est (lnstruments)

Race #78

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Official speed 87.30 wpm (118.76 seconds elapsed during race)
Without ending ping 87.40 wpm (135 ms delay sending score to TypeRacer’s server)
Timerless 87.90 wpm (672 ms elapsed before first character typed; 117.96 seconds elapsed during race)
Timerless minus one 87.80 wpm, ignoring the first character typed
Race Start September 14, 2023 2:20:32am UTC
Race Finish September 14, 2023 2:22:31am UTC
Outcome No win (3 of 5)
Opponents 1. andrew_the_guy (94.53 wpm)
2. cloudios (87.44 wpm)
Accuracy 96.7%
Points 235.71
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 tghat hat heklplps us understand uhow a change in one quantitiy is ererelated to a change in another. Hpow=ow does the speed of a falling object change as a function of time? How does the lever ofl of water in a barrel change as a function of the anoamount of liquid poreured into it? We asee ddchange occuriring in nearly everything ewe observe in the world and universe, and powerdfuful modern instryuumentsx h help us see more and more. In this section we introduce the ideas of avcerage and instatantaneous rates of change, and show that they are closely related tot the slope of a curve at a point P anioon the ncurve. WE e fgiguiveive precise developments of these impoertrtant concept ss in the next champtpter, but for now we use an informal approach so you will se e how they lead naturally to the main idea of this chapter, the limitl.. THe he idea of a limit polalays a founadational role throughout calculus.
Timing
Character C a l c u l u s i s a t o o l t g h a t
Milliseconds 672 127 75 187 94 203 170 124 46 79 95 62 109 63 125 47 141 139 63 61 126 0 30 62 46
Character - -t -a -h -g h a t h e k l p -p -l -k l p s u s u
Milliseconds 220 125 123 142 140 186 64 62 62 155 156 47 0 46 233 140 140 172 63 93 139 107 110 78 110
Character n d e r s t a n d u -u h o w a c h a n g e
Milliseconds 140 61 77 108 156 62 110 109 94 109 355 250 125 93 111 93 78 94 124 76 78 93 109 48 76
Character i n o n e q u a n t i t i -i y i s e r e -e
Milliseconds 47 156 64 109 140 61 93 108 78 140 186 188 78 140 62 357 205 123 48 107 95 233 0 111 251
Character -r -e r e l a t e d t o a c h a n g e i n
Milliseconds 141 139 93 63 62 186 142 378 167 62 125 17 92 111 78 159 108 78 77 93 48 46 47 155 46
Character a n o t h e r . H p o w = -= -w -o -p o w d o e s
Milliseconds 62 92 93 78 94 47 93 79 156 155 264 15 77 220 15 128 140 140 62 140 94 107 62 107 62
Character t h e s p e e d o f a f a l l i n g o
Milliseconds 47 140 48 127 47 156 79 92 127 154 16 78 137 94 109 63 172 93 78 125 156 123 47 93 63
Character b j e c t c h a n g e a s a f u n c t i o
Milliseconds 141 46 155 219 186 78 123 77 124 78 110 60 156 250 126 94 92 79 128 123 154 95 204 31 47
Character n o f t i m e ? H o w d o e s t h e l
Milliseconds 155 31 140 77 95 109 32 155 93 154 217 157 233 156 63 139 77 111 46 63 139 33 123 32 139
Character e v e r o f -f -o - -r l o f w a t e r i n
Milliseconds 63 80 138 96 61 92 108 155 127 138 142 216 110 109 77 75 63 111 90 127 77 76 63 172 47
Character a b a r r e l c h a n g e a s a f u n c
Milliseconds 141 46 157 62 79 171 78 78 93 141 79 78 93 94 47 79 108 77 77 109 62 124 76 141 77
Character t i o n o f t h e a n o -o -n -a a m o u n t
Milliseconds 172 15 62 138 62 127 154 356 171 77 109 63 124 62 155 158 139 78 435 93 185 31 156 108 78
Character o f l i q u i d p o r e -e -r u r e d i n t o
Milliseconds 79 92 61 110 155 93 123 125 155 124 139 49 244 172 218 124 248 78 62 173 78 47 140 77 94
Character i t ? W e a -a s e e d d -d -d c h a n g e
Milliseconds 63 94 110 153 217 109 309 124 79 249 155 61 172 62 156 188 233 124 95 92 78 94 62 47 93
Character o c c u r i -i r i n g i n n e a r l y e v e
Milliseconds 92 79 157 78 140 372 252 91 92 172 47 62 63 140 46 248 92 265 108 141 125 91 125 124 189
Character r y t h i n g e -e w e o b s e r v e i n t
Milliseconds 108 31 186 16 62 154 78 125 218 247 92 62 108 155 157 184 185 49 435 78 107 78 156 46 63
Character h e w o r l d a n d u n i v e r s e , a n
Milliseconds 79 93 47 125 46 108 92 94 281 294 125 77 94 140 170 158 124 124 94 140 62 78 93 139 62
Character d p o w e r d f u -u -f -d f u l m o d e r n i
