Test Bank for Precalculus, 6th Edition

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Ch. 11Introduction to Calculus11.1Finding Limits Using Tables and Graphs1Understand Limit NotationMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Choose the table which contains the best values of x for finding the requested limit of the given function.1)limx→2(x2+8x-2)A)x1.91.991.9992.0012.012.1f(x)B)x0.90.990.9991.0011.011.1f(x)C)x-1.9-1.99-1.9992.0012.012.1f(x)D)x-0.9-0.99-0.9991.0011.011.1f(x)2)limx→1x4-1x-1A)x0.90.990.9991.0011.011.1f(x)B)x1.91.991.9991.0011.011.1f(x)C)x-0.9-0.99-0.999-1.001-1.01-1.1f(x)D)x0.10.190.1191.991.091.9f(x)Page 1

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3)limx→0sin 2xxA)x-0.03-0.02-0.010.010.020.03f(x)B)x-0.01-0.02-0.030.030.020.01f(x)C)x-0.3-0.2-0.10.10.20.3f(x)D)x0.030.020.010.0010.0020.003f(x)Translate the given limit notation into a sentence.4)limx→4(x-2)=0A) The limit ofx-2 as x approaches 4 equals the number 0.B) The limit ofx-2 as x approaches 0 equals the number 4.C) The limit ofx-4 as x approaches 2 equals the number 0.D) The limit ofx-4 as x approaches 0 equals the number 2.5)limx→0sin 2xx=2A) The limit of sin 2xxas x approaches 0 equals the number 2.B) The limit of sin 2xxas x approaches 2 equals the number 0.C) The limit of sin 2xxas x approaches 0 from the left equals the number 2.D) The limit of sin 2xxas x approaches 0 from the right equals the number 2.2Find Limits Using TablesMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Complete the table for the function and find the indicated limit.1)limx→2(x2+8x-2)x1.91.991.9992.0012.012.1f(x)A) 16.810; 17.880; 17.988; 18.012; 18.120; 19.210limit=18.0B) 5.043; 5.364; 5.396; 5.404; 5.436; 5.763limit=5.40C) 16.692; 17.592; 17.689; 17.710; 17.808; 18.789limit=17.70D) 6.810; 7.880; 7.988; 8.012; 8.120; 9.210limit=8.0Page 2

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2)limx→1x4-1x-1x0.90.990.9991.0011.011.1f(x)A) 3.439; 3.940; 3.994; 4.006; 4.060; 4.641limit=4.0B) 1.032; 1.182; 1.198; 1.201; 1.218; 1.392limit=1.210C) 4.595; 5.046; 5.095; 5.105; 5.154; 5.677limit=5.10D) 7.439; 7.940; 7.994; 8.006; 8.060; 8.641limit=8.03)limx→0x3-6x+8x-2x-0.1-0.01-0.0010.0010.010.1f(x)A)-4.09476;-4.00995;-4.00100;-3.99900;-3.98995;-3.89526limit=-4.0B)-1.22843;-1.20298;-1.20030;-1.19970;-1.19699;-1.16858limit=-1.20C)-2.18529;-2.10895;-2.10090;-2.09910;-2.09096;-2.00574limit=-2.10D) 4.09476; 4.00995; 4.00100; 3.99900; 3.98995; 3.89526limit=4.04)limx→0(x2-5)x-0.1-0.01-0.0010.0010.010.1f(x)A)-4.9900;-4.9999;-5.0000;-5.0000;-4.9999;-4.9900limit=-5.0B)-1.4970;-1.4999;-1.5000;-1.5000;-1.4999;-1.4970limit=-1.50C)-2.9910;-2.9999;-3.0000;-3.0000;-2.9999;-2.9910limit=-3.0D) 1.4970; 1.4999; 1.5000; 1.5000; 1.4999; 1.4970limit=1.505)limx→0sin 2xxx-0.03-0.02-0.010.010.020.03f(x)A) 1.9988, 1.9995, 1.9999, 1.9999, 1.9995, 1.9988limit=2B) 1.9988, 1.9995, 1.9999, 1.9999, 1.9995, 1.9988limit=0C) 1.9988, 1.9995, 1.9999, 1.9999, 1.9995, 1.9988limit=1D) 1.9988, 1.9995, 1.9999, 1.9999, 1.9995, 1.9988limit=-2Page 3

