Thomas Calculus Early Transcendentals 13th Edition Thomas .
Thomas Calculus Early Transcendentals 13th Edition Thomas Test BankFull Download: /MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Find the average rate of change of the function over the given interval.1) y x2 2x, [3, 7]6348A)B)C) 9472) y 4x3 6x2 - 3, [-6, 2]53A)81)D) 122)53B)2C) 352B) 73C) 10D) 883) y 2x, [2, 8]1A)34) y 3)D) 23, [4, 7]x-24)A) 2B) 75) y 4x2 , 0,A) -D) -3105)3107) h(t) sin (3t), 0,B) 2D)C) -341D) 66)B) -27)B)8) g(t) 3 tan t, -13C) 7π66πA) -13746) y -3x2 - x, [5, 6]1A)2A)C)π6C)3πD) -6ππ π,4 4858)B) 0C)4πD) -4πFind the slope of the curve at the given point P and an equation of the tangent line at P.9) y x2 5x, P(4, 36)1x1A) slope is ; y 2020 5B) slope is 13; y 13x - 16C) slope is -39; y -39x - 80D) slope is -44x 8;y 2525 51Full download all chapters instantly please go to Solutions Manual, Test Bank site: testbanklive.com9)
10) y x2 11x - 15, P(1, -3)10)A) slope is -39; y -39x - 8044x 8B) slope is ;y 2525 5C) slope is 13; y 13x - 16D) slope is1x1;y 2020 511) y x3 - 9x, P(1, -8)A) slope is 3; y 3x - 11C) slope is -6; y -6xB) slope is 3; y 3x - 7D) slope is -6; y -6x - 212) y x3 - 3x2 4, P(3, 4)A) slope is 0; y -23C) slope is 1; y x - 23B) slope is 9; y 9x 4D) slope is 9; y 9x - 2311)12)13) y -3 - x3 , (1, -4)A) slope is 0; y -1C) slope is 3; y 3x - 113)B) slope is -3; y -3x - 1D) slope is -1; y -x - 1Use the slopes of UQ, UR, US, and UT to estimate the rate of change of y at the specified value of x.14) x 5y5U4T32S1RQ1A) 223456 xB) 1C) 52D) 014)
15) x 315)y6U5T43S2R1Q123A) 6xB) 0C) 2D) 416) x 516)y7U654T3S21RQ1A)2542345B)6 x52C)354D) 0
17) x 217)y54U3T2S1RQ12A) 33xB) 0C) 6D) 418) x 2.518)y54U32T1SQR1A) 7.523xB) 1.25C) 0D) 3.75Use the table to estimate the rate of change of y at the specified value of x.19) x 1.x y0 00.2 0.020.4 0.080.6 0.180.8 0.321.0 0.51.2 0.721.4 0.98A) 1.5B) 2C) 0.5419)D) 1
20) x 1.x y0 00.2 0.010.4 0.040.6 0.090.8 0.161.0 0.251.2 0.361.4 0.49A) 220)B) 1.5C) 1D) 0.521) x 1.x y0 00.2 0.120.4 0.480.6 1.080.8 1.921.0 31.2 4.321.4 5.88A) 621)B) 8C) 2D) 422) x 2.x y0 100.5 381.0 581.5 702.0 742.5 703.0 583.5 384.0 10A) 422)B) -8C) 8D) 023) x 1.xy0.900 -0.052630.990 -0.005030.999 -0.00051.000 0.00001.001 0.00051.010 0.004981.100 0.04762A) 0.523)B) 0C) 1Solve the problem.5D) -0.5
24) When exposed to ethylene gas, green bananas will ripen at an accelerated rate. The number ofdays for ripening becomes shorter for longer exposure times. Assume that the table below givesaverage ripening times of bananas for several different ethylene exposure times:Exposure time(minutes)1015202530Ripening Time(days)4.23.52.62.11.1Plot the data and then find a line approximating the data. With the aid of this line, find the limit ofthe average ripening time as the exposure time to ethylene approaches 0. Round your answer tothe nearest tenth.Days7654321510 15 20 25 30 35 40 MinutesA)B)DaysDays77665544332211510 15 20 25 30 35 40 Minutes52.6 days5.8 days610 15 20 25 30 35 40 Minutes24)
C)D)DaysDays77665544332211510 15 20 25 30 35 40 Minutes537.5 minutes10 15 20 25 30 35 40 Minutes0.1 day25) When exposed to ethylene gas, green bananas will ripen at an accelerated rate. The number ofdays for ripening becomes shorter for longer exposure times. Assume that the table below givesaverage ripening times of bananas for several different ethylene exposure times.Exposure time(minutes)1015202530Ripening Time(days)4.33.22.72.11.3Plot the data and then find a line approximating the data. With the aid of this line, determine therate of change of ripening time with respect to exposure time. Round your answer to twosignificant digits.Days7654321510 15 20 25 30 35 40 Minutes725)
