ㅤ (toptied)

Race #1448

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Official speed 99.02 wpm (104.71 seconds elapsed during race)
Without ending ping 99.15 wpm (133 ms delay sending score to TypeRacer’s server)
Timerless 99.37 wpm (236 ms elapsed before first character typed; 104.34 seconds elapsed during race)
Timerless minus one 99.26 wpm, ignoring the first character typed
Race Start January 12, 2024 8:40:39am UTC
Race Finish January 12, 2024 8:42:24am UTC
Outcome No win (2 of 3)
Accuracy 95.1%
Points 267.35
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 thja tat helps us understoand how a change in one quanittity is related to a chang ein e in another. Hoiw w does th espe speed of a falling objet ct change as a function of time> ? howHow does the level of water in a brearrel change as a function of the amount of liquid poured into utit> ? We see change occuring inring in nearly everything we observe in the world and universe, and pwoowerfulk mo mo,ddern instruments hekplp us see more and more. In thi sescs section we introcdduceduce the ideas o ff average an dinsd instantaneous rates of change, and show that they are closely reallated to the slope of as c curve a ta t a poiint nt P on the curve. We giviveve ve preceiise developm,enents of these important concetpts in the next chapter, but for now we use an informal approach so you dwill see how they lead naturally ot ehto the main idea of th is csi is chapter, th el eliel limit, th. The odidea of a linmimit paylays a foundational rolt ee throughout calculus;....
Timing
Character C a l c u l u s i s a t o l l - -l -l o l
Milliseconds 236 117 90 118 92 350 130 67 58 108 77 35 75 64 92 33 124 107 26 255 86 213 183 58 86
Character t h j a t -t - -a -j a t h e l p s u s u n d
Milliseconds 81 59 0 44 52 0 294 78 115 116 59 45 60 111 96 78 61 109 32 111 75 15 139 45 109
Character e r s t o -o a n d h o w a c h a n g e i n
Milliseconds 78 93 108 78 92 294 48 91 46 47 109 38 32 45 92 45 93 47 46 77 59 31 33 78 64
Character o n e q u a n i t -t -i t i t y i s r e l a
Milliseconds 78 191 30 80 78 219 121 82 107 80 62 287 78 91 67 73 126 64 92 46 63 167 76 98 47
Character t e d t o a c h a n g e i n - -n -i -e - e
Milliseconds 92 68 106 63 95 29 63 142 89 148 28 72 63 76 47 0 92 46 49 222 91 108 114 125 91
Character i n a n o t h e r . H o i w - -w -i w d o
Milliseconds 58 96 46 81 111 45 58 59 45 75 49 96 62 168 124 0 61 92 221 73 109 141 46 108 16
Character e s t h e s p -p -s -e - e s p e e d o f a
Milliseconds 107 81 74 93 48 75 16 98 25 251 94 119 114 62 49 102 75 33 132 77 100 65 64 43 92
Character f a l l i n g o b j e t - -t c t c h a n g
Milliseconds 105 192 61 31 120 90 78 30 32 94 47 107 47 206 90 201 107 46 233 78 392 60 64 75 48
Character e a s a f u n c t i o n o f t i m e >
Milliseconds 38 72 94 60 78 47 78 46 84 27 126 166 0 46 16 93 137 79 31 109 17 63 48 187 61
Character - -> - ? h o w -w -o -h H o w d o e s t h e
Milliseconds 338 117 284 368 126 88 198 74 15 262 94 112 163 104 62 72 67 49 89 56 73 81 69 63 17
Character l e v e l o f w a t e r i n a b r e -e -r
Milliseconds 100 48 72 84 76 30 122 15 77 74 91 61 84 92 62 97 46 74 80 60 93 49 44 257 110
Character a r r e l c h a n g e a s a f u n c t i o
Milliseconds 14 62 121 79 76 50 321 32 68 65 48 31 106 90 75 66 72 76 64 75 32 115 150 17 61
Character n o f t h e a m o u n t o f l i q u i d
Milliseconds 26 94 100 65 45 120 0 109 12 135 57 65 79 15 36 106 78 63 57 77 110 110 76 47 94
Character p o u r e d i n t o u t -t -u i t > - -> ?