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6)limx→0x2sin xx-0.03-0.02-0.010.010.020.03f(x)A)-0.0300,-0.0200,-0.0100, 0.0100, 0.0200, 0.0300limit=0B)-0.0300,-0.0200,-0.0100, 0.0100, 0.0200, 0.0300limit=1C)-0.0300,-0.0200,-0.0100, 0.0100, 0.0200, 0.0300limit=0.1D)-0.0300,-0.0200,-0.0100, 0.0100, 0.0200, 0.0300limit=-17)limx→-7x2-49x+7x-7.1-7.01-7.001-6.999-6.99-6.9f(x)A)-14.1,-14.01,-14.001,-13.999,-13.99,-13.9limit=-14B) 7.1, 7.01, 7.001, 6.999, 6.99, 6.9limit=7C)-14.1,-14.01,-14.001,-13.999,-13.99,-13.9limit=-14D)-7.1,-7.01,-7.001,-6.999,-6.99,-6.9limit=-78)limx→01-cos xsin xx-0.03-0.02-0.010.010.020.03f(x)A)-0.0150,-0.0100,-0.0050, 0.0050, 0.0100, 0.0150limit=0B)-0.0300,-0.0200,-0.0100, 0.0100, 0.0200, 0.0300limit=1C)-0.0300,-0.0200,-0.0100, 0.0100, 0.0200, 0.0300limit=0.1D)-0.0300,-0.0200,-0.0100, 0.0100, 0.0200, 0.0300limit=-19)limx→0f(x), where f(x)=x+5 if x<03x+5 if x≥0x-0.1-0.01-0.0010.0010.010.1f(x)A) 4.9, 4.99, 4.999, 5.003, 5.03, 5.3limit=5B) 2.9, 2.99, 2.999, 3.003, 3.03, 3.3limit=3C) 0.9, 0.99, 0.999, 1.003, 1.03, 1.3limit=1D) 1.9, 1.99, 1.999, 2.003, 2.03, 2.3limit=2Page 4

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3Find Limits Using GraphsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.The graph of a function is given. Use the graph to find the indicated limit and function value, or state that the limitor function value does not exist.1) a.limx→0f(x)b. f(0)x-6-5-4-3-2-1123456y4321-1-2-3-4x-6-5-4-3-2-1123456y4321-1-2-3-4A) a.limx→0f(x)=0b. f(0)=0B) a.limx→0f(x)=0b. f(0)=2C) a.limx→0f(x)=-2b. f(0)=-2D) a.limx→0f(x) does not existb. f(0) does not exist2) a.limx→0f(x)b. f(0)x-10-9 -8 -7 -6 -5 -4 -3 -2 -11 2 3 4 5 6 7 8 9 10y1-1x-10-9 -8 -7 -6 -5 -4 -3 -2 -11 2 3 4 5 6 7 8 9 10y1-1A) a.limx→0f(x)=1b. f(0)=1B) a.limx→0f(x)=0b. f(0)=0C) a.limx→0f(x)=-1b. f(0)=-1D) a.limx→0f(x) does not existb. f(0) does not existPage 5

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3) a.limx→0f(x)b. f(0)A) a.limx→0f(x)=1b. f(0) does not existB) a.limx→0f(x)= -1b. f(0) does not existC) a.limx→0f(x)=0b. f(0)=0D) a.limx→0f(x) does not existb. f(0) does not exist4) a.limx→0f(x)b. f(0)x-2-112345y108642-2x-2-112345y108642-2A) a.limx→0f(x)=0b. f(0)=6B) a.limx→0f(x)=6b. f(0)=6C) a.limx→0f(x)=6b. f(0)=0D) a.limx→0f(x) does not existb. f(0)=6Page 6