A)B)DaysDays77665544332211510 15 20 25 30 35 40 Minutes510 15 20 25 30 35 40 Minutes-6.7 days per minute5.6 daysC)D)DaysDays77665544332211510 15 20 25 30 35 40 Minutes5-0.14 day per minute10 15 20 25 30 35 40 Minutes38 minutes26) The graph below shows the number of tuberculosis deaths in the United States from 1989 to 089 90 91 92 93 94 95 96 97YearEstimate the average rate of change in tuberculosis deaths from 1991 to 1993.A) About -30 deaths per yearB) About -45 deaths per yearC) About -80 deaths per yearD) About -0.4 deaths per year826)
Use the graph to evaluate the limit.27) lim f(x)x -127)y1-6 -5 -4 -3 -2 -112345B) -346 x-1A) C)34D) -128) lim f(x)x 028)y4321-4-3-2-11234 x-1-2-3-4A) 3C) -3B) 09D) does not exist
29) lim f(x)x 029)6y54321-6 -5 -4 -3 -2 -1-1123456 x-2-3-4-5-6A) -3B) 0C) does not existD) 330) lim f(x)x 030)12y108642-2-112345x-2-4A) does not existB) -1C) 010D) 6
31) lim f(x)x 031)y4321-4-3-2-11234 x-1-2-3-4A) B) does not existC) 1D) -132) lim f(x)x 032)y4321-4-3-2-11234 x-1-2-3-4A) B) does not existC) 111D) -1
33) lim f(x)x 033)y4321-4-3-2-11234x-1-2-3-4B) -2A) 0C) 2D) does not exist34) lim f(x)x 034)y4321-4-3-2-11234x-1-2-3-4A) does not existB) -2C) 012D) 1
35) lim f(x)x 035)y4321-4-3-2-11234x-1-2-3-4A) does not existC) -1B) 2D) -236) lim f(x)x 036)y1-8 -7 -6 -5 -4 -3 -2 -11 2 3 4 5 6 7 8 9x-1A) -1B) 1C) does not existD) 0Find the limit.37) lim (4x 6)x 7A) 1037)B) 34C) -22D) 638) lim (x2 8x - 2)x 2A) does not exist38)B) 0C) 18D) -1839) lim (x2 - 5)x 0A) 039)B) 5C) does not exist13D) -5
40) lim ( x - 2)x 0A) 040)B) does not existD) -2C) 241) lim (x3 5x2 - 7x 1)x 2A) 1542)B) 0C) does not existD) 29lim (2x5 - 2x4 - 4x3 x2 5)x -2A) -5542)B) 9C) 41D) -119x2 2x 143) limx 743)B) 8A) 844)41)C) 64D) does not existxlim3x 2x -1A) -1544)B) 0C) does not existD) 1Find the limit if it exists.45) lim3x 15A)46)1546)B) 12C) 8D) -847)B) 125C) -115D) -12548)B) 54C) 34D) 46lim 8x(x 8)(x - 4)x -10A) -224050)D) 15lim (10x2 - 2x - 10)x -2A) 2649)C) 33lim (5 - 10x)x 12A) 11548)B)lim (10x - 2)x -1A) -1247)45)49)B) -20,160C) -960D) 22401lim 8x x 51x 8A)134050)B) -35C) -14340D) -3320
51)lim x1/2x 25A) 2552)B)C) 5D)1252)B) -125C) 1D) -31257x 73limx -8A) -1754)252lim (x 3)2 (x - 3)3x -2A) 2553)51)53)B)C) 1717D) - 17lim (x - 123)4/3x -2A) -62554)B) -125C) -3125D) 625Find the limit, if it exists.155) limx 12 x - 12A) Does not exist56) limx 055)B) 12C) 0D) 24x3 - 6x 8x-2A) 456)B) 0C) Does not existD) -42x - 757) limx 1 4x 5A) -1257)B) -59C) -75D) Does not exist3x2 7x - 258) limx 1 3x2 - 4x - 2A) -8358)B) 0C) Does not existD) -74x 659) limx 6 (x - 6)2B) -6A) 060) limx 559)C) 6D) Does not existx2 - 2x - 15x 3A) -860)B) 5C) 015D) Does not exist
23h 4 261) limh 0A) 1/262)61)B) 2C) Does not existD) 117x hlimxh 0 3(x - h)A) Does not exist62)B)17x4C)17x3D) 17x1 x-1x63) limx 0A) Does not exist63)B) 1/4C) 1/2D) 0(1 h)1/3 - 1h64) limh 0A) 064)B) Does not existC) 1/3D) 3x3 12x2 - 5x5x65) limx 0A) 565)B) 0C) Does not existD) -1x4 - 166) limx 1 x - 1A) 267)B) 0limx -3limx 2limx 4A)32C) Does not existD) 1x2 6x 9x 368)B) 0C) 6D) 36x2 3x - 10x-2A) 770)D) 467)B) 12A) Does not exist69)C) Does not existx2 - 36limx 6 x-6A) 668)66)69)B) Does not existC) 0D) 3x2 4x - 32x2 - 1670)B) -12C) 016D) Does not exist
