Test bank for thomas calculus early transcendentals 13th edition by thomas

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] 63 48 A) B) C) 2) y = 4x3 + 6x2 - 3, [-6, 2] 53 A) 1) D) 12 2) 53 B) C) 352 B) C) 10 D) 88 3) y = 2x, [2, 8] A) 4) y = 3) D) , [4, 7] x-2 4) A) B) 5) y = 4x2 , 0, A) - D) - 10 5) 10 7) h(t) = sin (3t), 0, B) D) C) -34 D) 6) B) -2 7) B) 8) g(t) = + tan t, - C) π 6 π A) - 6) y = -3x2 - x, [5, 6] A) A) C) π C) π D) - π π π , 4 8) B) C) π D) - π Find 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) x A) slope is ; y = + 20 20 B) slope is 13; y = 13x - 16 C) slope is -39; y = -39x - 80 D) slope is - 4x ;y=+ 25 25 From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas 9) 10) y = x2 + 11x - 15, P(1, -3) 10) A) slope is -39; y = -39x - 80 4x B) slope is ;y=+ 25 25 C) slope is 13; y = 13x - 16 D) slope is x ;y= + 20 20 11) y = x3 - 9x, P(1, -8) A) slope is 3; y = 3x - 11 C) slope is -6; y = -6x B) slope is 3; y = 3x - D) slope is -6; y = -6x - 12) y = x3 - 3x2 + 4, P(3, 4) A) slope is 0; y = -23 C) slope is 1; y = x - 23 B) slope is 9; y = 9x + D) slope is 9; y = 9x - 23 11) 12) 13) y = -3 - x3 , (1, -4) A) slope is 0; y = -1 C) slope is 3; y = 3x - 13) B) slope is -3; y = -3x - D) slope is -1; y = -x - Use the slopes of UQ, UR, US, and UT to estimate the rate of change of y at the specified value of x 14) x = y U T S R Q A) 2 x B) C) D) From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas 14) 15) x = 15) y U T S R Q A) x B) C) D) 16) x = 16) y U T S R Q A) 25 4 B) x C) D) From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas 17) x = 17) y U T S R Q A) 3 x B) C) D) 18) x = 2.5 18) y U T S Q R A) 7.5 x B) 1.25 C) D) 3.75 Use the table to estimate the rate of change of y at the specified value of x 19) x = x y 0 0.2 0.02 0.4 0.08 0.6 0.18 0.8 0.32 1.0 0.5 1.2 0.72 1.4 0.98 A) 1.5 B) C) 0.5 19) D) From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas 20) x = x y 0 0.2 0.01 0.4 0.04 0.6 0.09 0.8 0.16 1.0 0.25 1.2 0.36 1.4 0.49 A) 20) B) 1.5 C) D) 0.5 21) x = x y 0 0.2 0.12 0.4 0.48 0.6 1.08 0.8 1.92 1.0 1.2 4.32 1.4 5.88 A) 21) B) C) D) 22) x = x y 10 0.5 38 1.0 58 1.5 70 2.0 74 2.5 70 3.0 58 3.5 38 4.0 10 A) 22) B) -8 C) D) 23) x = x y 0.900 -0.05263 0.990 -0.00503 0.999 -0.0005 1.000 0.0000 1.001 0.0005 1.010 0.00498 1.100 0.04762 A) 0.5 23) B) C) D) -0.5 Solve the problem From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas 24) When exposed to ethylene gas, green bananas will ripen at an accelerated rate The number of days for ripening becomes shorter for longer exposure times Assume that the table below gives average ripening times of bananas for several different ethylene exposure times: Exposure time (minutes) 10 15 20 25 30 Ripening Time (days) 4.2 3.5 2.6 2.1 1.1 Plot the data and then find a line approximating the data With the aid of this line, find the limit of the average ripening time as the exposure time to ethylene approaches Round your answer to the nearest tenth Days 5 10 15 20 25 30 35 40 Minutes A) B) Days Days 7 6 5 4 3 2 1 10 15 20 25 30 35 40 Minutes 2.6 days 10 15 20 25 30 35 40 Minutes 5.8 days From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas 24) C) D) Days Days 7 6 5 4 3 2 1 10 15 20 25 30 35 40 Minutes 37.5 minutes 10 15 20 25 30 35 40 Minutes 0.1 day 25) When exposed to ethylene gas, green bananas will ripen at an accelerated rate The number of days for ripening becomes shorter for longer exposure times Assume that the table below gives average ripening times of bananas for several different ethylene exposure times Exposure time (minutes) 10 15 20 25 30 Ripening Time (days) 4.3 3.2 2.7 2.1 1.3 Plot the data and then find a line approximating the data With the aid of this line, determine the rate of change of ripening time with respect to exposure time Round your answer to two significant digits Days 5 10 15 20 25 30 35 40 Minutes From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas 25) A) B) Days Days 7 6 5 4 3 2 1 10 15 20 25 30 35 40 Minutes 10 15 20 25 30 35 40 Minutes -6.7 days per minute 5.6 days C) D) Days Days 7 6 5 4 3 2 1 10 15 20 25 30 35 40 Minutes -0.14 day per minute 10 15 20 25 30 35 40 Minutes 38 minutes 26) The graph below shows the number of tuberculosis deaths in the United States from 1989 to 1998 Deaths 2000 1900 1800 1700 1600 1500 1400 1300 