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5) a.limx→0f(x)b. f(0)A) a.limx→0f(x)=0b. f(0) does not existB) a.limx→0f(x)=1b. f(0)=1C) a.limx→0f(x)=-1b. f(0) does not existD) a.limx→0f(x) does not existb. f(0) does not exist6) a.limx→1f(x)b. f(1)x-3-2-112y21-1-2-3-4x-3-2-112y21-1-2-3-4A) a.limx→1f(x)=-3b. f(1)=-3B) a.limx→1f(x)=3b. f(1)=3C) a.limx→1f(x)=1b. f(1)=1D) a.limx→1f(x) does not existb. f(1)=-3Page 7

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7) a.limx→1f(x)b. f(1)x12345y4321-1x12345y4321-1A) a.limx→1f(x)=3b. f(1)=3B) a.limx→1f(x)=1b. f(1)=3C) a.limx→1f(x)=0b. f(1)=0D) a.limx→1f(x) does not existb. f(1) does not exist8) a.limx→2f(x)b. f(2)x12345y54321x12345y54321A) a.limx→2f(x)=2b. f(2)=1B) a.limx→2f(x)=1b. f(2)=1C) a.limx→2f(x)=1b. f(2)=2D) a.limx→2f(x) does not existb. f(2)=1Page 8

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9) a.limx→1f(x)b. f(1)x-3-2-112y21-1-2-3-4x-3-2-112y21-1-2-3-4A) a.limx→1f(x)=-3b. f(1)=1B) a.limx→1f(x)= -3b. (1)=-3C) a.limx→1f(x)=1b. f(1)=-3D) a.limx→1f(x)= -3b. f(1) does not existUse the graph and the viewing rectangle shown below the graph to find the indicated limit.10)limx→-2(x2-2)[-6, 6, 1] by [-6, 6, 1]A)limx→-2(x2-2)=2B)limx→-2(x2-2)=-6C)limx→-2(x2-2)=6D)limx→-2(x2-2)=-2Page 9

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11)limx→πsin x-π,π,π2by [-2, 2, 1]A)limx→πsin x=0B)limx→πsin x=1C)limx→πsin x= -1D)limx→πsin x=2Graph the function. Then use your graph to find the indicated limit.12) f(x)=3x+1,limx→6f(x)xyxyA) 19B) 6C) 18D) 7Page 10

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13) f(x)=2x-3,limx→-1f(x)xyxyA)-5B)-1C)-2D)-414) f(x)=3-x2,limx→2f(x)xyxyA)-1B) 3C)1D) 415) f(x)=5x ,limx→-3f(x)xyxyA) 15B) 3C)-15D)-3Page 11

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16) f(x)=sin x-2,limx→π/2f(x)xyxyA)-1B)-2C)3D) 117) f(x)=x2-36x-6,limx→6f(x)xyxyA) 12B) does not existC) 6D) 118) f(x)=x2-4x+2 ,limx→-2f(x)xyxyA)-4B) does not existC)-2D) 1Page 12

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19) f(x)=10ex,limx→0f(x)xyxyA) 10B)-10C) 1D) 020) f(x)=x+1if x<02x+1if x≥0 ,limx→0f(x)xyxyA)1B) does not existC) 3D) 021) f(x)=x+7x<-77-xx≥-7 ,limx→-7f(x)xyxyA) does not existB)0C) 14D)-7Page 13

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4Find One-Sided Limits and Use Them to Determine If a Limit ExistsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.The graph of a function is given. Use the graph to find the indicated limit and function value, or state that the limitor function value does not exist.1) a.limx→3f(x)b. f(3)x12345y54321x12345y54321A) a.limx→3f(x) does not existb. f(3)=5B) a.limx→3f(x)=5b. f(3)=5C) a.limx→3f(x)=3b. f(3)=5D) a.limx→3f(x)=4b. f(3) does not exist2) a.limx→1f(x)b. f(1)x-2-112345y54321-1-2x-2-112345y54321-1-2A) a.limx→1f(x) does not existb. f(1)=2B) a.limx→1f(x)=1b. f(1)=2C) a.limx→1f(x)=2b. f(1)=2D) a.limx→1f(x)=1b. f(1)=0Page 14

