(vixt)

Race #253795

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Official speed 124.72 wpm (83.13 seconds elapsed during race)
Without ending ping 125.89 wpm (775 ms delay sending score to TypeRacer’s server)
Timerless 126.60 wpm (460 ms elapsed before first character typed; 81.90 seconds elapsed during race)
Timerless minus one 126.45 wpm, ignoring the first character typed
Race Start October 14, 2023 7:29:39pm UTC
Race Finish October 14, 2023 7:31:02pm UTC
Outcome No win (2 of 4)
Opponents 1. joey172 (128.96 wpm)
Accuracy 98.0%
Points 336.75
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 undestrstand how a change in one quantity is related to a change in another. How does the speedof a f of a falling object change as funa function of time? How does the level of water in a barrel change as funa fnction ofunction of the amount of liiquid pliquid poured into it? We see change occurring in nearly everything we observe in the world and universe, and powerful modern instruments help us seseee more and more. In this section we introduce the ideas of average and insatntantaneous rates of chagnenge, and show that they are closely related to the slope of a curve at a point P on the curve. We give precise developmentse of t of these important concepts in the next chapter, but for now we use an informal approach so you will see how lthey lead naturally to the main ieadea of the is chapter, the limit. The idea of a limit plays a foundational 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 460 135 36 233 137 25 136 28 28 146 27 148 21 19 19 123 151 147 20 13 26 155 19 9 24
Character e l p s u s u n d e s t -t -s r s t a n d h o
Milliseconds 130 129 16 149 17 19 133 16 28 206 240 18 250 34 207 309 691 16 19 22 18 13 23 21 18
Character w a c h a n g e i n o n e q u a n t i t
Milliseconds 17 24 25 377 16 22 21 15 25 43 132 326 26 98 117 41 40 50 136 64 93 105 71 73 90
Character y i s r e l a t e d t o a c h a n g e
Milliseconds 68 44 91 65 46 71 62 21 93 68 68 139 16 49 66 68 43 109 75 65 92 16 134 50 134
Character i n a n o t h e r . H o w d o e s t h e
Milliseconds 18 75 136 21 90 34 43 80 19 52 80 97 148 57 75 55 85 50 127 17 11 41 73 56 35
Character s p e e d o f a f -f - -a - -f -o o f a f a
Milliseconds 110 115 90 102 184 126 22 124 16 87 16 427 131 99 201 85 119 145 102 621 20 14 16 12 27
Character l l i n g o b j e c t c h a n g e a s f u
Milliseconds 16 23 16 34 18 9 27 372 17 22 21 10 263 170 91 39 50 68 66 83 47 50 85 167 82
Character n -n -u -f a f u n c t i o n o f t i m e ? H
Milliseconds 134 300 138 128 119 34 98 133 182 65 46 61 45 36 99 78 106 65 50 67 33 33 132 88 169
Character o w d o e s t h e l e v e l o f w a t e
Milliseconds 61 46 65 91 94 115 65 60 39 58 64 44 78 34 115 51 65 83 94 40 145 316 158 60 70
Character r i n a b a r r e l c h a n g e a s f
Milliseconds 83 29 387 16 10 21 15 34 101 39 145 64 65 111 93 67 95 41 44 70 66 39 114 48 165
Character u n -n -u -f a f n c t i o n o -o -f -n -c -t -i -o -n -
Milliseconds 84 141 291 125 111 97 34 34 232 17 41 64 32 35 96 45 656 136 0 0 0 0 0 0 0
Character f u n c t i o n o f t h e a m o u n t o f
Milliseconds 150 49 151 14 53 49 20 48 68 45 68 43 70 66 16 139 386 51 17 14 26 72 27 20 134
Character l i i q u i d p -p -l -i -i -q -u -i -d - l i q u i d
Milliseconds 39 51 47 37 180 119 16 134 58 393 73 140 0 0 0 0 0 0 0 200 186 99 120 383 108
Character p o u r e d i n t o i t ? W e s e e c
Milliseconds 68 87 183 45 69 38 139 25 67 335 314 116 115 66 68 140 82 182 136 87 44 48 112 68 274
Character h a n g e o c c u r r i n g i n n e a r l y
Milliseconds 15 181 69 277 106 66 66 135 47 94 451 108 64 51 44 66 365 9 24 10 16 17 18 14 111
Character e v e r y t h i n g w e o b s e r v e i n
Milliseconds 108 98 111 107 49 45 69 84 66 53 69 14 101 16 92 345 78 96 37 50 135 68 83 77 42
Character t h e w o r l d a n d u n i v e r s e ,