71)x2 - 25lim2x 5 x - 6x 5A) Does not exist72)52C)54D) 072)B) -75C) - 1D)75(x h)3 - x3hlimh 073)B) 3x2A) 074)B)x2 - 5x - 6limx -1 x2 - 3x - 4A) Does not exist73)71)C) 3x2 3xh h2D) Does not exist10 - x10 - xlimx 10A) 174)C) -1B) 0D) Does not existFind the limit.75) lim (4 sin x - 1)x 0A) -176)limx -πB) 4 - 1A) 4C) 0D) 4x 1 cos(x π)A) - 1 - π77) limx 075)76)B) 1C)1-πD) 015 cos2 x77)B) 16C)1715D) 15
Provide an appropriate response.78) Suppose lim f(x) 1 and lim g(x) -3. Name the limit rules that are used to accomplish stepsx 0x 078)(a), (b), and (c) of the following calculation.lim (-3f(x) - 4g(x) )(a) x 0-3f(x) - 4g(x)lim lim (f(x) 3)1/2x 0 (f(x) 3)1/2x 0lim -3f(x) - lim 4g(x)-3 lim f(x) - 4 lim g(x)(b) x 0(c)x 0x 0x 0 1/2( lim f(x) 3 )( lim f(x) lim 3)1/2x 0x 0x 0 9-3 12 21/2(1 3)A) (a)(b)(c)B) (a)(b)(c)C) (a)(b)(c)D) (a)(b)(c)Difference RulePower RuleSum RuleQuotient RuleDifference Rule, Power RuleConstant Multiple Rule and Sum RuleQuotient RuleDifference Rule, Sum RuleConstant Multiple Rule and Power RuleQuotient RuleDifference RuleConstant Multiple Rule79) Let lim f(x) -9 and lim g(x) 6. Find lim [f(x) - g(x)].x 6x 6x 6A) 680) LetB) -3C) -979)D) -15lim f(x) 9 and lim g(x) 2. Find lim [f(x) g(x)].x -5x -5x -5A) 18B) 11C) 280)D) -5f(x)81) Let lim f(x) -1 and lim g(x) -5. Find lim.g(x)x 3x 3x 3A)82) Let15B) 5C) 381)D) 4lim f(x) 32. Find lim log2 f(x).x -8x -8A)52B) 2583) Let lim f(x) 49. Find limx 1x 1A) 182)C) 5D) -8f(x).83)B) 2.6458C) 4918D) 7
84) Let lim f(x) -5 and lim g(x) -7. Find lim [f(x) g(x)]2 .x 2x 2x 2A) -12B) 74C) 14484)D) 285) Let lim f(x) 2. Find lim (-4)f(x).x 4x 4A) 16B) -486) Let lim f(x) 32. Find limx 7x 7A) 75C) 256D) 2f(x).86)B) 3287) Let lim f(x) 6 and lim g(x) -9. Find limx 9x 9x 9A) - 1585)C) 2D) 5-4f(x) - 3g(x).2 g(x)B) 9C) -3787)D)517Because of their connection with secant lines, tangents, and instantaneous rates, limits of the formf(x h) - f(x)limoccur frequently in calculus. Evaluate this limit for the given value of x and function f.hh 088) f(x) 4x2, x 8A) 256B) 32C) 64D) Does not exist89) f(x) 4x2 - 2, x -1A) -8B) Does not existC) 4D) -1090) f(x) 2x 5, x 4A) 1391) f(x) 89)90)B) 2C) 8D) Does not existx 1, x 63A) Does not exist92) f(x) 88)91)B) 3C) 2D)132, x 8xA) -1692)14B) Does not existC)B) Does not exist5C)4D) -13293) f(x) 5 x, x 4A) 593)19D) 10
94) f(x) A)x, x 394)32B) Does not exist95) f(x) 3 x 5, x 163A)836C)D)3395)B) 24C) 6D) Does not existProvide an appropriate response.96) It can be shown that the inequalities -x x cos1 x hold for all values of x 0.x96)1Find lim x cosif it exists.xx 0A) 0.000797) The inequality 1Find limx 0B) 0C) does not existD) 1x2 sin x 1 holds when x is measured in radians and x 1.2xsin xif it exists.xA) 0.0007B) does not existC) 1D) 098) If x3 f(x) x for x in [-1,1], find lim f(x) if it exists.x 0A) 198)C) -1B) does not existD) 0Use the table of values of f to estimate the limit.99) Let f(x) x2 8x - 2, find lim f(x).x 9 2.001 2.012.1; limit 17.70f(x) 16.692 17.592 17.689 17.710 17.808 18.789B)x 1.91.99 1.999 2.001 2.01 2.1; limit f(x) 5.043 5.364 5.396 5.404 5.436 5.763C)x 1.91.99 1.999 2.001 2.01 2.1; limit 5.40f(x) 5.043 5.364 5.396 5.404 5.436 5.763D)x1.91.991.999 2.001 2.012.1; limit 18.0f(x) 16.810 17.880 17.988 18.012 18.120 19.21020