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3) a.limx→1f(x)b. f(1)A) a.limx→1f(x)=1b. f(1) does not existB) a.limx→1f(x)=0b. f(1)=1C) a.limx→1f(x)=-1b. f(1)=1D) a.limx→1f(x) does not existb. f(1) does not exist4) a.limx→-1f(x)b. f(-1)A) a.limx→-1f(x) does not existb. f(-1)=-1B) a.limx→-1f(x)=0b. f(-1)=-1C) a.limx→-1f(x)=-1b. f(-1) does not existD) a.limx→-1f(x)= -2b. f(-1)=-1Page 15

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5) a.limx→-1/2f(x)b. f(-1/2)A) a.limx→-1/2f(x)=-1b. f(-1/2)=-1B) a.limx→-1/2f(x)= -2b. f(-1/2)=-1C) a.limx→-1/2f(x)=0b. f(-1/2) does not existD) a.limx→-1/2f(x) does not existb. f(-1/2)=-16) a.limx→3-f(x)b. f(3)x12345y54321x12345y54321A) a.limx→3-f(x)=3b. f(3)=5B) a.limx→3-f(x)=3b. f(3)=3C) a.limx→3-f(x)=3b. f(3) does not existD) a.limx→3-f(x) does not existb. f(3)=5Page 16

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7) a.limx→3+f(x)b. f(3)x12345y54321x12345y54321A) a.limx→3+f(x)=5b. f(3)=5B) a.limx→3+f(x)=3b. f(3)=3C) a.limx→3+f(x)=3b. f(3) does not existD) a.limx→3+f(x) does not existb. f(3)=58) a.limx→1+f(x)b. f(1)x-2-112345y54321-1-2x-2-112345y54321-1-2A) a.limx→1+f(x)=2b. f(1)=2B) a.limx→1+f(x)=2b. f(1)=1C) a.limx→1+f(x)=1b. f(1)=0D) a.limx→1+f(x) does not existb. f(1)=2Page 17

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9) a.limx→-1-f(x)b. f(-1)A) a.limx→-1-f(x)=-1b. f(-1) does not existB) a.limx→-1-f(x)=0b. f(-1)=1C) a.limx→-1-f(x)=-1b. f(-1)=1D) a.limx→-1-f(x) does not existb. f(-1) does not exist10) a.limx→-2+f(x)b. f(-2)A) a.limx→-2+f(x)=-2b. f(-2)=-2B) a.limx→-2+f(x)= -1b. f(-2) does not existC) a.limx→-2+f(x)=-2b. f(-2)=-1D) a.limx→-2+f(x) does not existb. f(-2)=-1Page 18

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11) a.limx→2.5-f(x)b. f(2.5)A) a.limx→2.5-f(x)=1b. f(2.5)=1B) a.limx→2.5-f(x)=2b. f(2.5)=1C) a.limx→2.5-f(x)=0b. f(2.5)=2D) a.limx→2.5-f(x) does not existb. f(2.5)=212) a.limx→1-f(x)b. f(1)x-2-112345y54321-1-2x-2-112345y54321-1-2A) a.limx→1-f(x)=1b. f(1)=2B) a.limx→1-f(x)=2b. f(1)=2C) a.limx→1-f(x)=1b. f(1)=1D) a.limx→1-f(x) does not existb. f(1)=2Page 19

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5Solve Apps: Use LimitsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Solve the problem.1) You are riding your motorcycle along a freeway traveling x miles per hour. The functionf(x)=0.0014x2+x+9 describes the recommended safe distance, f(x), in feet, between your motorcycle andthe other motorcycles on the freeway. Use the values in the table below to solve this exercise.x49.949.9949.999→←50.00150.0150.1f(x)93.7693.97693.998→←94.00294.02494.24Findlimx→50f(x). Describe what this means in terms of your motorcycle's speed and the recommended safedistance.A) 94; This means that the recommended safe distance between motorcycles traveling at 50 miles perhour is 94 feet.B) 50; This means that the recommended safe distance between motorcycles traveling at 50 miles perhour is 50 feet.C) 93.999; This means that the recommended safe distance between motorcycles traveling at 50 miles perhour is 93.999 feet.D)limx→50f(x) does not exist.Page 20

