Aaron (declouxa)

Race #192

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Official speed 97.85 wpm (105.96 seconds elapsed during race)
Without ending ping 97.94 wpm (101 ms delay sending score to TypeRacer’s server)
Timerless 98.34 wpm (423 ms elapsed before first character typed; 105.43 seconds elapsed during race)
Timerless minus one 98.22 wpm, ignoring the first character typed
Race Start February 21, 2024 1:35:23am UTC
Race Finish February 21, 2024 1:37:09am UTC
Outcome Win (1 of 3)
Opponents 2. sweethan (96.84 wpm)
Accuracy 97.0%
Points 264.20
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 caa change in another. How does the speed of a falling object change ias funca function of time? How does the level of water ina ba a barrel change as a function of the amount of liquid poured into it? We see change occuring in ring in nearly evverything we obserev in tve in the world and univesre, rse, and powerful modern instruments help us see more and more. In this section we introduce the idaeeas of average and instatnntaneous rates of chhat tange, tand thshow tshow that they are closely related to the slop of ae of a curve at a pointn P o P on the curve. We give precise developments of thosese important concepts in the next chapter, but for now we use an infromaormal approach so you will see how they lead naturally to the main idea of this chaptper, the limit. The idea of a limit plays a fuoundational role throughtouout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 423 240 112 88 224 59 117 106 78 83 101 106 38 96 83 61 106 144 40 96 40 80 66 20 82
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 56 80 104 80 56 88 80 80 120 128 64 144 56 120 80 144 120 104 56 81 63 56 80 104 23
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 137 22 122 56 120 40 22 106 80 80 56 79 81 87 121 15 121 1416 0 0 0 0 14 98 80
Character r e l a t e d t o c -c a a - -a c h a n g
Milliseconds 288 336 80 120 80 80 80 120 56 104 64 80 80 432 144 95 145 232 113 423 96 80 104 80 104
Character e i n a n o t h e r . H o w d o e s t h
Milliseconds 40 78 138 64 64 120 80 56 64 80 56 64 104 14 146 184 81 79 80 80 80 64 40 104 56
Character e s p e e d o f a f a l l i n g o b j e
Milliseconds 80 64 96 80 80 128 120 80 96 80 87 57 80 104 56 80 144 104 40 80 64 104 198 82 104
Character c t c h a n g e i -i a s f u n c -c -n -u -f a
Milliseconds 56 176 56 144 40 104 56 105 40 79 80 272 80 80 38 226 104 144 80 272 120 136 120 160 96
Character f u n c t i o n o f t i m e ? H o w d o e
Milliseconds 104 80 144 80 160 40 56 64 96 64 78 58 104 40 80 43 117 160 184 199 97 104 96 88 80
Character s t h e l e v e l o f w a t e r i n a
Milliseconds 56 64 118 66 72 64 64 94 106 80 80 80 496 62 82 104 136 80 120 64 56 88 56 120 40
Character b a -a -b - - -a a b a r r e l c h a n g e
Milliseconds 102 82 120 200 128 136 136 128 168 192 96 128 135 57 144 80 104 56 296 64 104 81 79 56 64
Character a s a f u n c t i o n o f t h e a m o u
Milliseconds 96 88 80 328 104 136 104 160 62 162 40 80 40 96 240 64 120 56 64 56 88 80 56 80 80
Character n t o f l i q u i d p o u r e d i n t o
Milliseconds 144 64 80 80 80 81 42 165 120 94 66 96 88 120 128 80 85 59 152 88 325 0 0 0 139
Character i t ? W e s e e c h a n g e o c c u r i n
Milliseconds 272 80 144 160 120 184 40 288 64 136 64 104 55 105 80 56 64 80 56 104 368 160 104 80 56
Character g i n - -n -i - -g -n -i r i n g i n n e a r l
Milliseconds 64 96 38 90 80 224 136 136 128 136 160 120 176 78 66 80 56 64 56 88 134 106 80 104 56
Character y e v v -v e r y t h i n g w e o b s e r e v
Milliseconds 64 40 96 120 472 464 120 80 120 80 104 40 104 96 64 80 64 32 184 160 176 81 79 232 14
Character i n t -t - -n -i - -v -e v e i n t h e w o r
Milliseconds 66 80 56 80 40 208 136 136 144 160 112 352 104 56 80 167 57 80 64 80 64 72 104 40 80
Character l d a n d u n i v e s r e , - -, -e -r -s r s e
Milliseconds 62 98 22 169 81 104 79 121 144 80 14 146 168 24 80 104 56 248 136 136 152 136 120 104 40
Character , a n d p o w e r f u l m o d e r n i n s