1200 1100 89 90 91 92 93 94 95 96 97 Year Estimate the average rate of change in tuberculosis deaths from 1991 to 1993 A) About -30 deaths per year B) About -45 deaths per year C) About -80 deaths per year D) About -0.4 deaths per year From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas 26) Use the graph to evaluate the limit 27) lim f(x) x→-1 27) y -6 -5 -4 -3 -2 -1 B) - x -1 A) ∞ C) D) -1 28) lim f(x) x→0 28) y -4 -3 -2 -1 x -1 -2 -3 -4 A) C) -3 B) D) does not exist From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas 29) lim f(x) x→0 29) y -6 -5 -4 -3 -2 -1 -1 x -2 -3 -4 -5 -6 A) -3 B) C) does not exist D) 30) lim f(x) x→0 30) 12 y 10 -2 -1 x -2 -4 A) does not exist B) -1 C) D) 10 From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas 329) lim f(x) = 0, lim f(x) = ∞ x→∞ x→0 + 329) y -1 x -1 330) lim f(x) = 1, lim f(x) = -1, lim f(x) = -1, lim f(x) = x→-∞ x→∞ x→0 + x→0 330) y -10 -8 -6 -4 -2 -1 10 x -2 -3 -4 -5 MULTIPLE CHOICE Choose the one alternative that best completes the statement or answers the question Find the limit 331) lim (4x x→∞ 16x2 - 3x + 3) A) -12 332) B) 334) lim x→∞ A) C) -∞ D) 332) B) lim ( 2x2 + x→∞ A) x2 + 12x - x lim x→∞ A) 12 333) 331) 333) B) 2 13 D) ∞ 2x2 - 3) x2 + 7x - C) C) ∞ D) x2 - 6x 334) B) does not exist C) D) 13 73 From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas Provide an appropriate response 335) Which of the following statements defines lim f(x) = ∞? x→x0 335) I For every positive real number B there exists a corresponding δ > such that f(x) > B whenever x0 - δ < x < x0 + δ II For every positive real number B there exists a corresponding δ > such that f(x) > B whenever x0 < x < x0 + δ III For every positive real number B there exists a corresponding δ > such that f(x) > B whenever x0 - δ < x < x A) II B) III 336) Which of the following statements defines C) I D) None lim f(x) = ∞? x→(x0)- 336) I For every positive real number B there exists a corresponding δ > such that f(x) > B whenever x0 - δ < x < x0 + δ II For every positive real number B there exists a corresponding δ > such that f(x) > B whenever x0 < x < x0 + δ III For every positive real number B there exists a corresponding δ > such that f(x) > B whenever x0 - δ < x < x A) III B) I 337) Which of the following statements defines C) II D) None lim f(x) = ∞? x→(x0)+ 337) I For every positive real number B there exists a corresponding δ > such that f(x) > B whenever x0 - δ < x < x0 + δ II For every positive real number B there exists a corresponding δ > such that f(x) > B whenever x0 < x < x0 + δ III For every positive real number B there exists a corresponding δ > such that f(x) > B whenever x0 - δ < x < x A) III B) I 338) Which of the following statements defines C) II D) None lim f(x) = -∞? x→x0 338) I For every negative real number B there exists a corresponding δ > such that f(x) < B whenever x0 - δ < x < x0 + δ II For every negative real number B there exists a corresponding δ > such that f(x) < B whenever x0 < x < x0 + δ III For every negative real number B there exists a corresponding δ > such that f(x) < B whenever x0 - δ < x < x0 A) III B) II C) I D) None 74 From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas 339) Which of the following statements defines lim f(x) = -∞? x→(x0 )+ 339) I For every negative real number B there exists a corresponding δ > such that f(x) < B whenever x0 - δ < x < x0 + δ II For every negative real number B there exists a corresponding δ > such that f(x) < B whenever x0 < x < x0 + δ III For every negative real number B there exists a corresponding δ > such that f(x) < B whenever x0 - δ < x < x0 A) I B) III 340) Which of the following statements defines C) II D) None lim f(x) = -∞? x→(x0 )- 340) I For every negative real number B there exists a corresponding δ > such that f(x) < B whenever x0 - δ < x < x0 + δ II For every negative real number B there exists a corresponding δ > such that f(x) < B whenever x0 < x < x0 + δ III For every negative real number B there exists a corresponding δ > such that f(x) < B whenever x0 - δ < x < x0 A) II B) I 341) Which of the following statements defines C) III D) None lim f(x) = ∞? x→-∞ 341) I For every positive real number B there exists a corresponding positive real number N such that f(x) > B whenever x > N II For every positive real number B there exists a