Thomas' Calculus: Early Transcendentals, Single Variable , 12th Edition Test Bank

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ExamName___________________________________MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriategraph of the specified function.1)f(x)=11+6x-x31)A)[-10, 20] by [-50, 50]B)[-4, 5] by [-15, 25]C)[-10, 10] by [-10, 5]D)[-4, 5] by [-5, 5]Answer:BExplanation:A)B)C)D)2)f(x)=|x2-6|2)A)[-5, 5] by [-15, 15]B)[0, 5] by [-2, 10]C)[-5, 5] by [-2, 10]D)[-10, 10] by [-15, 15]Answer:CExplanation:A)B)C)D)3)f(x)=x2+110cos70x3)A)[-0.6, 0.6] by [-0.1, 0.6]B)[-0.1, 0.1] by [-0.1, 0.1]C)[-10, 10] by [-10, 10]D)[-2, 2] by [-1, 1]Answer:AExplanation:A)B)C)D)4)f(x)=7+6x-x24)A)[-10, 10] by [-10, 5]B)[-10, 20] by [-50, 50]C)[-4, 5] by [-5, 5]D)[-4, 5] by [-15, 25]Answer:DExplanation:A)B)C)D)1

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Match the equation with its graph.5)y=3x5)A)B)C)D)Answer:CExplanation:A)B)C)D)Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriategraph of the specified function.6)f(x)=x4-9x2+6x6)A)[-10, 15] by [-5, 5]B)[-5, 5] by [-10, 15]C)[-25, 15] by [-5, 5]D)[-5, 5] by [-25, 15]Answer:DExplanation:A)B)C)D)2

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Match the equation with its graph.7)y=x57)A)B)C)D)Answer:CExplanation:A)B)C)D)Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriategraph of the specified function.8)f(x)=x3-2x2-3x+178)A)[-20, 20] by [-100, 100]B)[-5, 25] by [-5, 5]C)[-2, 2] by [-10, 10]D)[-5, 5] by [-5, 25]Answer:DExplanation:A)B)C)D)3

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9)f(x)=3cos60x9)A)[-10, 10] by [-10, 10]B)[-0.2, 0.2] by [-4, 4]C)[-1, 1] by [-4, 4]D)[-0.2, 0.2] by [-1, 1]Answer:BExplanation:A)B)C)D)10)f(x)=x2/3(7-x)10)A)[-2, 2] by [-15, 15]B)[-4,10] by [-10, 10]C)[-4, 0] by [-5, 5]D)[0,10] by [-10, 10]Answer:BExplanation:A)B)C)D)11)f(x)=x2-1x2+111)A)[-5, 5] by [-15, 15]B)[-10, 10] by [-10, 10]C)[-10, 10] by [-2, 2]D)[-1, 1] by [-2, 2]Answer:CExplanation:A)B)C)D)4

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Match the equation with its graph.12)y=5x12)A)B)C)D)Answer:AExplanation:A)B)C)D)Use a graphing calculator or computer to determine which of the given viewing windows displays the most appropriategraph of the specified function.13)f(x)=10x2-613)A)[-5, 5] by [-10, 10]B)[-5, 0] by [-10, 10]C)[-2, 2] by [-10, 10]D)[0, 5] by [-10, 10]Answer:AExplanation:A)B)C)D)5

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SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.Solve the problem.14)What happens if you set B=-2Δin the angle sum formulas for the sine and cosinefunctions? Do the results agree with something you already know?14)Answer:If B=-2Δ, then cos (A+B)=cos A and sin (A+B)=sin A. Because the period ofboth of the sine and cosine functions is 2Δ, if B is replaced by a multiple of 2Δtheangle sum formulas must produce the same value as the sine or cosine function.Explanation:Provide an appropriate response.15)Derive the identitysec-1(-x)=Δ-sec-1x by combining the following two equations:cos-1(-x)=Δ-cos-1xsec-1x=cos-1(1/x)15)Answer:sec-1(-x)=cos-1(-1/x)=Δ-cos-1(1/x)=Δ-sec-1xExplanation:Use the addition formulas to derive the identity.16)sinx-Δ2=-cos x16)Answer:sinx-Δ2=sin x cos-Δ2+cos x sin-Δ2=sin x (0)+cos x (-1)=0-cos x=-cos xExplanation:17)cosx+Δ2=-sin x17)Answer:cosx+Δ2=cos x cosΔ2-sin x sinΔ2=cos x (0)-sin x (1)=0-sin x=-sin xExplanation:6

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Solve the problem.18)Let f(x)=x-6and g(x)=x2. Graph f and g together with fHg and gHf.18)Answer:Explanation:Use the addition formulas to derive the identity.19)cosx-Δ2=sin x19)Answer:cosx-Δ2=cos x cos-Δ2-sin x sin-Δ2=cos x (0)-sin x (-1)=0+sin x=sin xExplanation:7

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Solve the problem.20)The standard formula for the tangent of the difference of two angles istan (A-B)=tan A-tan B1+tan A tan B.Derive the formula.20)Answer:tan (A-B)=sin (A-B)cos (A-B)=sin A cos B-sin B cos Acos A cos B+sin A sin B=(cos A cos B)-1(sin A cos B-sin B cos A)(cos A cos B)-1(cos A cos B+sin A sin B)=tan A-tan B1+tan A tan B.Explanation:Use the addition formulas to derive the identity.21)sinx+Δ2=cos x21)Answer:sinx+Δ2=sin x cosΔ2+cos x sinΔ2=sin x (0)+cos x (1)=0+cos x=cos xExplanation:8

