Solution Manual For Calculus
5th Edition By Robert T Smith,
Rafhi Solution
, (b) The slope appears to be 12.
Chapter 1 Second point msec
(3, 27) 19
(2.1, 11.261) 12.61
(2.01, 10.120601) 12.0601
Limits and Continuity (1, 3) 7
(1.9, 8.859) 11.41
(1.99, 9.880599) 11.9401
3. (a) The slope appears to be 0.
Second point msec
(1, 0.5403) −0.4597
1.1 A Brief Preview of Calculus (0.1, 0.995) −0.05
(0.01, 0.99995) −0.005
1. (a) The slope appears to be 2.
(-1, 0.5403) 0.4597
Second point msec (-0.1, 0.995) 0.05
(2, 5) 3 (-0.01, 0.99995) 0.005
(1.1, 2.21) 2.1
(b) The slope appears to be 1.
(1.01, 2.0201) 2.01
Second point msec
(0, 1) 1
(1, 0.5403) 0.9466
(0.9, 1.81) 1.9
(1.5, 0.0707) 0.9986
(0.99, 1.9801) 1.99
(1.57, 0.0008) 1
(b) The slope appears to be 4.
(2.5, -0.8011) 0.8621
Second point msec (2, -0.4161) 0.9695
(3, 10) 5 (1.6, -0.0292) 1
(2.1, 5.41) 4.1
1
4. (a) The slope appears to be 2
.
(2.01, 5.0401) 4.01
(1, 2) 3 Second point msec
(1.9, 4.61) 3.9 (1, 2) 0.4142
(1.99, 4.9601) 3.99 (0.1, 1.0488) 0.488
(0.01, 1.004988) 0.4988
2. (a) The slope appears to be 3.
(-1, 0) 1
Second point msec (-0.1, 0.9487) 0.513
(2, 10) 7 (-0.01, 0.99499) 0.501
(1.1, 3.331) 3.31
(b) The slope appears to be 0.25.
(1.01, 3.030301) 3.0301
Second point msec
(0, 2) 1
(2, 1.7321) 0.2679
(0.9, 2.729) 2.71
(2.9, 1.9748) 0.252
(0.99, 2.970299) 2.9701
(2.99, 1.9975) 0.25
(4, 2.2361) 0.2361
(3.1, 2.0248) 0.248
(3.01, 2.0025) 0.25
42
,1.1. A BRIEF PREVIEW OF CALCULUS 43
5. (a) The slope appears to be 1. 7. (a) For the x-values of our points here we use
Second point msec (approximations of) 0, 8 , 4 , 38 , and 2 .
(1, e) 1.718282
Left Right Length
(0.1, 1.1052) 1.051709
(0, 1) (0.393, 0.92) 0.400
(0.01, 1.0101) 1.005017
(0.393, 0.92) (0.785, 0.71) 0.449
(-1, 0.3679) 0.632121
(0.785, 0.71) (1.18, 0.383) 0.509
(-0.1, 0.9048) 0.951626
(1.18, 0.383) (1.571, 0) 0.548
(-0.01, 0.9901) 0.995017
Total 1.906
(b) The slope appears to be 2.72.
(b) For the x-values of our points here we use
Second point msec (approximations of) 0, 16 , 8 , 316 , 4 , 516 ,
(0, 1) 1.7183 3 7
8
, 16
, and 2
.
(0.9, 2.4596) 2.587
(0.99, 2.6912) 2.71 Left Right Length
(2, 7.3891) 4.6708 (0, 1) (0.196, 0.98) 0.197
(1.1, 3.0042) 2.859 (0.196, 0.98) (0.393, 0.92) 0.204
(1.01, 2.7456) 2.73 (0.393, 0.92) (0.589, 0.83) 0.217
6. (a) The slope appears to be 1. (0.589, 0.83) (0.785, 0.71) 0.232
(0.785, 0.71) (0.982, 0.56) 0.248
Second point msec
(0.982, 0.56) (1.178, 0.38) 0.262
(0.1, -2.3026) 2.5584
(1.178, 0.38) (1.37, 0.195) 0.272
(0.9, -0.1054) 1.054
(1.37, 0.195) (1.571, 0) 0.277
(0.99, -0.01005034) 1.005034
Total 1.909
(2, 0.6931) 0.6931
(1.1, 0.09531) 0.9531 (c) Actual length approximately 1.9101.