Milliseconds 62 93 62 201 45 113 59 110 188 78 46 62 76 119 61 200 105 138 27 169 61 297 86 217 90
Character W e s e e c h a n g e o c c u r i n g i n
Milliseconds 172 184 64 66 61 134 74 89 64 27 116 80 0 80 146 74 120 108 72 81 29 60 30 102 46
Character -n -i - -g -n -i r i n g i n n e a r l y e v e r
Milliseconds 225 78 132 122 119 120 61 126 29 49 48 121 61 86 135 122 74 51 137 59 59 102 80 119 43
Character y t h i n g w e o b s e r v e i n t h e
Milliseconds 34 126 12 72 59 109 30 77 31 108 296 61 139 77 75 165 95 74 44 75 51 17 82 42 80
Character w o r l d a n d u n i v e r s e , a n d p
Milliseconds 48 153 32 131 34 44 62 60 78 0 77 49 109 28 110 76 76 94 77 61 79 77 47 45 186
Character w o -o -w o w e r f u l k m o -o -m - -k m o , d -d
Milliseconds 79 77 223 100 122 31 47 31 142 0 125 0 46 112 74 154 77 109 124 109 109 17 0 282 147
Character -, d e r n i n s t r u m e n t s h e k p -p -k l
Milliseconds 110 82 60 90 31 84 77 57 290 79 144 64 109 64 74 59 84 15 93 199 15 64 308 219 107
Character p u s s e e m o r e a n d m o r e . I
Milliseconds 93 93 110 62 49 170 187 138 61 31 47 62 49 29 124 31 90 16 58 61 75 29 107 13 185
Character n t h i s e s c -c -s -e -s - s s e c t i o n
Milliseconds 115 94 58 52 60 79 0 147 13 124 294 107 126 126 114 92 48 81 77 81 211 29 33 15 63
Character w e i n t r o c d -d d u c e -e -c -u -d -c d u c e
Milliseconds 129 156 94 123 50 276 170 89 108 145 178 77 93 48 45 125 91 108 124 123 78 141 45 32 77
Character t h e i d e a s o f -f - f a v e r a g e
Milliseconds 78 46 78 31 110 94 61 70 121 93 79 107 16 294 93 91 47 76 96 120 76 125 94 46 46
Character a n d i n s -s -n -i -d - d i n s t a n t a n e o
Milliseconds 108 48 77 0 134 28 76 201 93 119 128 118 58 63 112 30 134 179 92 106 99 205 91 146 97
Character u s r a t e s o f c h a n g e , a n d s
Milliseconds 47 110 66 145 62 91 62 88 80 43 78 46 121 47 63 81 90 30 80 142 139 31 85 0 134
Character h o w t h a t t h e y a r e c l o s e l y
Milliseconds 32 51 74 30 110 45 94 34 278 94 47 81 30 77 170 79 32 64 105 47 111 13 64 139 89
Character r e a l -l -a l a t e d t o t h e s l o p e
Milliseconds 54 178 35 63 73 260 100 75 66 45 77 107 305 78 59 62 61 46 75 48 93 49 144 75 94
Character o f a s c -c - -s c u r v e a t a - -a
Milliseconds 17 108 63 46 93 18 31 93 266 93 125 80 92 79 65 153 49 53 114 70 15 190 31 170 78
Character -t - t a p o i i n t - -t -n -i n t P o n
Milliseconds 112 122 65 77 63 75 0 106 30 279 16 29 158 184 87 112 114 126 47 44 120 84 150 32 75
Character t h e c u r v e . W e g i v -v i v e -e -v v e
Milliseconds 94 45 64 47 253 75 92 141 42 63 47 156 131 59 79 104 60 235 278 95 30 219 93 148 31
Character - -e -v -i v e p r e c e i -i -e i s e d e v e l
Milliseconds 45 196 104 105 122 56 49 31 115 61 66 348 45 79 255 81 148 33 59 17 148 45 130 63 12