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Solve the problem.22)Graph the functions f(x)=xand g(x)=3-xtogether with their sum, product, twodifferences, and two quotients.22)Answer:Explanation:23)Use the angle sum formulas to derive sin (A-B)=sin A cos B-cos A sin B.23)Answer:sin (A-B)=sin (A+(-B))=sin A cos (-B)+cos A sin (-B)=sin A cos B-cos A sin BExplanation:24)Graph y=cos 2x and y=sec 2x together for-3Δ4KxK3Δ4. Comment on the behavior ofsec 2x in relation to the signs and values of cos 2x.24)Answer:When y=cos 2x is at a maximum point, which is at any multiple ofΔ, y=sec 2x is aminimum point. Similarly, when cos (2x) is at a minimum point, which is at anyodd multiple ofΔ2, y=sec 2x is a at maximum point.Explanation:9

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25)Graph y=sinx2and y=cscx2together for-2ΔKxK2Δ. Comment on the behavior ofcscx2in relation to the signs and values ofsinx2.25)Answer:When y=sinx2is at a maximum point, which is at x=(4n+1)Δfor all integers n, y=cscx2is at a minimum point. Similarly, when y=sinx2is at minimum point, ,which is at x=(4n-1)Δfor all integers n, y=cscx2is at a maximum point.Explanation:MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Express as a single logarithm and, if possible, simplify.26)ln (7secΌ)+ln (7cosΌ)26)A)ln (49)B)ln (49cotΌ)C)ln1D)ln (7secΌ+7cosΌ)Answer:AExplanation:A)B)C)D)Provide an appropriate response.27)If f(x) is one-to-one, is g(x)=f(-x) also one-to-one? Explain.27)A)g(x) is a reflection of f(x) across the line y=x. It will not be one-to-one.B)g(x) is a reflection of f(x) across the y-axis. It will be one-to-one.C)There is not enough information to determine whether g(x) is one-to-one.D)g(x) is a reflection of f(x) across the x-axis. It will be one-to-one.Answer:BExplanation:A)B)C)D)One of sin x, cos x, and tan x is given. Find the other two if x lies in the specified interval.28)cos x=-15,x inΔ,3Δ228)A)sin x=265, tan x=-26B)sin x=-265, tan x=-26C)sin x=-265, tan x=26D)sin x=265, tan x=26Answer:CExplanation:A)B)C)D)10

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Solve for the angleΌ, where 0KȱΌK2Δ29)sin2Ό=3429)A)Ό=0,Δ, 2ΔB)Ό=Δ6,śΔ6,ŝΔ6,11Δ6C)Ό=Δ4,řΔ4,śΔ4,ŝΔ4D)Ό=Δ3,ŘΔ3,ŚΔ3,śΔ3Answer:DExplanation:A)B)C)D)Solve the problem.30)The accompanying figure shows the graph of y=x2shifted to a new position. Write the equationfor the new graph.30)A)y=x2-6B)y=(x+6)2C)y=(x-6)2D)y=x2+6Answer:BExplanation:A)B)C)D)31)Suppose the consumption of electricity grows at8.6% per year, compounded continuously. Findthe number of years before the use of electricity has tripled. Round the answer to the nearesthundredth.31)A)12.77yrB)0.13yrC)34.88yrD)1.28yrAnswer:AExplanation:A)B)C)D)11

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Use a graph to find an approximate solution to the equation. Round to the nearest thousandth.32)43x=6x+132)A)2.292B)0.757C)1.292D)-4.419Answer:BExplanation:A)B)C)D)Graph the function.33)y=(-6x)2/3-333)A)B)12

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C)D)Answer:CExplanation:A)B)C)D)Find the formula for the function.34)Express the length d of a square's diagonal as a function of its side length x.34)A)d=2xB)d=x2C)d=xD)d=x3Answer:BExplanation:A)B)C)D)Find the function value.35)cos2Δ1235)A)2+34B)1+32C)2-34D)2+3Answer:AExplanation:A)B)C)D)The problem tells by what factor and direction the graph of the given function is to be stretched or compressed. Give anequation for the stretched or compressed graph.36)y=x+1compressed vertically by a factor of336)A)y=3x+3B)y=x+13C)y=3x+1D)y=3x+1Answer:BExplanation:A)B)C)D)13

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The equation of an ellipse is given. Put the equation in standard form and sketch the ellipse.37)16x2+64y2=102437)A)x264+y216=1B)x216+y264=1C)x264+y216=1D)x216+y264=1Answer:CExplanation:A)B)C)D)14

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Graph the function in the ts-plane (t-axis horizontal, s-axis vertical). State the period and symmetry of the function.38)s=sect338)A)Period6Δ, symmetric about the s-axisB)Period6Δ, symmetric about the t-axisC)Period6Δ, symmetric about the t-axisD)Period6Δ, symmetric about the s-axisAnswer:AExplanation:A)B)C)D)15

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