(1.01, 0.00995) 0.995 8. (a) For the x-values of our points here we use
(approximations of) 0, 8 , 4 , 38 , and 2 .
Note that we used 0.1 rather than 0 as an
evaluation point because ln x is not defined at Left Right Length
0.
(0, 0) (0.393, 0.38) 0.548
(b) The slope appears to be 0.5.
(0.393, 0.38) (0.785, 0.71) 0.509
Second point msec (0.785, 0.71) (1.18, 0.924) 0.449
(1, 0) 0.6931 (1.18, 0.924) (1.57, 1) 0.400
(1.9, 0.6419) 0.512 Total 1.906
(1.99, 0.6881) 0.5
(b) For the x-values of our points here we use
(3, 1.0986) 0.4055
(approximations of) 0, 16 , 8 , 316 , 4 , 516 ,
(2.1, 0.7419) 0.488 3 7
8
, 16
, and 2
.
(2.01, 0.6981) 0.5
, 44 CHAPTER 1. LIMITS AND CONTINUITY
Left Right Length (b)
(0, 0) (0.196, 0.2) 0.277 Left Right Length
(0.196, 0.2) (0.39, 0.38) 0.272 (1, 1) (1.125, 0.89) 0.167
(0.39, 0.38) (0.589, 0.56) 0.262 (1.125, 0.89) (1.25, 0.8) 0.153
(0.589, 0.56) (0.785, 0.71) 0.248 (1.25, 0.8) (1.375, 0.73) 0.145
(0.785, 0.71) (0.982, 0.83) 0.232 (1.375, 0.73) (1.5, 0.67) 0.139
(0.982, 0.83) (1.18, 0.924) 0.217 (1.5, 0.67) (1.625, 0.62) 0.135
(1.18, 0.924) (1.374, 0.98) 0.204 (1.625, 0.62) (1.75, 0.57) 0.133
(1.374, 0.98) (1.571, 1) 0.197 (1.75, 0.57) (1.875, 0.53) 0.131
Total 1.909 (1.875, 0.53) (2, 0.5) 0.129
(c) Actual length approximately 1.9101. Total 1.132
(c) Actual length approximately 1.1321.
9. (a)
Left Right Length 11. (a)
(0, 1) (0.75, 1.323) 0.817 Left Right Length
(0.75, 1.323) (1.5, 1.581) 0.793 (-2, 5) (-1, 2) 3.162
(1.5, 1.581) (2.25, 1.803) 0.782 (-1, 2) (0, 1) 1.414
(2.25, 1.803) (3, 2) 0.776 (0, 1) (1, 2) 1.414
Total 3.167 (1, 2) (2, 5) 3.162
(b) Total 9.153
Left Right Length (b)
(0, 1) (0.375, 1.17) 0.413 Left Right Length
(0.375, 1.17) (0.75, 1.323) 0.404 (-2, 5) (-1.5, 3.25) 1.820
(0.75, 1.323) (1.125, 1.46) 0.399 (-1.5, 3.25) (-1, 2) 1.346
(1.125, 1.46) (1.5, 1.58) 0.395 (-1, 2) (-0.5, 1.25) 0.901
(1.5, 1.58) (1.88, 1.696) 0.392 (-0.5, 1.25) (0, 1) 0.559
(1.88, 1.696) (2.25, 1.80) 0.390 (0, 1) (0.5, 1.25) 0.559
(2.25, 1.80) (2.63, 1.904) 0.388 (0.5, 1.25) (1, 2) 0.901
(2.63, 1.904) (3, 2) 0.387 (1, 2) (1.5, 3.25) 1.346
Total 3.168 (1.5, 3.25) (2, 5) 1.820
(c) Actual length approximately 3.168. Total 9.253
(c) Actual length approximately 9.2936.
10. (a)
Left Right Length 12. (a)
(1, 1) (1.25, 0.8) 0.3202 Left Right Length
(1.25, 0.8) (1.5, 0.67) 0.2833 (-1, 1) (-0.5, 1.0078
1.875)
(1.5, 0.67) (1.75, 0.571) 0.2675
(1.75, 0.571) (2, 0.5) 0.2600 (-0.5, 1.875) (0, 2) 0.5154
(0, 2) (0.5, 2.125) 0.5154
Total 1.1310
(0.5, 2.125) (1, 3) 1.0078
Total 3.0463
5th Edition By Robert T Smith,
Rafhi Solution
, (b) The slope appears to be 12.
