Ben (ben_cheeseman)

Race #230

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Official speed 112.86 wpm (91.87 seconds elapsed during race)
Without ending ping 113.02 wpm (129 ms delay sending score to TypeRacer’s server)
Timerless 113.84 wpm (665 ms elapsed before first character typed; 91.07 seconds elapsed during race)
Timerless minus one 113.71 wpm, ignoring the first character typed
Race Start October 13, 2023 1:16:56pm UTC
Race Finish October 13, 2023 1:18:28pm UTC
Outcome No win (3 of 5)
Opponents 1. rayer (130.06 wpm)
2. tebond (117.27 wpm)
Accuracy 97.5%
Points 304.72
Text #4940058 (Length: 864 characters)

Calculus is a tool that helps us understand how a change in one quantity is related to a change in another. How does the speed of a falling object change as a function of time? How does the level of water in a barrel change as a function of the amount of liquid poured into it? We see change occurring in nearly everything we observe in the world and universe, and powerful modern instruments help us see more and more. In this section we introduce the ideas of average and instantaneous rates of change, and show that they are closely related to the slope of a curve at a point P on the curve. We give precise developments of these important concepts in the next chapter, but for now we use an informal approach so you will see how they lead naturally to the main idea of this chapter, the limit. The idea of a limit plays a foundational role throughout calculus.
Characters typed Calculus is a toll ol that helps us understand how a chang ein e in one quantity is related toa a change in another. How does the speed of a falling object change a s a function of time? How does the level of water ina a barrel schange as a function of the amoutnt of liquid poured into it? We see change occurring in nearly everything we observe in the wold rld and universe, and powerful modern instruments help us see more and more. In this section we interreooduce the ideas of average and instanteaneous rates of change, and show that they are closely related tot he the slope ofa a curve at a point P on the curve. We give precise develloopments of thsese important concepts in the enxt cnext chapter, but for now we use an informal approach so you will see how they lead naturally to the main idea of this chapter, the limit. The idea of a limit palys lays a foundational role throguhughout calculus.
Timing
Character C a l c u l u s i s a t o l l - -l -l o l
Milliseconds 665 838 165 106 118 114 80 118 46 84 109 73 67 65 110 16 179 129 116 208 117 141 434 162 114
Character t h a t h e l p s u s u n d e r s t a n d
Milliseconds 107 75 52 59 41 112 143 65 143 77 61 81 74 70 100 48 25 117 77 123 90 82 95 72 94
Character h o w a c h a n g e i n - -n -i -e - e i n
Milliseconds 67 72 40 91 86 77 81 43 93 67 91 65 0 69 77 94 267 109 113 130 150 180 84 114 90
Character o n e q u a n t i t y i s r e l a t e d
Milliseconds 45 125 60 75 78 123 78 146 88 240 115 91 160 70 115 71 110 94 59 65 80 88 57 133 108
Character t o a - -a a c h a n g e i n a n o t h e
Milliseconds 60 60 123 126 311 116 85 94 83 112 120 174 104 73 61 45 31 79 76 65 79 77 64 98 66
Character r . H o w d o e s t h e s p e e d o f
Milliseconds 34 92 151 193 227 100 79 80 78 63 69 80 56 105 70 76 97 53 104 156 143 62 95 75 88
Character a f a l l i n g o b j e c t c h a n g e a
Milliseconds 62 91 124 59 66 120 80 79 35 88 40 93 103 72 58 162 68 112 90 184 100 80 61 50 83
Character - s a f u n c t i o n o f t i m e ? H
Milliseconds 93 304 113 83 70 84 70 275 104 60 160 46 61 43 89 92 67 109 62 88 71 71 188 34 171
Character o w d o e s t h e l e v e l o f w a t e
Milliseconds 180 90 87 58 70 58 66 73 77 60 139 76 160 72 64 110 36 66 137 17 80 85 54 94 87
Character r i n a - -a a b a r r e l s -s c h a n g
Milliseconds 97 46 64 53 112 168 246 117 128 112 68 90 89 50 144 91 57 81 90 278 66 104 69 90 43
Character e a s a f u n c t i o n o f t h e a m
Milliseconds 53 95 92 66 149 60 98 120 100 75 28 157 63 64 60 57 91 65 99 55 71 70 66 59 105
Character o u t -t n t o f l i q u i d p o u r e d i
Milliseconds 95 91 224 297 199 150 62 90 82 40 101 104 105 86 64 98 49 79 82 107 70 60 130 86 51
Character n t o i t ? W e s e e c h a n g e o c c
Milliseconds 74 86 73 81 145 72 189 74 136 174 100 67 68 120 81 84 48 82 80 98 49 73 68 108 145
Character u r r i n g i n n e a r l y e v e r y t h i