Character o p m , e n -n -e -, e n t s o f t h e s e i m
Milliseconds 112 91 109 46 170 78 341 125 110 140 93 48 91 62 48 93 32 124 15 93 77 95 61 93 31
Character p o r t a n t c o n c e t -t p t s i n t h e
Milliseconds 93 46 94 139 62 64 47 62 138 0 32 122 66 201 278 106 83 61 104 53 60 66 58 62 46
Character n e x t c h a p t e r , b u t f o r n o
Milliseconds 65 63 33 121 256 106 90 62 48 79 82 94 73 43 32 155 58 30 86 109 67 76 44 33 64
Character w w e u s e a n i n f o r m a l a p p r
Milliseconds 97 137 151 31 110 119 44 47 92 64 78 103 108 75 364 84 65 29 147 62 77 89 62 109 32
Character o a c h s o y o u d -d w i l l s e e h o
Milliseconds 273 65 81 46 73 94 55 59 72 33 42 51 102 341 111 32 61 123 109 63 46 108 75 94 47
Character w t h e y l e a d n a t u r a l l y o t
Milliseconds 48 62 76 49 106 16 109 174 62 77 63 79 43 104 95 155 93 110 92 106 50 75 93 0 93
Character e h -h -e - -t -o t o t h e m a i n i d e a o
Milliseconds 109 33 184 80 106 123 125 134 45 74 62 49 53 78 26 92 86 57 61 86 271 69 49 61 101
Character f t h i s c -c - -s -i - s i - -i -s i s c h
Milliseconds 57 77 63 27 0 52 64 47 106 174 92 100 139 124 154 15 76 299 81 122 170 50 43 109 31
Character a p t e r , t h e l -l -e - e l i -i -l -e - e l
Milliseconds 46 110 107 162 57 146 113 177 91 112 17 116 305 85 123 49 48 126 77 230 96 108 123 94 108
Character - -l l i m i t , t h -h -t - -, . T h e o d
Milliseconds 16 340 77 100 41 159 59 94 95 78 46 92 78 187 79 103 134 108 79 94 77 59 32 98 121
Character -d -o i d e a o f a l i n m i -i -m -n m i t p
Milliseconds 171 140 206 44 17 62 77 77 77 48 124 46 234 107 51 28 77 222 91 119 140 90 63 80 62
Character a y -y -a l a y s a f o u n d a t i o n a l r
Milliseconds 126 97 146 109 111 75 67 152 93 138 79 218 110 15 46 64 91 111 61 14 49 529 46 95 119
Character o l t e -e - -t e t h r o u g h o u t c a l c
Milliseconds 44 154 62 79 126 170 78 127 82 31 143 46 92 46 31 94 36 95 46 63 62 161 67 86 142
Character u l u s ; . -. . -. . -. -; .
Milliseconds 73 139 207 68 75 129 216 79 383 118 235 207 149
WPM Timing
Seconds WPM
2.09 91.69
4.19 77.36
6.28 95.51
8.38 98.85
10.47 107.73
12.56 105.06
14.66 98.23
16.75 103.15
18.85 103.15
20.94 100.28
23.04 98.98
25.13 101.71
27.22 105.79
29.32 109.29
31.41 105.82
33.51 106.37
35.6 105.17
37.69 106.97
39.79 110.38
41.88 107.73
43.98 107.78
46.07 107.31
48.16 106.14
50.26 106.01
52.35 104.98
54.45 104.03
56.54 103.36
58.64 105.4
60.73 106.31
62.82 106.78
64.92 105.18
67.01 104.22
69.11 104.19
71.2 102.3
73.29 101.34
75.39 102.83
77.48 102.99
79.58 104.35
81.67 104.76
83.76 105.58
85.86 105.24
87.95 105.74
90.05 104.21
92.14 102.76
94.24 101.36
96.33 101.15
98.42 100.22
100.52 100.4
102.61 100.57
104.71 99.02