Chapter 1 Second point msec
(3, 27) 19
(2.1, 11.261) 12.61
(2.01, 10.120601) 12.0601
Limits and Continuity (1, 3) 7
(1.9, 8.859) 11.41
(1.99, 9.880599) 11.9401
3. (a) The slope appears to be 0.
Second point msec
(1, 0.5403) −0.4597
1.1 A Brief Preview of Calculus (0.1, 0.995) −0.05
(0.01, 0.99995) −0.005
1. (a) The slope appears to be 2.
(-1, 0.5403) 0.4597
Second point msec (-0.1, 0.995) 0.05
(2, 5) 3 (-0.01, 0.99995) 0.005
(1.1, 2.21) 2.1
(b) The slope appears to be 1.
(1.01, 2.0201) 2.01
Second point msec
(0, 1) 1
(1, 0.5403) 0.9466
(0.9, 1.81) 1.9
(1.5, 0.0707) 0.9986
(0.99, 1.9801) 1.99
(1.57, 0.0008) 1
(b) The slope appears to be 4.
(2.5, -0.8011) 0.8621
Second point msec (2, -0.4161) 0.9695
(3, 10) 5 (1.6, -0.0292) 1
(2.1, 5.41) 4.1
1
4. (a) The slope appears to be 2
.
(2.01, 5.0401) 4.01
(1, 2) 3 Second point msec
(1.9, 4.61) 3.9 (1, 2) 0.4142
(1.99, 4.9601) 3.99 (0.1, 1.0488) 0.488
(0.01, 1.004988) 0.4988
2. (a) The slope appears to be 3.
(-1, 0) 1
Second point msec (-0.1, 0.9487) 0.513
(2, 10) 7 (-0.01, 0.99499) 0.501
(1.1, 3.331) 3.31
(b) The slope appears to be 0.25.
(1.01, 3.030301) 3.0301
Second point msec
(0, 2) 1
(2, 1.7321) 0.2679
(0.9, 2.729) 2.71
(2.9, 1.9748) 0.252
(0.99, 2.970299) 2.9701
(2.99, 1.9975) 0.25
(4, 2.2361) 0.2361
(3.1, 2.0248) 0.248
(3.01, 2.0025) 0.25
42
,1.1. A BRIEF PREVIEW OF CALCULUS 43
5. (a) The slope appears to be 1. 7. (a) For the x-values of our points here we use
Second point msec (approximations of) 0, 8 , 4 , 38 , and 2 .
(1, e) 1.718282
Left Right Length
(0.1, 1.1052) 1.051709
(0, 1) (0.393, 0.92) 0.400
(0.01, 1.0101) 1.005017
(0.393, 0.92) (0.785, 0.71) 0.449
(-1, 0.3679) 0.632121
(0.785, 0.71) (1.18, 0.383) 0.509
(-0.1, 0.9048) 0.951626
(1.18, 0.383) (1.571, 0) 0.548
(-0.01, 0.9901) 0.995017
Total 1.906
(b) The slope appears to be 2.72.
(b) For the x-values of our points here we use
Second point msec (approximations of) 0, 16 , 8 , 316 , 4 , 516 ,
(0, 1) 1.7183 3 7
8
, 16
, and 2
.
(0.9, 2.4596) 2.587
(0.99, 2.6912) 2.71 Left Right Length
(2, 7.3891) 4.6708 (0, 1) (0.196, 0.98) 0.197
(1.1, 3.0042) 2.859 (0.196, 0.98) (0.393, 0.92) 0.204
(1.01, 2.7456) 2.73 (0.393, 0.92) (0.589, 0.83) 0.217
6. (a) The slope appears to be 1. (0.589, 0.83) (0.785, 0.71) 0.232
(0.785, 0.71) (0.982, 0.56) 0.248
Second point msec
(0.982, 0.56) (1.178, 0.38) 0.262
(0.1, -2.3026) 2.5584
(1.178, 0.38) (1.37, 0.195) 0.272
(0.9, -0.1054) 1.054
(1.37, 0.195) (1.571, 0) 0.277
(0.99, -0.01005034) 1.005034
Total 1.909
(2, 0.6931) 0.6931
(1.1, 0.09531) 0.9531 (c) Actual length approximately 1.9101.