Milliseconds 45 31 55 48 34 35 16 99 32 78 66 144 82 89 26 83 94 36 54 54 105 18 49 90 84
Character a n d p o w e r f u l m o d e r n i n s t r
Milliseconds 74 140 101 68 75 40 47 19 48 114 70 36 51 91 28 61 114 35 36 64 89 47 42 44 115
Character u m e n t s h e l p u s s e s e e -e -e -s e
Milliseconds 46 89 113 69 51 32 98 419 116 46 67 86 50 69 64 185 25 490 44 90 271 132 133 68 48
Character m o r e a n d m o r e . I n t h i s s e
Milliseconds 162 36 50 35 31 88 114 48 31 39 23 60 17 78 89 95 149 35 36 68 31 36 65 115 114
Character c t i o n w e i n t r o d u c e t h e i d
Milliseconds 132 53 60 11 57 69 40 48 68 113 46 26 107 43 94 90 159 108 92 16 122 64 37 49 68
Character e a s o f a v e r a g e a n d i n s a t n
Milliseconds 117 47 65 85 118 36 47 235 384 26 18 8 20 61 41 89 160 92 29 103 48 66 136 20 196
Character -n -t -a t a n t a n e o u s r a t e s o f c h
Milliseconds 234 136 110 106 50 68 185 245 117 103 132 50 68 67 92 39 95 40 78 56 72 72 64 109 49
Character a g n e -e -n -g n g e , a n d s h o w t h a t
Milliseconds 185 64 14 96 388 83 164 84 86 33 61 67 34 79 45 34 153 61 17 102 48 16 82 49 68
Character t h e y a r e c l o s e l y r e l a t e d
Milliseconds 29 83 71 17 93 67 43 364 8 22 18 13 19 7 45 47 135 40 50 46 43 91 45 70 183
Character t o t h e s l o p e o f a c u r v e
Milliseconds 13 26 31 59 41 67 50 67 46 70 164 53 117 32 34 91 40 52 84 67 147 16 154 48 131
Character a t a p o i n t P o n t h e c u r v e
Milliseconds 16 39 33 74 208 400 25 41 44 69 89 298 84 66 32 82 32 37 46 39 114 70 93 135 111
Character . W e g i v e p r e c i s e d e v e l o p
Milliseconds 67 140 63 154 93 40 118 67 45 67 74 61 68 502 14 8 19 8 37 129 93 40 68 167 62
Character m e n t s e o f t -t - -f -o - -e o f t h e s
Milliseconds 87 118 66 68 31 16 18 115 34 101 44 223 134 160 186 250 151 111 91 86 68 65 42 25 117
Character e i m p o r t a n t c o n c e p t s i n t
Milliseconds 64 48 69 49 44 60 48 162 20 69 65 58 286 57 48 48 136 111 84 327 266 169 42 45 36
Character h e n e x t c h a p t e r , b u t f o r
Milliseconds 79 76 30 61 209 62 112 42 364 112 66 41 118 90 62 62 116 103 166 15 17 120 15 381 16
Character n o w w e u s e a n i n f o r m a l a p
Milliseconds 28 16 19 125 26 15 18 206 149 25 9 132 17 48 236 17 16 25 60 133 26 154 152 25 160
Character p r o a c h s o y o u w i l l s e e h o
Milliseconds 134 59 185 19 20 50 207 21 12 43 577 10 21 23 19 23 19 25 16 16 42 362 14 16 53
Character w l -l t h e y l e a d n a t u r a l l y t
Milliseconds 21 18 30 241 103 67 64 117 17 68 49 33 81 70 83 66 68 50 113 35 17 130 65 66 34
Character o t h e m a i n i e a -a -e d e a o f t h
Milliseconds 107 31 54 22 70 51 20 86 66 45 88 75 200 22 435 100 52 131 45 39 67 99 37 46 49
Character e - -e i s c h a p t e r , t h e l i m i t
Milliseconds 68 67 297 103 182 17 66 54 92 107 146 106 66 66 95 65 88 48 70 112 16 88 115 68 133
Character . T h e i d e a o f a l i m i t p l a
Milliseconds 404 27 19 20 15 24 43 17 111 68 86 213 61 44 64 95 42 115 66 91 109 33 86 65 92
Character y s a f o u n d a t i o n a l r o l e t h
Milliseconds 60 97 65 48 104 43 56 20 89 41 53 27 55 68 33 132 108 91 65 68 134 25 61 15 60
Character r o u g h o u t c a l c u l u s .
Milliseconds 91 14 50 68 84 216 61 67 21 93 108 133 136 113 34 197 89 111
WPM Timing
Seconds WPM
1.66 108.26
3.33 126.31
4.99 103.45
6.65 119.09
8.31 128.47
9.98 134.73
11.64 129.92
13.3 115.48
14.96 125.1
16.63 117.65
18.29 121.39
19.95 123.3
21.61 126.03
23.28 118.06
24.94 116.93
26.6 115.03
28.26 110.81
29.93 110.27
31.59 109.78
33.25 108.99
34.91 112.04
36.58 115.15
38.24 117.99
39.9 118.79
41.57 116.35
43.23 118.81
44.89 120.29
46.55 121.15
48.22 119.46
49.88 120.05
51.54 118.74
53.2 121.35
54.87 123.14
56.53 122.91
58.19 123.52
59.85 123.9
61.52 121.53
63.18 122.13
64.84 121.96
66.5 121.62
68.17 122.35
69.83 123.04
71.49 123.37
73.15 125
74.82 124.3
76.48 123.8
78.14 124.08
79.8 125.26
81.47 126.09
83.13 124.72