100) Let f(x) xf(x)x-4, find lim f(x).x-2x 43.93.99100)3.9994.0014.014.1A)x 3.93.993.9994.0014.014.1; limit 5.10f(x) 5.07736 5.09775 5.09978 5.10022 5.10225 5.12236B)x 3.93.993.9994.0014.014.1; limit 1.20f(x) 1.19245 1.19925 1.19993 1.20007 1.20075 1.20745C)x 3.93.993.9994.0014.014.1; limit f(x) 1.19245 1.19925 1.19993 1.20007 1.20075 1.20745D)x 3.93.993.9994.0014.014.1; limit 4.0f(x) 3.97484 3.99750 3.99975 4.00025 4.00250 4.02485101) Let f(x) x2 - 5, find lim f(x).x 0xf(x)-0.1-0.01101)-0.0010.0010.010.1A)x -0.1f(x) -2.9910-0.01-2.9999-0.001-3.00000.0010.010.1; limit -3.0-3.0000 -2.9999 -2.9910x -0.1f(x) -1.4970-0.01-1.4999-0.001-1.50000.0010.010.1; limit -1.5000 -1.4999 -1.4970x -0.1f(x) -4.9900-0.01-4.9999-0.001-5.00000.0010.010.1; limit -5.0-5.0000 -4.9999 -4.9900x -0.1f(x) -1.4970-0.01-1.4999-0.001-1.50000.0010.010.1; limit -15.0-1.5000 -1.4999 -1.4970B)C)D)21
102) Let f(x) xf(x)x-1x2 3x - 40.9, find lim f(x).x 10.99102)0.9991.0011.011.1A)x0.90.990.999 1.0011.011.1 ; limit 0.1f(x) 0.1041 0.1004 0.1000 0.1000 0.0996 0.0961B)x0.90.990.999 1.0011.011.1 ; limit 0.3f(x) 0.3041 0.3004 0.3000 0.3000 0.2996 0.2961C)x0.90.990.999 1.0011.011.1 ; limit 0.2f(x) 0.2041 0.2004 0.2000 0.2000 0.1996 0.1961D)x0.90.990.9991.0011.011.1; limit -0.2f(x) -0.2041 -0.2004 -0.2000 -0.2000 -0.1996 -0.1961103) Let f(x) xf(x)x2 - 4x 3, find lim f(x).x2 - 7x 12x .013.1; limit -2.1f(x) -1.8273 -2.0703 -2.0970 -2.1030 -2.1303 -2.4333B)x2.92.992.9993.0013.013.1; limit -2f(x) -1.7273 -1.9703 -1.9970 -2.0030 -2.0303 -2.3333C)x2.92.992.999 3.0013.013.1 ; limit 0.5714f(x) 0.5775 0.5720 0.5715 0.5714 0.5708 0.5652D)x2.92.992.9993.0013.013.1; limit -1.9f(x) -1.6273 -1.8703 -1.8970 -1.9030 -1.9303 -2.2333104) Let f(x) xf(x)sin(4x), find lim f(x).xx ) limit 3.5C) limit 00.1B) limit does not existD) limit 422
105) Let f(θ) cos (8θ), find lim f(θ).θθ 0x-0.1f(θ) -6.9670671-0.01-0.001105)0.0010.01A) limit 8C) limit does not exist0.16.9670671B) limit 6.9670671D) limit 0Find the limit.f(x) - 1106) If lim 2, find lim f(x).x 3 x - 1x 3A) 6106)B) 3C) 5D) Does not existf(x)107) If lim 3, find lim f(x).x 2 xx 2A) 2107)B) 6C) 3D) Does not existf(x)f(x)108) If lim. 4, find lim2xx 2x 2 xA) 8108)B) 2C) 16D) 4f(x)109) If lim 1, find lim f(x).x 0 xx 0A) 2109)B) 0C) 1D) Does not existf(x)f(x)110) If lim. 1, find lim2xx 0x 0 xA) 0110)B) 2C) 1D) Does not existf(x) - 3111) If lim 2, find lim f(x).x 1 x - 1x 1A) 1111)B) 2C) 3D) Does not existUse a CAS to plot the function near the point x 0 being approached. From your plot guess the value of the limit.112)x-8limx- 64x 64A) 8113) limx 1A) 1112)B)18C)116D) 01- x1-x113)B) 2C)2312D) 0
9 xx114) limx 09-xA) 3B) 016D)13115)A) 9118B) -C) 18D)11881 2x - 9x116) limx 0A) 811932C)2912D)3118)B) 6C)16D) 0x2 - 9x2 7 - 4A) 3limx -1D)9 - x2x13119) limx 3118117)B)3-C)3A) 0118) limx 0116)B)3 3x x117) limx 0120)C)81 - x - 9x115) limx 0A)114)119)B) 4C)14D) 8x2 - 1x2 3 - 2A) 1120)B) 4C)14D) 2SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.Provide an appropriate response.121) It can be shown that the inequalities 1 -x2x sin(x) 1 hold for all values of x close62 - 2 cos(x)to zero. What, if anything, does this tell you aboutx sin(x)? Explain.2 - 2 cos(x)24121)
MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.122) Write the formal notation for the principle "the limit of a quotient is the quotient of the limits" andinclude a statement of any restrictions on the principle.lim g(x)x ag(x)MA) If lim g(x) M and lim f(x) L, then lim , provided thatf(x)limf(x)Lx ax ax ax a122)f(a) 0.lim g(x)x ag(x)MB) If lim g(x) M and lim f(x) L, then lim , provided thatlim f(x)Lx ax ax a f(x)x aL 0.g(x) g(a)C) lim. f(a)x a f(x)g(x) g(a)D) lim, provided that f(a) 0. f(a)x a f(x)123) What conditions, when present, are sufficient to conclude that a function f(x) has a limit as xapproaches some value of a?A) Either the limit of f(x) as x a