Milliseconds 144 40 80 80 136 64 264 152 96 41 63 160 64 80 80 96 79 65 160 64 56 104 78 66 56
Character t r u m e n t s h e l p u s s e e m o r e
Milliseconds 80 144 22 154 80 88 56 64 56 64 96 88 112 105 103 79 121 160 40 151 105 56 80 56 88
Character a n d m o r e . I n t h i s s e c t i o
Milliseconds 56 119 81 80 64 40 80 63 57 104 56 144 240 144 80 80 64 54 82 104 14 146 192 40 64
Character n w e i n t r o d u c e t h e i d a e -e -a
Milliseconds 56 80 80 64 79 97 63 81 144 80 80 96 80 88 80 80 79 56 81 88 40 174 34 392 192
Character e a s o f a v e r a g e a n d i n s t a t
Milliseconds 104 104 96 81 103 80 80 144 56 144 64 95 81 104 40 80 80 104 56 88 56 23 81 136 80
Character n -n -t n t a n e o u s r a t e s o f c h h a
Milliseconds 144 392 120 272 143 81 120 96 143 81 80 80 120 104 80 80 80 2003 0 0 0 0 0 11 58
Character t t -t - -t -a -h a n g e , t -t a n d t h -h s h
Milliseconds 104 40 144 320 112 144 136 136 248 104 120 56 128 80 136 312 96 80 120 40 199 129 216 120 80
Character o w t -t - -w -o -h -s -t s h o w t h a t t h e y
Milliseconds 64 63 81 56 280 120 134 145 129 144 160 304 80 40 96 64 104 80 79 65 40 120 56 104 24
Character a r e c l o s e l y r e l a t e d t o t
Milliseconds 96 40 104 56 40 102 82 136 80 55 81 104 64 416 64 144 40 80 80 135 65 295 81 80 80
Character h e s l o p o f a -a - -f -o - e o f a c
Milliseconds 80 56 88 80 80 119 120 105 96 80 104 96 176 136 128 128 136 135 129 120 96 80 256 96 120
Character u r v e a t a p o i n t n P o -o - -P - -n
Milliseconds 119 81 152 64 96 120 104 120 64 78 82 184 80 64 80 80 16 120 144 80 231 129 136 144 136
Character P o n t h e c u r v e . W e g i v e
Milliseconds 294 226 200 168 96 120 104 56 80 80 144 64 80 168 80 64 80 160 160 120 86 82 56 104 80
Character p r e c i s e d e v e l o p m e n t s o f t
Milliseconds 56 63 105 118 122 56 64 104 55 145 80 80 16 160 120 144 80 80 80 78 16 106 63 121 56
Character h o s -s -o e s e i m p o r t a n t c o n c e p
Milliseconds 104 54 66 312 304 104 80 103 97 128 111 65 152 80 135 81 40 118 90 120 96 22 106 56 80
Character t s i n t h e n e x t c h a p t e r , b
Milliseconds 96 88 38 98 22 98 64 119 81 80 64 40 158 58 104 80 104 78 82 95 121 64 40 104 79
Character u t f o r n o w w e u s e a n i n f r
Milliseconds 97 80 88 80 80 56 87 73 63 41 96 64 64 95 105 40 56 105 159 104 608 200 80 104 144
Character o m a -a -m -o -r o r m a l a p p r o a c h s o
Milliseconds 40 136 80 248 120 136 119 239 82 80 104 56 104 79 65 120 80 96 64 78 66 80 40 80 79
Character y o u w i l l s e e h o w t h e y l e a
Milliseconds 743 0 138 160 142 82 38 122 80 80 40 144 63 97 40 80 77 91 56 104 40 56 120 41 79
Character d n a t u r a l l y t o t h e m a i n i
Milliseconds 104 80 64 120 56 104 80 56 40 128 56 64 80 79 57 88 96 64 80 40 81 79 56 80 89
Character d e a o f t h i s c h a p t p -p e r , t h
Milliseconds 55 120 64 80 80 104 56 80 80 64 40 80 120 38 674 96 144 56 431 289 40 80 96 80 104
Character e l i m i t . T h e i d e a o f a l i
Milliseconds 63 81 40 96 80 104 120 80 64 136 124 59 81 55 65 144 56 40 80 80 80 79 89 96 223
Character m i t p l a y s a f u -u o u n d a t i o n a
Milliseconds 97 86 98 65 55 112 40 120 104 64 96 79 105 120 288 168 56 160 64 104 55 39 42 64 80
Character l r o l e t h r o u g h t o u -u -o -t o u t c
Milliseconds 79 97 144 64 136 80 96 64 64 96 45 35 80 64 80 96 128 240 144 103 168 81 40 80 120
Character a l c u l u s .
Milliseconds 64 80 96 80 64 120 80 104
WPM Timing
Seconds WPM
2.12 90.6
4.24 116.08
6.36 126.47
8.48 109.01
10.6 99.66
12.71 102.87
14.83 109.21
16.95 109.01
19.07 102.56
21.19 105.32
23.31 106.56
25.43 100.98
27.55 101.06
29.67 103.54
31.79 104.19
33.91 104.05
36.03 99.6
38.14 98.78
40.26 98.65
42.38 95.98
44.5 95.99
46.62 95.23
48.74 97.5
50.86 99.1
52.98 100.34
55.1 99.97
57.22 100.46
59.34 99.7
61.46 97.44
63.57 95.51
65.69 92.98
67.81 93.96
69.93 94.38
72.05 93.1
74.17 93.51
76.29 91.7
78.41 92.59
80.53 93.73
82.65 93.36
84.77 94.71
86.89 95.85
89 94.11
91.12 94.29
93.24 95.49
95.36 96.89
97.48 96.39
99.6 96.99
101.72 97.56
103.84 98.23
105.96 97.85