(1.01, 0.00995) 0.995 8. (a) For the x-values of our points here we use
(approximations of) 0, 8 , 4 , 38 , and 2 .
Note that we used 0.1 rather than 0 as an
evaluation point because ln x is not defined at Left Right Length
0.
(0, 0) (0.393, 0.38) 0.548
(b) The slope appears to be 0.5.
(0.393, 0.38) (0.785, 0.71) 0.509
Second point msec (0.785, 0.71) (1.18, 0.924) 0.449
(1, 0) 0.6931 (1.18, 0.924) (1.57, 1) 0.400
(1.9, 0.6419) 0.512 Total 1.906
(1.99, 0.6881) 0.5
(b) For the x-values of our points here we use
(3, 1.0986) 0.4055
(approximations of) 0, 16 , 8 , 316 , 4 , 516 ,
(2.1, 0.7419) 0.488 3 7
8
, 16
, and 2
.
(2.01, 0.6981) 0.5
, 44 CHAPTER 1. LIMITS AND CONTINUITY
Left Right Length (b)
(0, 0) (0.196, 0.2) 0.277 Left Right Length
(0.196, 0.2) (0.39, 0.38) 0.272 (1, 1) (1.125, 0.89) 0.167
(0.39, 0.38) (0.589, 0.56) 0.262 (1.125, 0.89) (1.25, 0.8) 0.153
(0.589, 0.56) (0.785, 0.71) 0.248 (1.25, 0.8) (1.375, 0.73) 0.145
(0.785, 0.71) (0.982, 0.83) 0.232 (1.375, 0.73) (1.5, 0.67) 0.139
(0.982, 0.83) (1.18, 0.924) 0.217 (1.5, 0.67) (1.625, 0.62) 0.135
(1.18, 0.924) (1.374, 0.98) 0.204 (1.625, 0.62) (1.75, 0.57) 0.133
(1.374, 0.98) (1.571, 1) 0.197 (1.75, 0.57) (1.875, 0.53) 0.131
Total 1.909 (1.875, 0.53) (2, 0.5) 0.129
(c) Actual length approximately 1.9101. Total 1.132
(c) Actual length approximately 1.1321.
9. (a)
Left Right Length 11. (a)
(0, 1) (0.75, 1.323) 0.817 Left Right Length
(0.75, 1.323) (1.5, 1.581) 0.793 (-2, 5) (-1, 2) 3.162
(1.5, 1.581) (2.25, 1.803) 0.782 (-1, 2) (0, 1) 1.414
(2.25, 1.803) (3, 2) 0.776 (0, 1) (1, 2) 1.414
Total 3.167 (1, 2) (2, 5) 3.162
(b) Total 9.153
Left Right Length (b)
(0, 1) (0.375, 1.17) 0.413 Left Right Length
(0.375, 1.17) (0.75, 1.323) 0.404 (-2, 5) (-1.5, 3.25) 1.820
(0.75, 1.323) (1.125, 1.46) 0.399 (-1.5, 3.25) (-1, 2) 1.346
(1.125, 1.46) (1.5, 1.58) 0.395 (-1, 2) (-0.5, 1.25) 0.901
(1.5, 1.58) (1.88, 1.696) 0.392 (-0.5, 1.25) (0, 1) 0.559
(1.88, 1.696) (2.25, 1.80) 0.390 (0, 1) (0.5, 1.25) 0.559
(2.25, 1.80) (2.63, 1.904) 0.388 (0.5, 1.25) (1, 2) 0.901
(2.63, 1.904) (3, 2) 0.387 (1, 2) (1.5, 3.25) 1.346
Total 3.168 (1.5, 3.25) (2, 5) 1.820
(c) Actual length approximately 3.168. Total 9.253
(c) Actual length approximately 9.2936.
10. (a)
Left Right Length 12. (a)
(1, 1) (1.25, 0.8) 0.3202 Left Right Length
(1.25, 0.8) (1.5, 0.67) 0.2833 (-1, 1) (-0.5, 1.0078
1.875)
(1.5, 0.67) (1.75, 0.571) 0.2675
(1.75, 0.571) (2, 0.5) 0.2600 (-0.5, 1.875) (0, 2) 0.5154
(0, 2) (0.5, 2.125) 0.5154
Total 1.1310
(0.5, 2.125) (1, 3) 1.0078
Total 3.0463