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2) You rent a moving van from a company that charges $10 per hour plus $0.50 per mile. The van is driven 40miles in the first hour. The figure below shows the graph of the cost, f(x), in dollars, as a function of themiles, x, that you drive the van.(i) Findlimx→20f(x). Interpret the limit, referring to miles driven and cost.(ii) For the first hour hour only, what is the rental cost approaching as the mileage gets closer to 40?(iii) What is the cost to rent the van at the start of the second hour?A) (i) 20; the cost to rent the van for one hour and drive it 20 miles is $20.(ii) $30(iii) $40B) (i) 30; the cost to rent the van for one hour and drive it 20 miles is $30.(ii) $40(iii) $40C) (i) 40; the cost to rent the van for one hour and drive it 20 miles is $40.(ii) $30(iii) $40D) (i) 20; the cost to rent the van for one hour and drive it 20 miles is $20.(ii) $30(iii) $303) You are building a screened-in porch attached to your house. Because the house will be used for one sideof the enclosure, only three sides will need to be enclosed. You have 24 yards of material to enclose thethree walls. The function f(x)=x(24-2x) describes the area of the screened-in porch that you can enclose,f(x), in square yards, if the width of the screened-in porch is x yardsXY15.75.85.966.16.26.371.8271.9271.9871.9871.9271.82Y1=X * (24-2X)(i) Use the table shown to findlimx→6f(x).(ii) Use the graph of f(x)=x(24-2x) shown to findlimx→6f(x). Do you get the same limit as you did in part(i)? What information about the limit is shown by the graph that might not be obvious from the table?Page 21

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[-5, 15, 5] by [0, 80, 10]A) (i) 72(ii) 72; Yes, the same limit is obtained. The graph shows that the limit is the maximum area.B) (i) 80(ii) 80; Yes, the same limit is obtained. The graph shows that the limit is the maximum area.C) (i) 72(ii) 80; No, the same limit is not obtained. The graph shows that the limit is the maximum amount ofmaterial that can be used.D) (i) 80(ii) 72; No, the same limit is not obtained. The graph shows that the limit is the maximum amount ofmaterial that can be used.11.2Finding Limits Using Properties of Limits1Find Limits of Constant Functions and the Identity FunctionMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limitproperties can be applied.1)limx→10-6A)-6B) 10C)6D) 02)limx→-8xA)-8B)8C) 0D) 12Find Limits Using Properties of LimitsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limitproperties can be applied.1)limx→-715x3A)-5145B)-7C)-343D)152)limx→0(x2-5)A)-5B) 5C) 0D) does not existPage 22

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3)limx→2(x2+8x-2)A) 18B)-18C) 0D) does not exist4)limx→2(x3+5x2-7x+1)A) 15B) 29C) 0D) does not exist5)limx→0(x-2)A)-2B) 0C) 2D) does not exist6)limx→1(3x2-19)2A) 256B)-352C) 144D) 1007)limx→4(x-4)(x-2)A) 0B) 2C) 4D) does not exist8)limx→1(x2-2)3A)-1B) 1C) 3D)-39)limx→3 (3x2-2x+2)2A) 529B)-529C) 81D) does not exist10)limx→13x-2A) 1B)2C)-1D) does not exist11)limx→12x-74x+5A)-59B)-12C)-75D) does not exist12)limx→12x-74x+5A)-59B)-12C)-75D) does not exist13)limx→5x2-2x-15x+3A) 0B)-8C) 5D) does not exist14)limx→0x3-6x+8x-2A)-4B) 0C) 4D) does not existPage 23

