.36.37.38.39.40.Key1. 2. 3. 4. 5. 6. 7. 8.
Boise State - MATH - 160
Definite Integrals Worksheet Evaluate the following definite integrals 1.)4 - 2( 3 x - 5)dx =2.) ( 2x - 10e x )dx =3.) (0 2 14x dx =)4.2 + x x 1 = dx 5.) ) )1 0( u ) ( u + 3 u ) du =1 dx = x6.8 47.
Boise State - MATH - 160
Definite Integrals Worksheet Key Evaluate the following definite integrals 1.)4 - 2( 3 x - 5)dx =4 2 3 3 3 48 12 x - 5 x = ( 4) 2 - 5 ( 4) ( - 2) 2 - 5 ( - 2) - 20 + 10 4 - 16 = - 12 - = - = 2 2 2 2 2 2 2.
Boise State - MATH - 160
Differential Equations Worksheet1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30.31.32.33.34.35.36.37.38.39.40.Key1. 2. 3. 4. 5. 6. 7.
Boise State - MATH - 160
Definite Integral Word ProblemsExample 1 An empty bucket is placed under a tap and filled with water. t minutes after the bucket has been placed under the tap. The rate of flow of water into the bucket is equal to 2.3 - 0.1t gallons per minute. How
Boise State - MATH - 160
Derivatives - Chain Rule Worksheet Key 1. f ( x ) = ( 1 - x )3f ' ( x ) = -3 ( 1 - x )22. f ( x ) = 2 ( x 3 - 1) 3. f ( x ) =5f ' ( x ) = 30 x 2 ( x 3 - 1)4-3 1 ( 2x 2 + x ) 23 ( 1+ 4x ) df =- dy 2 ( 2x 2 + x )1 d ( y ) = ( 3 ) ( 3
Boise State - MATH - 160
Derivatives - Chain Rule 1. f ( x ) = ( 1 - x )3f' ( x) =2. f ( x ) = 2 ( x 3 - 1)5f' ( x) =3. f ( x ) =-3 1 ( 2x 2 + x ) 2df = dy4. y = ( 3 x 2 - 2 x + 1) 23d ( y) = dx dy = dx45. y = 3 x 2 - x6. y = ( x - 1)2( 2 x + 1)
Boise State - MATH - 160
Derivative Problems Use the definition of derivative to solve the following. 1. f ( x ) = 3x + 5 f' ( x) =2. y = x 3dy = dx3. f ( x ) = x 3 - 4 x 2df = dx4. y =1 5xd ( y) = dx5. f ( x ) = - x 2 + 3xf' ( x) =Use the rules of differ
Boise State - MATH - 160
Derivative Worksheet Use the definition of derivative to solve the following. 1. f ( x ) = 3 x + 5 f' ( x) =2. y = x 3dy = dx3. f ( x ) = x 3 - 4 x 2df = dx4. y =1 5xd ( y) = dx5. f ( x ) = - x 2 + 3 xf' ( x) =Use the rules of dif
Boise State - MATH - 160
Continuityy = f ( x)1. What is the domain of f ' ( x ) ? 2. What is the range of f ' ( x ) ? 3. Find the x -intercept(s) of f ( x ) ? 4. Find the y -intercept(s) of f ( x ) ? 5. f ( -8 ) = _ f ( 2 ) = _ f ( -4 ) = _ f ( 8 ) = __6.x - 6-lim f
Boise State - MATH - 160
Continuity and DerivativesDefinition of continuous functionSecant becoming the tangent line
Boise State - MATH - 160
Derivatives - Product Rule Worksheet 1. f ( x ) = ( 2 x 2 - 1) ( x 3 + 3 ) f' ( x) =2. f ( x ) = ( x 3 - 12 x ) ( 3 x 2 + 2 x )f' ( x) =3. f ( x ) = 3 x 2 ( x - 1)df = dy4. y = ( 5 x 2 + 1) 2 x - 1()d ( y) = dx dy = dx5. y = ( x 3 -
Boise State - MATH - 160
Derivatives - Product Rule Worksheet Key 1. f ( x ) = ( 2 x 2 - 1) ( x 3 + 3 ) f ' ( x ) = 10 x 4 - 3 x 2 + 12 x2. f ( x ) = ( x 3 - 12 x ) ( 3 x 2 + 2 x )f ' ( x ) = 15 x 4 + 8 x 3 - 108 x 2 - 48 x3. f ( x ) = 3 x 2 ( x - 1)df = 9x 2 - 6x dy
Boise State - MATH - 160
Derivatives - Quotient Rule Worksheet 11. f ( x ) = 1 x -2 x -1 2x + 1 x 2x - 4 f' ( x) =12. f ( x ) =f' ( x) =13. f ( x ) =df = dy14. y =x2 + 1 x2 - 1d ( y) = dx15. y =x x +12dy = dxx2 + 2 16. y = 2 x + x +1 x2 + 1 xy' =17
Boise State - MATH - 160
Derivatives - Quotient Rule Worksheet Key 11. f ( x ) = 1 x -2 f' ( x) = -1( x - 2)3212. f ( x ) =x -1 2x + 1f' ( x) =( 2 x + 1)213. f ( x ) =x 2x - 4df -4 = dy ( 2 x - 4 ) 2 d -4 x ( y) = 2 2 dx ( x - 1)14. y =x2 + 1 x2 - 1
Boise State - MATH - 160
Simple Linear RegressionLeast Square Curve Fitting1PurposeAssume that two quantitative variables that are measured on the same items are sampled from a population. We get n pairs of observations: (x1, y1),.,(xn ,yn) Our aim is to develop a mode
Boise State - MATH - 160
Math 160 Calculus Problem 27, page 42 Regression ExampleFirst, we enter the 5 columns of data into lists, L1 - Year, L2 - Men's 100 Times, L3 - Women's 100 Times, L4 - Men's 200 Times, L5 - Women's 200 Times.For each set of times we need to: a) l
Boise State - MATH - 160
Math 160 Calculus Problem 27, page 42 Regression ExampleFirst, we enter the 5 columns of data into lists, L1 - Year, L2 - Men's 100 Times, L3 - Women's 100 Times, L4 - Men's 200 Times, L5 - Women's 200 Times.For each set of times we need to: a) l
Boise State - MATH - 160
Multi-variable Extrema Worksheet1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30.31.32.33.34.35.36.37.38.39.40.Key1. 2. 3. 4. 5. 6. 7.
Boise State - MATH - 160
Partial Derivatives Worksheet1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30.31.32.33.34.35.36.37.38.39.40.Key1. 2. 3. 4. 5. 6. 7. 8.
Boise State - MATH - 160
Microeconomics with Calculus: Tutorial #1Calculus and EconomicsDaniel S. Christiansen ALBION COLLEGE christiansen@albion.edu August 14, 2002 Instructions for Viewing View Full Screen Table of Contents Begin tutorialc Copyright 19992002 Daniel
Boise State - MATH - 160
1.011 Project Evaluation Carl D. Martland Assignment 2 Cost &amp; Revenue Functions Assigned: Due: Monday, February 10, 2003 Tuesday, February 18, 2003Problems from Text 1 Be sure that you understand all of the elements of 2-3 and 2-37 (basic terminolo
Boise State - MATH - 160
Cost, Revenue and Profit Functions Michael Cooney1Many business situations allow us to model how cost, revenue and vary with respect to different parameters, and how they combine to yield a functional expression for profit. In most cases, it is t