Twillerdog (twillerdog)

Race #638

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Official speed 93.41 wpm (110.99 seconds elapsed during race)
Without ending ping 93.64 wpm (269 ms delay sending score to TypeRacer’s server)
Timerless 93.68 wpm (53 ms elapsed before first character typed; 110.67 seconds elapsed during race)
Timerless minus one 93.57 wpm, ignoring the first character typed
Race Start October 11, 2023 4:25:01am UTC
Race Finish October 11, 2023 4:26:52am UTC
Outcome No win (2 of 5)
Opponents 1. slithical (117.85 wpm)
3. rubikstyper (88.92 wpm)
5. player10987 (67.05 wpm)
Accuracy 97.8%
Points 252.21
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 understand how a change in one quantity is related to a change in aonother. How does the speed of a falling aoobject change as a function of time? How does the levevl of water in a barrel cahhange as a function of the amount of liquid poured into it? We see change occurring in nearly everything we obsefrve in thew or wolrrld and universe, and powerful omodern instruments help us see more and more. TIn this section we indttroduc e the ideas o ff average and instantenaneous rates of achange, and hshow that they are closely related to the slope of acur curve at a point P on the curve. We give precise developments of these important concepts in the next chasptpter, but for now ewwe use an informal approach so you will see how they lead naturally to the main ide aeaa of this chapter, the limit. The idea of a limit plays a foundational role throughout calcullus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 53 216 104 136 112 89 247 152 96 96 97 80 87 91 93 88 161 200 89 79 113 55 89 71 64
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 280 137 151 120 81 112 103 72 137 191 88 176 96 120 105 143 80 144 80 112 56 128 120 80 113
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 88 128 103 104 105 127 56 88 88 104 88 96 104 112 144 104 120 80 240 136 128 216 137 191 104
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 80 159 97 89 167 88 137 151 64 80 88 96 32 136 112 96 120 56 96 104 56 80 176 136 120
Character o -o n o t h e r . H o w d o e s t h e s p
Milliseconds 104 288 152 79 73 129 87 88 89 143 160 192 104 88 128 88 81 71 72 56 112 112 136 89 151
Character e e d o f a f a l l i n g a o -o -a o b j e
Milliseconds 97 168 175 32 120 80 88 32 144 88 88 48 185 95 81 95 56 104 104 296 128 192 72 128 80
Character c t c h a n g e a s a f u n c t i o n o
Milliseconds 192 96 72 161 39 192 112 88 96 88 65 159 40 136 24 112 112 152 88 96 16 96 104 192 97
Character f t i m e ? H o w d o e s t h e l e v e
Milliseconds 87 64 112 56 144 176 248 104 265 183 97 95 104 80 97 82 70 47 104 88 80 72 120 112 104
Character v -v l o f w a t e r i n a b a r r e l
Milliseconds 24 344 240 80 120 72 64 104 112 120 136 80 32 80 88 161 47 136 80 144 112 144 184 96 215
Character c a h -h -a h a n g e a s a f u n c t i o n
Milliseconds 147 142 8 328 176 209 95 88 105 103 104 80 112 72 96 40 128 88 160 88 80 32 112 32 200
Character o f t h e a m o u n t o f l i q u i d p
Milliseconds 88 64 80 104 40 89 111 56 112 121 88 160 87 48 112 104 32 137 63 112 96 88 112 87 146
Character o u r e d i n t o i t ? W e s e e c h a
Milliseconds 152 111 96 120 176 80 56 104 80 88 112 144 80 240 121 231 96 184 136 88 160 96 128 112 120
Character n g e o c c u r r i n g i n n e a r l y e
Milliseconds 80 120 120 64 136 112 169 143 96 152 128 96 104 72 72 80 96 200 120 96 89 64 143 112 128
Character v e r y t h i n g w e o b s e f -f r v e i n
Milliseconds 384 128 112 104 80 120 80 96 80 31 138 79 112 136 136 137 103 160 296 104 208 111 89 97 95
Character t h e w o r -r -o - -w w o l r -r -l r l d a n
Milliseconds 96 32 128 65 111 15 121 120 248 144 136 152 120 88 120 200 7 329 112 120 120 88 136 80 104
Character d u n i v e r s e , a n d p o w e r f u l
Milliseconds 72 64 120 168 112 96 160 1063 265 168 184 105 103 96 128 40 168 136 64 72 136 152 80 120 112