from the left exists or the limit of f(x) as x a from the rightexistsB) The limit of f(x) as x a from the left exists, the limit of f(x) as x a from the right exists, andthese two limits are the same.C) The limit of f(x) as x a from the left exists, the limit of f(x) as x a from the right exists, andat least one of these limits is the same as f(a).D) f(a) exists, the limit of f(x) as x a from the left exists, and the limit of f(x) as x a from theright exists.123)124) Provide a short sentence that summarizes the general limit principle given by the formal notationlim [f(x) g(x)] lim f(x) lim g(x) L M, given that lim f(x) L and lim g(x) M.x ax ax ax ax a124)A) The sum or the difference of two functions is continuous.B) The sum or the difference of two functions is the sum of two limits.C) The limit of a sum or a difference is the sum or the difference of the limits.D) The limit of a sum or a difference is the sum or the difference of the functions.125) The statement "the limit of a constant times a function is the constant times the limit" follows froma combination of two fundamental limit principles. What are they?A) The limit of a product is the product of the limits, and the limit of a quotient is the quotient ofthe limits.B) The limit of a constant is the constant, and the limit of a product is the product of the limits.C) The limit of a function is a constant times a limit, and the limit of a constant is the constant.D) The limit of a product is the product of the limits, and a constant is continuous.125)Given the interval (a, b) on the x-axis with the point c inside, find the greatest value for δ 0 such that for all x,0 x - c δ a x b.126) a -10, b 0, c -8126)A) δ 4B) δ 1C) δ 2D) δ 825
127) a 294,b ,c 999A) δ 127)59B) δ 19C) δ 128) a 1.373, b 2.751, c 1.859A) δ 0.892B) δ 129D) δ 2128)C) δ 1.378D) δ 0.486Use the graph to find a δ 0 such that for all x, 0 x - c δ f(x) - L ε.129)129)yy 2x 3f(x) 2x 3c 1L 5ε 0.25.254.80x0.9 1 1.1NOT TO SCALEA) δ 0.1B) δ 0.4C) δ 4D) δ 0.2130)130)yy 5x - 28.2f(x) 5x - 2c 2L 8ε 0.287.8 2 01.96x2.04NOT TO SCALEA) δ 6B) δ 0.08C) δ 0.426D) δ 0.04
131)131)yy -4x - 17.2f(x) -4x - 1c -2L 7ε 0.276.8 -2 -2.050x-1.95NOT TO SCALEA) δ -0.05B) δ 0.05C) δ 0.5D) δ 11132)132)yy -2x 37.2f(x) -2x 3c -2L 7ε 0.276.8-2.1 -2 -1.9x0NOT TO SCALEA) δ 0.2B) δ -0.1C) δ 927D) δ 0.1
133)133)yy 3x 225.2f(x) 5c 2L 5ε 0.24.803x 22x1.9 2 2.1NOT TO SCALEA) δ 0.1B) δ 3C) δ -0.2D) δ 0.2134)134)y -y3x 324.73f(x) - x 324.5c -1L 4.5ε 0.24.3-1.1-10-0.9xNOT TO SCALEA) δ 0.1B) δ -0.2C) δ 0.228D) δ 5.5
135)135)yf(x) 2 xc 3L 2 31ε 4y 2 x3.713.463.2102.583133.4481xNOT TO SCALEA) δ 0.46B) δ 0.4169C) δ 0.4481D) δ 0.865136)136)yy f(x) c 4L 11ε 4x-3x-31.2510.7503.5625 44.5625xNOT TO SCALEA) δ 0.5625B) δ 0.4375C) δ 129D) δ 3
137)137)yy 2x2f(x) 2x2c 2L 8ε 1987 2 01.87x2.12NOT TO SCALEA) δ 0.13B) δ 0.12C) δ 0.25D) δ 6138)138)yy x2 - 23f(x) x2 - 2c 2L 2ε 1210 2 1.73x2.24NOT TO SCALEA) δ 0.27B) δ 0.24C) δ 0D) δ 0.51A function f(x), a point c, the limit of f(x) as x approaches c, and a positive number ε is given. Find a number δ 0 suchthat for all x, 0 x - c δ f(x) - L ε.139) f(x) 5x 9, L 29, c 4, and ε 0.01139)A) δ 0.01B) δ 0.002C) δ 0.004D) δ 0.0025140) f(x) 10x - 1, L 29, c 3, and ε 0.01A) δ 0.002B) δ 0.001C) δ 0.003333D) δ 0.0005141) f(x) -7x 10, L -18, c 4, and ε 0.01A) δ 0.001429B) δ 0.005714C) δ -0.0025D) δ 0.002857140)141)30