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15)limx→13x2+7x-23x2-4x+2A) 8B)-74C) 0D) does not exist16)limx→2 [(x-3)3(5x+1)2]A)-121B)121C)-288D) does not exist17)limx→7x-7x-49A) 16-742B) 0C)742-16D) does not exist3Find One-Sided Limits Using Properties of LimitsMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.A piecewise function is given. Use the properties of limits to find the indicated limits, or state that the limit doesnot exist.1) f(x)=4x-3if x<1-3x+4if x>1a.limx→1-f(x)b.limx→1+f(x)c.limx→1f(x)A) a.1b.1c.1B) a.1b.1c. does not existC) a.-3b.4c. does not existD) a.4b.-3c. does not exist2) f(x)=x2-1if x<0-4if x≥0a.limx→-5-f(x)b.limx→-5+f(x)c.limx→-5f(x)A) a.24b.24c.24B) a.-1b.-4c. does not existC) a.-4b.-1c. does not existD) a.-1b.-4c.-43) f(x)=1x-5if x>5x2-2xif x≤5a.limx→5-f(x)b.limx→5+f(x)c.limx→5f(x)A) a. 15b. does not existc. does not existB) a. does not existb. 15c. does not existC) a. 15b. does not existc. 15D) a. does not existb. 15c. 15Page 24

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4) f(x)=x2-9x-3if x≠35if x=3a.limx→3-f(x)b.limx→3+f(x)c.limx→3f(x)A) a. 6b. 6c. 6B) a. 6b. 6c. 5C) a. 3b. 3c. does not existD) a. 3b. 3c. 55) f(x)=4x-5if x<11if x=1-3x-4if x>1a.limx→1-f(x)b.limx→1+f(x)c.limx→1f(x)A) a.-1b.-7c. does not existB) a.-7b.-1c. does not existC) a.-1b.-7c.-8D) a.-7b.-1c.-86) f(x)=6-xif x<14if x=1x2+4 if x>1a.limx→1-f(x)b.limx→1+f(x)c.limx→1f(x)A) a. 5b. 5c. 5B) a. 5b. 4c. does not existC) a. 4b. 6c. does not existD) a. 5b. 5c. 44Find Limits of Fractional Expressions in Which the Limit of the Denominator is ZeroMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Use properties of limits to find the indicated limit. It may be necessary to rewrite an expression before limitproperties can be applied.1)limx→1x4-1x-1A) 4B) 2C) 0D) does not exist2)limx→-3x2-2x-15x+3A)-8B) 0C) 5D) does not exist3)limx→0x3+12x2-5x5xA)-1B) 0C) 5D) does not exist4)limx→1x3+5x2+3x-9x-1A) 16B)-16C) 0D) does not existPage 25

Test Bank for Precalculus, 6th Edition - Page 27 preview image

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5)limx→04+x-2xA) 14B) 12C) 4D) 06)limx→91x-19x-9A)-181B) 19C) 0D) does not exist7)limx→4x-4x-2A) 4B) 1/4C) 0D) does not exist8)limx→4x-2x-4A) 1/4B) 4C) 0D) does not exist9)limx→5x2-25x3-125A)215B)-215C)115D) does not exist10)limh→0(x+h)3-x3hA) 3x2B) 0C) 3x2+3xh+h2D) does not exist11.3Limits and Continuity1Determine Whether a Function is Continuous at a NumberMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Use the definition of continuity to determine whether f is continuous at a.1) f(x)=5x4-9x3+x-6a=0A) ContinuousB) Not continuous2) f(x)=3x4-9x3+x-5a=5A) ContinuousB) Not continuous3) f(x)=5x+2a=-2A) Not continuousB) ContinuousPage 26

Test Bank for Precalculus, 6th Edition - Page 28 preview image

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4) f(x)=5x-8a=0A) ContinuousB) Not continuous5) f(x)=x+7x+2a=-7A) ContinuousB) Not continuous6) f(x)=x-6x+3a=0A) ContinuousB) Not continuous7) f(x)=x+7x+3a=-3A) Not continuousB) Continuous8) f(x)=7x2+8xa=0A) Not continuousB) Continuous9) f(x)=1x2-9xa=9A) Not continuousB) Continuous10) f(x)=1x2-3xa=-1A) ContinuousB) Not continuous11) f(x)=x2-16x-4a=0A) ContinuousB) Not continuous12) f(x)=x2-64x-8a=8A) Not continuousB) Continuous13) f(x)=x2-5,if x<03,if x≥0a=-4A) ContinuousB) Not continuousPage 27

