Naoyuzu (naoyuzu)

Race #21

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Official speed 91.58 wpm (113.21 seconds elapsed during race)
Without ending ping 91.77 wpm (239 ms delay sending score to TypeRacer’s server)
Timerless 91.98 wpm (252 ms elapsed before first character typed; 112.72 seconds elapsed during race)
Timerless minus one 91.87 wpm, ignoring the first character typed
Race Start April 19, 2024 8:30:31pm UTC
Race Finish April 19, 2024 8:32:24pm UTC
Outcome No win (2 of 3)
Opponents 1. racen55 (98.34 wpm)
Accuracy 96.0%
Points 247.28
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 tool that helps us undesrtrstrstand how achang 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 levcevelel of water in a barrel change theas ta fuicunctgionion of the ammoount of luiquid poured into it? we seWWe see changes occ occuring rrign ng in enearly everythiingng wer observe in the world and universe, and powerful modern instruments help us anseesee more and more. In this section we introduice cce the ideas of average and instantenaneous rates of change, and hshow that they are closely related to the slop[ee of a curve and tt a point P pon the curbvvve. WEree give preciose sse devlveloelopments of these improtantoortant concepts ion n in t=tthe next chapter, but for now we use an informal appraoroaoach so you will see how they lead naturally to the main idea of this chapter, the limit. The idea of a limit playus as a fouindanndational role throughout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 252 101 85 88 144 160 144 65 0 88 125 85 66 84 49 38 104 136 48 41 88 39 65 25 40
Character e l p s u s u n d e s r t -t -r r s t -t -s -r -s r
Milliseconds 86 90 142 65 17 88 111 39 91 141 16 91 62 112 0 240 120 200 83 85 311 97 119 121 107
Character s t a n d h o w a c h a n g -g -n -a -h -c c h a
Milliseconds 85 87 105 83 68 41 63 144 40 44 85 82 69 65 83 85 159 106 118 120 362 127 63 112 65
Character n g e i n o n e q u a n t i t y i s r e
Milliseconds 65 86 82 63 0 143 42 86 136 48 40 88 88 104 64 107 149 42 126 64 104 64 43 62 88
Character l a t e d t o a c h a n g e i n a n o t
Milliseconds 111 41 65 87 105 47 120 47 64 64 83 69 64 41 127 42 90 44 82 119 65 46 64 138 63
Character h e r . H o w d o e s t h e s p e e d o
Milliseconds 88 63 24 106 65 151 181 44 69 82 46 64 42 64 74 60 64 88 82 66 85 143 64 66 65
Character f a f a l l i n g o b j e c t c h a n g e
Milliseconds 85 66 82 86 103 87 18 126 136 120 46 42 64 115 143 38 112 177 22 145 42 126 41 113 102
Character a s a f u n c t i o n o f t i m e ? H
Milliseconds 67 125 64 112 41 107 21 65 128 78 160 42 126 177 47 105 65 62 64 44 140 19 173 88 152
Character o w d o e s t h e l e v c e -e -c v e l -l -e -v
Milliseconds 144 41 64 69 60 70 82 48 39 64 87 48 81 23 113 63 41 199 120 88 162 65 278 122 141
Character e l o f w a t e r i n a b a r r e l c
Milliseconds 490 63 222 107 86 42 89 63 87 105 65 47 63 137 22 88 90 38 64 66 120 112 39 129 65