Character o -o m o d e r n i n s t r u m e n t s h e l p
Milliseconds 128 336 168 80 64 144 104 72 104 88 80 89 95 169 87 176 88 96 72 120 72 96 128 81 143
Character u s s e e m o r e a n d m o r e . T -T
Milliseconds 128 128 104 88 120 72 152 72 120 80 56 96 72 88 200 184 176 104 80 32 96 144 80 216 289
Character I n t h i s s e c t i o n w e i n d t -t -d
Milliseconds 239 192 104 32 80 64 72 105 87 112 216 72 48 120 64 176 104 96 128 160 96 104 136 256 136
Character t r o d u c - e t h e i d e a s o f -f -
Milliseconds 72 136 80 168 120 112 7 329 208 96 104 88 48 96 72 96 144 96 136 48 120 160 7 409 128
Character f a v e r a g e a n d i n s t a n t e n -n -e
Milliseconds 144 64 176 120 136 112 144 96 88 56 88 88 40 120 87 90 71 152 304 176 168 160 137 351 168
Character a n e o u s r a t e s o f a -a c h a n g e ,
Milliseconds 192 144 216 152 112 128 88 280 120 120 103 81 96 80 72 88 96 313 143 88 89 111 64 121 95
Character a n d h -h s h o w t h a t t h e y a r e
Milliseconds 80 88 128 81 79 128 368 120 96 89 119 8 184 64 72 112 40 304 144 120 88 112 56 112 72
Character c l o s e l y r e l a t e d t o t h e s
Milliseconds 48 152 48 161 55 72 120 128 128 80 96 88 128 88 112 160 64 144 104 80 39 89 72 136 65
Character l o p e o f a c u r -r -u -c c u r v e a t
Milliseconds 88 192 143 136 64 128 48 136 7 202 127 88 248 152 143 129 88 160 160 208 112 104 64 288 121
Character a p o i n t P o n t h e c u r v e . W
Milliseconds 95 96 104 72 72 64 88 136 200 208 256 104 112 48 128 32 152 80 112 88 256 104 153 95 192
Character e g i v e p r e c i s e d e v e l o p m e n
Milliseconds 168 128 80 120 96 98 79 111 104 112 192 120 104 112 103 225 176 152 104 160 568 192 192 104 120
Character t s o f t h e s e i m p o r t a n t c o n
Milliseconds 64 112 48 104 64 72 104 48 72 88 168 128 136 80 104 96 48 152 104 88 120 192 224 112 79
Character c e p t s i n t h e n e x t c h a s p t -t
Milliseconds 121 192 105 79 104 72 88 88 104 32 112 40 121 55 120 200 104 80 240 112 56 7 137 128 232
Character -p -s p t e r , b u t f o r n o w e w -w -e w
Milliseconds 152 248 240 96 112 97 55 104 168 144 80 128 145 79 88 89 79 64 88 96 113 6 313 176 104
Character e u s e a n i n f o r m a l a p p r o a c
Milliseconds 72 127 153 96 64 200 129 127 160 79 97 80 104 104 88 128 144 120 225 104 143 104 97 160 143
Character h s o y o u w i l l s e e h o w t h e
Milliseconds 88 112 96 144 88 120 104 104 56 80 80 64 120 128 72 88 224 185 167 80 120 104 80 88 80
Character y l e a d n a t u r a l l y t o t h e m
Milliseconds 112 136 128 56 89 135 104 96 71 89 144 88 120 56 168 128 136 88 80 88 40 72 64 104 80
Character a i n i d e a -a - e a -a -e a o f t h i s
Milliseconds 88 112 64 136 96 96 168 7 17 353 119 71 97 224 120 88 96 135 41 96 80 48 64 88 112
Character c h a p t e r , t h e l i m i t . T h e i
Milliseconds 88 88 64 120 80 136 96 40 104 72 80 80 80 136 80 95 145 96 144 112 176 112 136 112 112
Character d e a o f a l i m i t p l a y s a f o
Milliseconds 112 160 72 104 136 72 168 63 121 160 104 104 176 128 112 56 192 160 136 128 96 112 256 208 119
Character u n d a t i o n a l r o l e t h r o u g h o u
Milliseconds 97 152 64 80 104 63 105 64 168 120 72 72 160 160 80 152 72 128 136 96 176 120 168 240 120
Character t c a l c u l l -l u s .
Milliseconds 144 104 160 160 56 208 136 104 232 448 176 88 80
WPM Timing
Seconds WPM
2.22 97.3
4.44 100
6.66 104.51
8.88 102.71
11.1 104.87
13.32 101.81
15.54 104.25
17.76 100.68
19.98 103.31
22.2 103.25
24.42 102.71
26.64 99.1
28.86 101.46
31.08 102.71
33.3 102.35
35.52 102.71
37.74 102.39
39.96 101.51
42.18 97.59
44.4 96.22
46.62 96.02
48.84 95.58
51.06 96.6
53.28 95.73
55.5 95.36
57.72 95.02
59.94 94.3
62.16 92.86
64.38 92.64
66.6 92.62
68.82 93.12
71.04 93.75
73.26 92.72
75.48 92.85
77.7 93.13
79.92 92.5
82.14 93.07
84.36 93.46
86.58 92.45
88.8 92.57
91.02 92.69
93.24 93.05
95.46 93.28
97.68 93.99
99.9 93.46
102.11 94.01
104.33 94.2
106.55 94.15
108.77 94.21
110.99 93.41