corresponding negative real number N such that f(x) > B whenever x < N III For every negative real number B there exists a corresponding negative real number N such that f(x) < B whenever x < N IV For every negative real number B there exists a corresponding positive real number N such that f(x) < B whenever x > N A) I B) IV C) III D) II SHORT ANSWER Write the word or phrase that best completes each statement or answers the question 342) Use the formal definitions of limits to prove lim =∞ x→0 x 342) lim =∞ x x→0 + 343) 343) Use the formal definitions of limits to prove 75 From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas Answer Key Testname: UNTITLED2 1) 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) 41) 42) 43) 44) 45) 46) 47) 48) 49) 50) D D A D C C A C B C D D B A D B C D D D A D A B C B C D B C B B B B D B B C D D A A A D B A C C A C 76 From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas Answer Key Testname: UNTITLED2 51) 52) 53) 54) 55) 56) 57) 58) 59) 60) 61) 62) 63) 64) 65) 66) 67) 68) 69) 70) 71) 72) 73) 74) 75) 76) 77) 78) 79) 80) 81) 82) 83) 84) 85) 86) 87) 88) 89) 90) 91) 92) 93) 94) 95) 96) 97) 98) 99) 100) C B B D A D B A D C A C C C D D B B A A B D B D C C A B D A A C D C A C C C A B D D C C A B C D D D 77 From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas Answer Key Testname: UNTITLED2 101) 102) 103) 104) 105) 106) 107) 108) 109) 110) 111) 112) 113) 114) 115) 116) 117) 118) 119) 120) C C B D C C B A B A C C C D B B B D D B x2 121) Answers may vary One possibility: lim = lim = According to the squeeze theorem, the function x→0 x→0 x sin(x) x2 , which is squeezed between and 1, must also approach as x approaches Thus, - cos(x) x sin(x) lim = x→0 - cos(x) 122) 123) 124) 125) 126) 127) 128) 129) 130) 131) 132) 133) 134) 135) 136) 137) 138) 139) 140) 141) 142) 143) B B C B C C D A D B D A A B B B B B B A A D 78 From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas Answer Key Testname: UNTITLED2 144) 145) 146) 147) 148) 149) 150) 151) 152) 153) B C C A A D A A B Let ε > be given Choose δ = ε/2 Then < x - < δ implies that (2x - 3) + = 2x - = 2(x - 1) = x - < 2δ = ε Thus, < x - < δ implies that (2x - 3) + < ε 154) Let ε > be given Choose δ = ε Then < x - < δ implies that x2 - (x - 3)(x + 3) -6 = -6 x-3 x-3 for x ≠ = (x + 3) - = x -3 < δ=ε x2 - Thus, < x - < δ implies that -6 be given Choose δ = ε/3 Then < x - < δ implies that 3x2 - 5x- (x - 2)(3x + 1) -7 = -7 x-2 x-2 for x ≠ = (3x + 1) - = 3x - = 3(x - 2) = x - < 3δ = ε 3x2 - 5x- Thus, < x - < δ implies that -7 be given Choose δ = min{7/2, 49ε/2} Then < x - < δ implies that 1 7-x = x 7x = 1 ∙ ∙ x-7 x < 1 49ε ∙ ∙ =ε 7/2 Thus, < x - < δ implies that 157) 158) 159) 160) 161) 162) 163) 1 -4, x < y -10 -8 -6 -4 -2-2 -4 -6 10 x -8 -10 329) (Answers may vary.) Possible answer: f(x) = x y -1 x -1 1, x < 330) (Answers may vary.) Possible answer: f(x) = -1, x > y -10 -8 -6 -4 -2 -1 10 x -2 -3 -4 -5 331) 332) 333) 334) 335) 336) 337) 338) 339) 340) 341) B C D A C A C C C C D 86 From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas Answer Key Testname: UNTITLED2 342) Given B > 0, we want to find δ > such that < x - < δ implies Now, > B x 7 > B if and only if x < x B Thus, choosing δ = 7/B (or any smaller positive number), we see that 7 x < δ implies > ≥ B x δ Therefore, by definition lim =∞ x→0 x 343) Given B > 0, we want to find δ > such that x0 < x < x0 + δ implies Now, > B x 8 > B if and only if x < x B We know x0 = Thus, choosing δ = 8/B (or any smaller positive number), we see that x < δ implies 8 > ≥ B x δ Therefore, by definition lim =∞ x x→0 + 87 From https://testbankgo.eu/p/Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas ... https://testbankgo.eu/p /Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas 14) 15) x = 15) y U T S R Q A) x B) C) D) 16) x = 16) y U T S R Q A) 25 4 B) x C) D) From https://testbankgo.eu/p /Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas. .. 0.6 0.18 0.8 0.32 1.0 0.5 1.2 0.72 1.4 0.98 A) 1.5 B) C) 0.5 19) D) From https://testbankgo.eu/p /Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas 20) x = x y 0 0.2 0.01... 1.010 0.00498 1.100 0.04762 A) 0.5 23) B) C) D) -0.5 Solve the problem From https://testbankgo.eu/p /Test-Bank-for-Thomas-Calculus-Early-Transcendentals-13th-Edition-by-Thomas 24) When exposed to ethylene