Milliseconds 305 100 114 108 48 82 60 61 55 83 327 93 66 11 146 68 89 70 83 142 189 171 122 103 77
Character n g w e o b s e r v e i n t h e w o l d
Milliseconds 364 126 114 79 55 105 126 84 82 58 44 157 80 25 64 65 76 13 95 62 76 112 21 250 89
Character - -d -l r l d a n d u n i v e r s e , a n d
Milliseconds 123 234 120 128 126 86 91 69 71 70 84 56 70 89 91 47 136 95 187 89 144 87 55 126 73
Character p o w e r f u l m o d e r n i n s t r u m e
Milliseconds 81 51 88 25 12 77 156 21 84 60 109 95 35 91 82 82 35 103 63 34 86 55 56 153 76
Character n t s h e l p u s s e e m o r e a n d
Milliseconds 95 56 64 20 92 87 80 152 70 91 67 93 67 90 132 49 32 87 30 53 80 69 110 70 60
Character m o r e . I n t h i s s e c t i o n w e
Milliseconds 64 97 39 58 136 424 194 220 160 76 65 51 89 77 81 61 88 156 47 7 74 52 68 49 89
Character i n t e r -r -e r e o -o -e o d u c e t h e i d e
Milliseconds 92 64 25 88 112 314 123 23 72 261 238 111 173 103 193 167 137 118 66 83 42 124 72 25 94
Character a s o f a v e r a g e a n d i n s t a n t
Milliseconds 79 116 95 92 67 98 72 47 144 65 128 106 57 110 93 110 104 62 95 74 76 120 130 113 211
Character e -e a n e o u s r a t e s o f c h a n g e ,
Milliseconds 151 324 83 90 193 137 83 80 92 72 86 87 73 55 90 56 59 101 94 55 80 74 66 57 60
Character a n d s h o w t h a t t h e y a r e c
Milliseconds 60 37 139 70 73 89 32 83 61 99 87 74 69 73 82 70 115 47 103 55 92 63 67 76 95
Character l o s e l y r e l a t e d t o t h e - -e -h
Milliseconds 63 144 66 51 95 74 34 150 76 52 184 88 70 142 98 86 70 77 42 112 12 129 200 112 102
Character - -t t h e s l o p e o f a - - -a a c
Milliseconds 296 166 200 84 45 93 66 84 111 164 112 59 44 146 70 94 30 105 257 113 123 146 389 87 429
Character u r v e a t a p o i n t P o n t h e
Milliseconds 128 45 144 70 60 103 73 78 52 95 76 117 186 76 78 87 143 170 122 63 107 30 77 58 93
Character c u r v e . W e g i v e p r e c i s e d e
Milliseconds 93 63 76 145 80 61 52 152 170 125 58 85 69 77 71 39 70 66 115 97 66 82 70 165 93
Character v e l l o -o -l o p m e n t s o f t h s -s e s e
Milliseconds 100 82 64 363 173 321 114 226 90 124 116 76 64 69 40 72 65 73 94 53 148 312 110 70 99
Character i m p o r t a n t c o n c e p t s i n t h
Milliseconds 65 59 112 92 72 41 86 84 109 29 102 89 61 84 71 69 110 106 64 66 50 77 62 30 95
Character e e n x t c -c - -t -x -n -e n e x t c h a p t e
Milliseconds 46 119 94 0 92 69 66 111 206 124 113 118 117 125 198 79 54 46 64 130 49 140 40 97 104
Character r , b u t f o r n o w w e u s e a n
Milliseconds 60 49 36 129 77 40 101 64 78 72 50 69 65 38 123 49 60 85 106 14 71 69 170 5 75
Character i n f o r m a l a p p r o a c h s o y o u
Milliseconds 93 72 43 92 75 76 83 96 29 116 60 145 105 228 162 78 91 57 132 52 88 54 84 78 76
Character w i l l s e e h o w t h e y l e a d n a
Milliseconds 42 82 121 130 81 34 72 126 74 73 64 99 78 99 70 78 62 45 134 49 48 104 89 44 82
Character t u r a l l y t o t h e m a i n i d e a
Milliseconds 60 90 75 50 75 124 65 105 60 50 96 42 80 50 78 61 94 80 50 37 101 32 87 58 65
Character o f t h i s c h a p t e r , t h e l i m i
Milliseconds 107 30 122 32 95 53 29 107 61 69 146 121 113 135 56 54 61 78 61 75 72 52 53 138 91
Character t . T h e i d e a o f a l i m i t p a
Milliseconds 120 91 96 98 146 67 113 87 13 76 52 76 81 49 106 42 83 107 82 100 100 87 72 47 120
Character l y s - -s -y -l -a l a y s a f o u n d a t i o
Milliseconds 8 61 96 129 164 123 121 110 130 188 72 50 68 100 74 70 91 87 56 174 72 61 83 60 30
Character n a l r o l e t h r o g u h -h -u -g u g h o u t
Milliseconds 56 114 87 70 130 82 143 55 74 63 92 22 128 74 0 173 290 117 123 247 118 85 115 68 62
Character c a l c u l u s .
Milliseconds 74 118 86 75 122 159 111 96 94 68
WPM Timing
Seconds WPM
1.84 26.13
3.67 52.25
5.51 69.67
7.35 89.8
9.19 82.29
11.02 88.17
12.86 86.77
14.7 93.07
16.54 97.97
18.37 101.23
20.21 101.53
22.05 103.41
23.89 104
25.72 104.5
27.56 107.55
29.4 106.13
31.23 107.57
33.07 108.13
34.91 108.63
36.75 108.42
38.58 107.3
40.42 108.66
42.26 111.03
44.1 112.94
45.93 112.6
47.77 111.28
49.61 110.79
51.44 111.5
53.28 110.36
55.12 112.12
56.96 113.35
58.79 111.44
60.63 110.64
62.47 109.11
64.31 109.54
66.14 110.31
67.98 108.74
69.82 108.8
71.66 110.19
73.49 108.42
75.33 109.6
77.17 110.25
79 111.18
80.84 112.22
82.68 113.35
84.52 113.87
86.35 113.81
88.19 113.62
90.03 113.03
91.87 112.86