Character h a n g e t h e -e -h -t a s t -t a f u i c -c -i
Milliseconds 63 46 108 62 106 62 65 45 65 177 103 119 115 37 168 64 218 88 87 63 114 0 102 176 136
Character -u u n c t g i o n -n -o -i -g i o n o f t h e a
Milliseconds 120 617 135 65 139 0 21 105 119 183 96 104 136 322 142 136 113 145 62 64 40 67 66 68 65
Character m m o -o -m o u n t o f l u -u i q u i d p o u
Milliseconds 18 124 176 177 144 319 312 144 40 43 71 62 40 66 182 360 120 128 41 144 127 88 145 163 158
Character r e d i n t o i t ? w e s e -e -s - -e W -W -w
Milliseconds 46 89 63 40 25 119 65 87 65 87 141 203 177 183 44 68 105 88 138 127 119 119 107 285 145
Character W e s e e c h a n g e s o c c -c -c -o - -s o
Milliseconds 82 151 262 49 41 159 49 83 68 66 62 89 79 42 45 66 86 99 182 127 123 135 273 286 127
Character c c u r i n g - -g -n -i r r -r i g n - -n -g n g
Milliseconds 64 139 87 110 64 120 65 48 249 126 145 481 335 183 416 224 192 24 200 243 102 143 240 65 88
Character i n e -e n e a r l y e v e r y t h i i n g -g -n
Milliseconds 186 101 64 65 279 161 41 49 85 82 65 45 122 86 65 39 88 65 41 160 40 216 23 257 166
Character -i n g w e r - -r o b s e r v e i n t h e
Milliseconds 114 518 41 66 85 88 64 64 224 120 160 528 160 83 45 65 106 69 82 89 120 21 44 108 64
Character w o r l d a n d u n i v e r s e , a n d
Milliseconds 44 44 107 21 107 88 46 39 66 48 62 84 100 123 21 129 39 88 64 88 130 86 89 66 39
Character p o w e r f u l m o d e r n i n s t r u m e n
Milliseconds 64 103 43 44 41 144 17 128 62 66 158 91 102 65 86 131 103 120 64 47 65 39 129 120 113
Character t s h e l p u s a n -n s e e -e -e -s -a s e e
Milliseconds 87 129 102 131 85 66 121 80 84 65 67 84 43 197 104 42 145 223 102 104 140 109 64 120 392
Character m o r e a n d m o r e . I n t h i s s e
Milliseconds 87 136 24 41 65 86 49 82 64 47 119 49 38 106 89 149 144 64 43 45 122 62 0 131 0
Character c t i o n w e i n t r o d u i c e - -e -c c -c
Milliseconds 149 178 22 113 135 27 61 65 63 88 122 38 47 83 86 90 0 86 81 64 144 104 120 143 298
Character -i c e t h e i d e a s o f a v e r a g e
Milliseconds 159 42 125 66 64 65 87 47 87 64 120 64 88 91 55 66 69 63 105 47 43 125 42 86 40
Character a n d i n s t a n t e n -n -e a n e o u s r a t
Milliseconds 65 47 64 89 64 119 64 64 122 302 125 277 150 200 106 97 71 83 107 143 67 65 142 65 319
Character e s o f c h a n g e , a n d h -h s h o w
Milliseconds 87 64 64 65 87 65 104 64 81 128 22 122 46 84 69 63 64 65 41 224 103 64 118 19 65
Character t h a t t h e y a r e c l o s e l y r e l
Milliseconds 85 65 66 86 64 87 64 88 83 86 111 88 64 64 105 17 127 40 48 105 64 66 127 61 89
Character a t e d t o t h e s l o p [ e -e -[ e o f
Milliseconds 66 85 82 86 89 80 23 89 39 89 89 38 65 47 120 186 0 80 184 144 206 41 156 62 89
Character a c u r v e a n d - -d t -t -n t a p o i n
Milliseconds 77 65 89 63 89 126 64 44 84 53 80 85 158 141 243 122 216 125 64 104 64 45 117 166 160
Character t P p -p o n t h e c u r b v -v v -v -b v e .