142) f(x) -9x - 1, L -19, c 2, and ε 0.01A) δ 0.001111B) δ 0.000556142)C) δ 0.002222D) δ -0.005143) f(x) x 2, L 2, c 2, and ε 1A) δ 1B) δ 9C) δ 5D) δ 3144) f(x) 7 - x, L 2, c 3, and ε 1A) δ 4B) δ 3C) δ 6D) δ -5145) f(x) 7x2, L 567, c 9, and ε 0.4A) δ 0.00318B) δ 9.00317C) δ 0.00317D) δ 8.99682146) f(x) 143)144)145)11, L , c 9, and ε 0.1x9A) δ 81146)B) δ 0.4737C) δ 4.2632147) f(x) mx, m 0, L 6m, c 6, and ε 0.050.05A) δ B) δ 6 - mm148) f(x) mx b, m 0, L A) δ D) δ 810147)0.05C) δ 6 mD) δ 0.05m1 b, c , and ε c 088cmB) δ 1c 8 m148)C) δ c8D) δ 8mFind the limit L for the given function f, the point c, and the positive number ε. Then find a number δ 0 such that, forall x, 0 x - c δ f(x) - L ε.149) f(x) 6x - 2, c -3, ε 0.12149)A) L 16; δ 0.03B) L -16; δ 0.02C) L -20; δ 0.03D) L -20; δ 0.02150) f(x) x2 2x -80, c -10, ε 0.03x 10150)A) L -18; δ 0.03C) L 2; δ 0.04B) L -16; δ 0.04D) L 0; δ 0.03151) f(x) 8 - 2x, c -4, ε 0.5A) L 4; δ 1.88C) L 4; δ 2.13152) f(x) 151)B) L j-3; δ 0.88D) L 5; δ 1.8836, c 9, ε 0.2xA) L 4; δ 4.74152)B) L 4; δ 0.47C) L 4; δ 0.9531D) L 4; δ 0.43
SHORT ANSWER. Write the word or phrase that best completes each statement or answers the question.Prove the limit statement153) lim (2x - 3) -1x 1153)x2 - 9154) lim 6x 3 x - 3155) limx 2154)3x2 - 5x- 2 7x-2155)1 1156) lim x 7 x 7156)MULTIPLE CHOICE. Choose the one alternative that best completes the statement or answers the question.Solve the problem.157) You are asked to make some circular cylinders, each with a cross-sectional area of 6 cm 2 . To dothis, you need to know how much deviation from the ideal cylinder diameter of x0 2.65 cm you157)can allow and still have the area come within 0.1 cm 2 of the required 6 cm 2 . To find out, letx 2A πand look for the interval in which you must hold x to make A - 6 0.1. What interval2do you find?A) (4.8580, 4.9396)B) (2.7408, 2.7869)C) (0.5642, 0.5642)D) (1.9381, 1.9706)158) Ohm's Law for electrical circuits is stated V RI, where V is a constant voltage, R is the resistancein ohms and I is the current in amperes. Your firm has been asked to supply the resistors for acircuit in which V will be 10 volts and I is to be 5 0.1 amperes. In what interval does R have to liefor I to be within 0.1 amps of the target value I0 5?100 10010 10100 10051 49A),B),C),D),51 4949 5149 51100 100158)159) The cross-sectional area of a cylinder is given by A πD2/4, where D is the cylinder diameter.Find the tolerance range of D such that A - 10 0.01 as long as Dmin D Dmax.A) Dmin 3.567, Dmax 3.578B) Dmin 3.558, Dmax 3.578C) Dmin 3.558, Dmax 3.570D) Dmin 3.567, Dmax 3.570159)160) The current in a simple electrical circuit is given by I V/R, where I is the current in amperes, V isthe voltage in volts, and R is the resistance in ohms. When V 12 volts, what is a 12Ω resistor'stolerance for the current to be within 1 0.01 amp?A) 10%B) 1%C) 0.01%D) 0.1%160)Provide an appropriate response.161) The definition of the limit, lim f(x) L, means if given any number ε 0, there exists a number δx c 0, such that for all x, 0 x - c δ impliesA) f(x) - L ε.B) f(x) - L εC) f(x) - L δ32D) f(x) - L δ161)
162) Identify the incorrect statements about limits.I. The number L is the limit of f(x) as x approaches c if f(x) gets closer to L as x approaches x0 .162)II. The number L is the limit of f(x) as x approaches c if, for any ε 0, there corresponds a δ 0such that f(x) - L ε whenever 0 x - c δ.III. The number L is the limit of f(x) as x approaches c if, given any ε 0, there exists a value of xfor which f(x) - L ε.A) II and IIIB) I and IIIC) I and IID) I, II, and IIIUse the graph to estimate the specified limit.163) Findlim f(x) andlimf(x)x (-1)x (-1) 163)y2-4-22x4-2-4-6A) -2; -7B) -5; -2C) -7; -2D) -7; -5164) Find lim f(x)x 0164)5y4321-5-4-3-2-112345 x-1-2-3-4-5A) 1B) -1C) 033D) does not exist