Milliseconds 126 108 122 172 92 201 46 217 0 48 309 140 123 93 77 171 94 141 109 95 94 111 187 124 94
Character n s t r y u -u -y u m e n t s x h -h - -x h e l p
Milliseconds 170 64 76 218 233 15 295 139 108 171 62 109 92 109 32 46 61 265 110 169 155 156 251 78 78
Character u s s e e m o r e a n d m o r e . I n
Milliseconds 138 127 125 77 140 94 142 46 108 46 78 30 64 94 77 80 60 79 46 63 47 93 186 155 186
Character t h i s s e c t i o n w e i n t r o d u c
Milliseconds 62 124 78 46 78 77 109 93 219 186 48 46 156 264 77 62 109 251 155 93 156 47 171 64 139
Character e t h e i d e a s o f a v c -c e r a g e
Milliseconds 110 108 107 63 108 48 76 154 171 63 108 93 78 262 110 264 94 15 311 219 62 140 219 32 77
Character a n d i n s t a t a -a -t n t a n e o u s r a t
Milliseconds 140 65 94 62 61 186 31 125 92 141 186 232 138 203 94 154 234 187 172 62 171 109 152 110 403
Character e s o f c h a n g e , a n d s h o w t h
Milliseconds 201 78 79 60 109 63 155 92 48 110 110 30 96 140 108 78 93 63 155 47 61 109 62 124 93
Character a t t h e y a r e c l o s e l y r e l a t
Milliseconds 30 79 80 94 108 94 61 62 62 94 47 93 156 77 172 94 63 156 204 92 125 46 231 215 171
Character e d t o t - -t t h e s l o p e o f a
Milliseconds 204 173 80 124 31 172 0 330 126 76 141 186 109 124 111 127 168 140 123 78 78 93 79 78 78
Character c u r v e a t a p o i n t P a n -n -a i o
Milliseconds 125 79 108 202 30 94 141 92 109 109 109 126 61 139 156 48 46 202 170 155 78 171 126 93 16
Character -o -i o n t h e n -n c u r v e . W E - -E e
Milliseconds 296 125 107 202 94 78 78 124 62 141 264 95 77 125 230 32 62 138 158 108 107 250 155 109 47
Character f g i -i -g -f g u i v e -e -v -i -u i v e p r e c i s
Milliseconds 188 0 46 234 140 155 156 123 0 92 79 107 140 141 140 93 111 46 95 187 108 47 330 110 154
Character e d e v e l o p m e n t s o f t h e s e i
Milliseconds 77 78 173 78 187 62 154 171 62 171 64 108 76 124 0 107 94 78 91 63 124 92 124 313 109
Character m p o e r t -t -r -e r t a n t c o n c e p t s -s
Milliseconds 203 140 32 76 0 172 170 140 155 61 202 95 76 124 93 125 47 171 79 61 216 94 123 125 188
Character - s i n t h e n e x t c h a m p t -t -p -m p
Milliseconds 142 93 62 62 171 46 63 93 96 47 109 94 173 218 96 204 62 77 108 126 77 202 125 172 63
Character t e r , b u t f o r n o w w e u s e a
Milliseconds 93 92 93 140 155 155 64 91 78 234 92 125 63 126 78 75 93 261 31 124 202 125 63 63 140
Character n i n f o r m a l a p p r o a c h s o y o
Milliseconds 62 78 125 171 156 96 106 77 125 61 78 156 63 155 79 108 123 187 79 78 139 61 112 140 63
Character u w i l l s e - e h o w t h e y l e a
Milliseconds 32 94 62 78 167 141 77 123 30 110 373 170 109 95 61 124 62 109 78 109 61 46 187 92 78
Character d n a t u r a l l y t o t h e m a i n i
Milliseconds 138 62 141 155 93 125 93 61 93 123 95 92 110 61 79 77 94 93 60 202 250 79 140 61 250
Character d e a o f t h i s c h a p t e r , t h e
Milliseconds 79 202 60 109 155 157 109 140 79 94 93 78 125 78 156 63 201 76 109 108 174 125 78 94 62
Character l i m i t l . -. -l . T H e - -e -H h e i d e a
Milliseconds 93 170 125 171 93 63 47 296 155 109 124 170 124 109 79 219 139 142 155 78 63 94 125 190 47
Character o f a l i m i t p o l a -a -l -o l a y s a
Milliseconds 171 156 109 93 141 156 172 155 140 141 62 109 79 15 47 93 140 139 140 154 78 94 185 79 108
Character f o u n a -a d a t i o n a l r o l e t h r o
Milliseconds 77 142 80 30 156 94 404 92 79 186 46 62 174 121 94 93 187 63 167 62 78 144 31 155 31
Character u g h o u t c a l c u l u s .
Milliseconds 47 173 140 264 30 109 125 172 326 124 188 109 186 157 93 77
WPM Timing
Seconds WPM
2.38 80.83
4.75 65.68
7.13 74.1
9.5 82.1
11.88 76.79
14.25 79.15
16.63 79.39
19 84.62
21.38 86.45
23.75 88.92
26.13 89.1
28.5 89.67
30.88 92.49
33.25 89.13
35.63 88.92
38 88.73
40.38 87.97
42.75 87.01
45.13 87.21
47.51 87.65
49.88 88.05
52.26 87.03
54.63 86.11
57.01 86.1
59.38 87.7
61.76 88.22
64.13 87.76
66.51 87.15
68.88 87.28
71.26 89.09
73.63 88.98
76.01 88.73
78.38 88.95
80.76 87.82
83.13 86.46
85.51 86.03
87.88 86.57
90.26 86.28
92.64 86.4
95.01 86.01
97.39 86.5
99.76 87.21
102.14 87.41
104.51 87.84
106.89 88.24
109.26 87.75
111.64 87.39
114.01 87.36
116.39 87.54
118.76 87.3