Milliseconds 41 49 142 65 128 215 123 161 20 49 64 84 44 89 84 106 137 24 322 127 193 118 66 141 66
Character W E -E r e -e -r e g i v e p r e c i o s e -
Milliseconds 126 192 88 393 143 25 315 136 85 115 84 66 66 135 21 230 64 61 125 89 0 63 46 83 201
Character -e -s s -s -o s e d e v l -l v e l o -o -l -e -v e l o p
Milliseconds 110 139 270 179 119 102 50 101 152 65 146 61 289 560 124 59 152 265 122 141 144 411 134 200 143
Character m e n t s o f t h e s e i m p r o t a n t -t
Milliseconds 139 125 66 86 105 42 69 104 92 84 41 111 88 64 40 90 118 120 115 0 152 101 65 87 352
Character -n -a -t -o o -o -r o r t a n t c o n c e p t s i o
Milliseconds 507 32 29 92 316 146 119 88 107 120 124 64 83 69 161 65 119 40 87 106 50 166 38 65 0
Character n - -n -o n i n t -t - -n = t -t -= -i t h e n e
Milliseconds 160 17 182 122 118 249 104 112 113 88 66 276 123 167 483 107 144 119 145 161 111 65 66 182 63
Character x t c h a p t e r , b u t f o r n o w w
Milliseconds 144 88 42 119 47 87 121 65 87 40 89 120 64 143 18 65 84 67 66 44 63 121 64 424 112
Character e u s e a n i n f o r m a l a p p r a o -o
Milliseconds 63 91 167 39 65 65 89 46 104 87 120 87 104 65 113 79 66 141 154 17 128 62 265 0 334
Character -a r o a -a -o -r o a c h s o y o u w i l l s
Milliseconds 123 366 87 169 319 115 144 151 110 129 111 83 205 40 91 104 119 142 43 63 46 163 126 128 41
Character e e h o w t h e y l e a d n a t u r a l l
Milliseconds 89 166 40 44 141 65 69 121 65 81 69 41 107 44 65 106 69 106 42 110 103 88 83 69 119
Character y t o t h e m a i n i d e a o f t h i
Milliseconds 89 40 127 66 104 63 40 88 63 42 102 258 166 66 103 128 120 90 37 88 64 65 64 49 143
Character s c h a p t e r , t h e l i m i t . T h e
Milliseconds 39 45 85 88 62 171 69 83 49 102 87 64 64 115 37 129 136 143 122 63 132 88 316 127 112
Character i d e a o f a l i m i t p l a y u s a
Milliseconds 40 89 38 146 47 104 66 46 82 40 86 23 124 118 143 25 19 84 120 63 110 0 43 64 65
Character -a - -s -u s a f o u i n d a -a -d -n n -n -i n d a t
Milliseconds 167 119 121 144 215 88 81 113 18 47 120 21 121 42 85 139 104 119 367 183 100 157 65 87 90
Character i o n a l r o l e t h r o u g h o u t c a l
Milliseconds 21 105 119 83 72 62 39 67 120 45 67 39 64 88 87 144 79 40 122 126 41 41 129 125 19
Character c u l u s .
Milliseconds 168 89 182 137 47 446
WPM Timing
Seconds WPM
2.26 137.79
4.53 98.05
6.79 86.56
9.06 99.37
11.32 112.36
13.59 118.36
15.85 121.14
18.11 122.56
20.38 113.65
22.64 117.12
24.91 110.81
27.17 104.23
29.44 102.73
31.7 102.59
33.96 98.22
36.23 96.39
38.49 92.59
40.76 88.04
43.02 89.26
45.28 86.39
47.55 88.83
49.81 91.54
52.08 92.4
54.34 91.64
56.61 93.91
58.87 93.15
61.13 94.41
63.4 94.45
65.66 95.94
67.93 97.87
70.19 97.28
72.46 96.39
74.72 95.72
76.98 94.77
79.25 92.97
81.51 90.98
83.78 91.1
86.04 89.96
88.31 89.01
90.57 87.98
92.83 88.93
95.1 89.34
97.36 88.12
99.63 89.25
101.89 90.21
104.16 91.25
106.42 91.9
108.68 91.53
110.95 91.5
113.21 91.58