Test Bank for Precalculus, 6th Edition - Page 29 preview image

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14) f(x)=4x+3,if x<11,if x=14x-7,if x>1a=1A) Not continuousB) Continuous15) f(x)=1x+4 ,if x>-4x2-4x,if x≤-4a=-4A) Not continuousB) Continuous2Determine For What Numbers a Function is DiscontinuousMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Determine for what numbers, if any, the given function is discontinuous.1) f(x)=2x+5A) NoneB)52C)-52D)-52) f(x)=-3x2+5xA) NoneB)-56C) 56D)-33) f(x)=-3 cos xA) NoneB) 0C) 1D)-34) f(x)=4 tan xA) nπ2and-nπ2B) 0C) nπ4and-nπ4D) None5) f(x)=2x-1x2-25A)-5 and 5B) 5C)-5 and 5 and-12D) None6) f(x)=x-4if x≤4x2-8if x>4A) 4B) NoneC)-4, 4D) 07) f(x)=x-3if x≤3x2if x>3A) 3B) [the set of numbers 1, 2, 3, . . . 8]C) [the set of numbers 1, 2, 3, . . . 9]D) None8) f(x)=x2-9x-3if x≠36if x=3A) NoneB) 3C) 9D) 3, 9Page 28

Test Bank for Precalculus, 6th Edition - Page 30 preview image

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9) f(x)=8xif x<755if x=7x2+7if x>7A) 7B) 0, 7C) 8, 7D) None3Solve Apps: Limits and ContinuitySHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.Solve the problem.1) The figure shows the cost of renting a car, f(x), as a function of distance driven, x, in miles, for distancesnot exceeding 70 miles.Cost(dollars)xyxy49474543413937204060Distance (miles)(i) Findlimx→60-f(x).(ii) Findlimx→60+f(x).(iii) What can you conclude aboutlimx→60f(x)? How is this shown by the graph?(iv) What aspect of costs of renting a car causes the graph to jump vertically by the same amount at itsdiscontinuities?Page 29

Test Bank for Precalculus, 6th Edition - Page 31 preview image

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2) The following piecewise function gives the tax owed, T(x), by a single taxpayer on a taxable income of xdollars.T(x)=0.11xif 0<x≤7593759.30+0.18(x-7593)if 7593<x≤31,6875096.22+0.26(x-31,687)if 31,687<x≤72,78415,781.44+0.29(x-72,784)if 72,784<x≤149,89738,144.21+0.32(x-149,897) if 149,897<x≤325,12794,217.81+0.36(x-325,127) if x>325,127(i) Determine whether T is continuous at 7593.(ii) Determine whether T is continuous at 31,687.(iii) If T had discontinuities, use one of these discontinuities to describe a situation where it might beadvantageous to earn less money in taxable income.11.4Introduction to Derivatives1Find Slopes and Equations of Tangent LinesMULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the slope of the tangent line to the graph of f at the given point.1) f(x)=-2x+20 at (8, 4)A)-2B) 20C)-20D)-122) f(x)=x2+5x at (4, 36)A) 13B) 9C) 3D) 213) f(x)=5x2+x at (-4, 76)A)-39B)-41C) 6D)-144) f(x)=-4x2+7x at (5,-65)A)-33B) 33C)-13D) 35) f(x)=2x2+x-3 at (4, 33)A) 17B) 15C) 5D) 196) f(x)=x2+11x-15 at (1,-3)A) 13B)-9C) 26D) 117) f(x)=x at (64, 8)A)116B) 4C) 16D) 148) f(x)=3x at (1, 3)A)-3B) 3C) 6D) 32Find the slope-intercept equation of the tangent line to the graph of f at the given point.9) f(x)=x2+5x at (4, 36)A) y=13x-16B) y=13x-72C) y=2x-5D) y=2x+5Page 30

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