165) Find lim f(x)x 0165)5y4321-5-4-3-2-112345 x-1-2-3-4-5A) 2166) FindC) -2B) 0D) does not existlim f(x)x 3 14166)y12108642-4-2246810x-2A)73B) -7 33C)347 33D) -3
167) Findlimf(x) andlimf(x)x (π/2) x (π/2) 6167)y54321- -12-2- 2 3 22 x-3-4-5-6A) 4; 3168) FindB) π; πC) 3; 4D)π π;2 2lim f(x) and lim f(x)x 0 x 0 87654321-8 -7 -6 -5 -4 -3 -2 -1-1-2-3-4-5-6-7-8A) 1; 1168)y1 2 3 4 5 6 7 8 xB) 1; -1C) -1; -135D) -1; 1
169) Findlim f(x) and lim f(x)x 2 x 2 169)y12108642-6 -5 -4 -3 -2 -1-2-4-6123456 x-8-10-12A) 1; 1C) -2; 4B) 4; -2D) does not exist; does not exist170) Find lim f(x)x 012170)y108642-2-112345x-2-4A) 6B) 0C) does not existD) -1Determine the limit by sketching an appropriate graph.for x 1171) lim f(x), where f(x) -4x - 62x5for x 1x 1A) -4171)B) -5C) -1036D) -3
172)lim f(x), where f(x) -5x - 45x - 3x 4 A) -24173)174)lim f(x), where f(x) x 1-A) Does not exist172)B) -32lim f(x), where f(x) x 30x -4 A) 16for x 4for x 4C) -2for x -4for x -4173)B) 01 - x214D) 17C) 13D) 190 x 11 x 4x 4174)B) 1C) 037D) 4
175)lim f(x), where f(x) x -7 A) 6-7 x 0, or 0 x 3x 0x -7 or x 3x10B) Does not exist175)C) -0D) -7Find the limit.176)x 5x 6limx -0.5 -176)A) Does not exist177)limx -1 B)xlimx 2x 2 A)179)A)180)A)181)B)h 2 7h 13 h32D) 7C)34D) Does not exist13179)726B)limx 3x -1 7178)B)5-C)-73x 6C)72 13D) Does not exist3h 2 7h 5h-72 5A) 4911x2 2x726limh 0 -D)177)13limh 0 1113C)7x22 xA) Does not exist178)911180)B)7C)2 5-710D) Does not existx 1x 1181)B) 2C) Does not exist38D) -2
182)x 2x 2limx 5x -2 A) 7183)limx 2-B) Does not existlimx 4 183)B)C) - 88D) Does not existto find the limit.185)xlim (x x 2 B) 7Find the limit using limx 0C) 0D) -7)186)A) 4187) limx 0D) 0184)B)A) 1186)C) - 1010Use the graph of the greatest integer function y limx 7-D) -32x x - 4x-4A) 0185)C) 35x x - 2x-2A) Does not exist184)182)B) 0C) -4D) 2sinx 1.xsin 5xxA) 1187)B) does not existC)15D) 5x188) limx 0 sin 3xA)189) limx 013188)B) 3C) 1D) does not existtan 4xxA) 1189)B) does not existC) 4D)14sin 5x190) limx 0 sin 4xA) 0190)B) does not existC)3954D)45
sin 4x191) limx 0 sin 5xA)45191)B)54C) 0D) does not existsin x cos 4x192) limx 0 x x cos 5xA)45192)B)12C) 0D) does not exist193) lim 6x2 (cot 3x)(csc 2x)x 0A)13194) limx 0B) does not existD)12194)B) -1C) 0D) 1sin(sin x)sin xA) 0196) limx 0C) 1x2 - 2x sin xxA) does not exist195) limx 0193)195)B) does not existC) 1D) -1sin 3x cot 4xcot 5xA) 0196)B)125C)154D) does not existProvide an appropriate response.197) Given lim f(x) Ll, lim f(x) Lr, and Ll Lr, which of the following statements is true?x 0 x 0 I.lim f(x) Llx 0II.lim f(x) Lrx 0III. lim f(x) does not exist.x 0A) noneB) IIIC) II40D) I197)
lim f(x) Ll, lim f(x) Lr , and Ll Lr, which of the following statements is false?x 0 x 0 198) GivenI.lim f(x) Llx 0II.lim f(x) Lrx 0198)III. lim f(x) does not exist.x 0A) IIB) noneC) ID) III199) If lim f(x) L, which of the following expressions are true?x 0I.lim f(x) does not exist.x 0 -II.lim f(x) does not exist.x 0 III.lim f(x) Lx 0 -IV.lim f(x) Lx 0 A) III and IV only200) IfB) I and IV only199)C) II and III onlyD) I and II onlylim f(x) 1 and f(x) is an odd function, which of the following statements are true?x 0 I.lim f(x) 1x 0II.lim f(x) -1x 0 200)III. lim f(x) does not exist.x 0A) II and III onlyB) I and III onlyC) I, II, and IIID) I and II only201) If lim f(x) 1, lim f(x) -1, and f(x) is an even function, which of the following statementsx 1 x 1 201)are true?I.lim f(x) -1x -1II.lim f(x) -1x -1 III.lim f(x) does not exist.x -1A) I, II, and IIIB) II and III onlyC) I and II only202) Given ε 0, find an interval I (6, 6 δ), δ 0, such that if x lies in I, thenbeing verified and what is its value?A) limx-6 0B) limx 6x 0 x 6 C)limx 6 x-6 0D)41limx 6 -x-6 0D) I and III onlyx - 6 ε. What limit is202)
203) Given ε 0, find an interval I (1 - δ, 1), δ 0, such that if x lies in I, then 1 - x ε. What limit isbeing verified and what is its value?A) lim1-x 0B) lim1-x 0x 1 x 1 C)limx 0 -1-x 0D)limx 1 -x 1Find all points where the function is discontinuous.204)A) None203)204)B) x 2C) x 4D) x 4, x 2205)205)A) x -2B) x -2, x 1C) NoneD) x 1206)206)A) x -2, x 0C) x -2, x 0, x 2B) x 0, x 2D) x 2207)207)A) x 6B) x -2C) x -2, x 642D) None
208)208)A) x 1, x 4, x 5C) NoneB) x 4D) x 1, x 5209)209)A) x 1C) x 0B) NoneD) x 0, x 1210)210)A) x 3B) x 0C) NoneD) x 0, x 3211)211)A) NoneB) x 2C) x -2212)D) x -2, x 2212)A) x -2, x 2C) NoneB) x -2, x 0, x 2D) x 043
Answer the question.213) Does lim f(x) exist?x (-1) 213)6-x2 1,4x,f(x) -4,-4x 81,-1 x 00 x 1x 11 x 33 x 5d54321-6 -5 -4 -3 -2 -1-1123456t-2-3-4-5(1, -4)-6A) Yes214) DoesB) Nolim f(x) f(-1)?x -1 -x2 1,2x,f(x) -5,-2x 44,-1 x 00 x 1x 11 x 33 x 5214)6d54321-6 -5 -4 -3 -2 -1-112-2-3-4-5-6A) Yes(1, -5)B) No443456t
215) Does lim f(x) exist?x 1215)6-x2 1,3x,f(x) -4,-3x 63,-1 x 00 x 1x 11 x 33 x 5d54321-6 -5 -4 -3 -2 -1-1123456t-2-3-4-5(1, -4)-6A) NoB) Yes216) Is f continuous at f(1)?-x2 1,3x,f(x) -3,-3x 64,216)-1 x 00 x 1x 11 x 33 x 56d54321-6 -5 -4 -3 -2 -1-1123456t-2-3-4(1, -3)-5-6A) NoB) Yes217) Is f continuous at f(3)?-x2 1,5x,f(x) -2,-5x 104,217)-1 x 00 x 1x 11 x 33 x 56d54321-6 -5 -4 -3 -2 -1-112-2-3(1, -2)-4-5-6A) NoB) Yes453456t
218) Does lim f(x) exist?x 0218)10x3 ,f(x) -4x,7,0,-2 x 00 x 22 x 4x 2d8642(2, 0)-5-4-3-2-112345 t-2-4-6-8-10A) NoB) Yes219) Does lim f(x) f(2)?x 2219)10x3 ,f(x) -2x,4,0,-2 x 00 x 22 x 4x 2d8642(2, 0)-5-4-3-2-112345 t-2-4-6-8-10A) NoB) Yes220) Is f continuous at x 0?220)10x3 ,f(x) -2x,6,0,-2 x 00 x 22 x 4x 2d8642(2, 0)-5-4-3-2-1123-2-4-6-8-10A) YesB) No4645 t
221) Is f continuous at x 4?221)10x3 ,f(x) -2x,6,0,-2 x 00 x 22 x 4x 2d8642(2, 0)-5-4-3-2-112345 t-2-4-6-8-10A) YesB) No222) Is f continuous on (-2, 4]?222)10x3 ,f(x) -4x,2,0,-2 x 00 x 22 x 4x 2d8642(2, 0)-5-4-3-2-112345 t-2-4-6-8-10A) NoB) YesSolve the problem.223) To what new value should f(1) be changed to remove the discontinuity?x2 2,x 1f(x) 1,x 1x 2,A) 4223)x 1B) 3C) 2224) To what new value should f(2) be changed to remove the discontinuity?2x - 4, x 2f(x) 2x 2x - 2, x 2A) -8B) 0C) -7D) 1224)D) -1Find the intervals on which the function is continuous.2225) y - 4xx 5225)B) discontinuous only when x -5D) discontinuous only when x 5A) continuous everywhereC) discontinuous only when x -947
226) y 1226)(x 2)2 4A) discontinuous only when x 8C) discontinuous only when x -2227) y B) discontinuous only when x -16D) continuous everywherex 2227)x2 - 8x 7A) discontinuous only when x 1 or x 7C) discontinuous only when x -7 or x 1228) y B) discontinuous only when x 1D) discontinuous only when x -1 or x 73228)x2 - 9A) discontinuous only when x -9 or x 9C) discontinuous only when x 9229) y B) discontinuous only when x -3D) discontinuous only when x -3 or x 32x2x 37229)A) discontinuous only when x -3C) discontinuous only when x -7 or x -3230) y B) continuous everywhereD) discontinuous only when x -10sin (4θ)2θ230)π2A) con
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