(jesterc)

Race #32338

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Official speed 139.62 wpm (74.26 seconds elapsed during race)
Without ending ping 140.08 wpm (244 ms delay sending score to TypeRacer’s server)
Timerless 140.86 wpm (408 ms elapsed before first character typed; 73.61 seconds elapsed during race)
Timerless minus one 140.69 wpm, ignoring the first character typed
Race Start April 1, 2024 11:16:27am UTC
Race Finish April 1, 2024 11:17:42am UTC
Outcome Win (1 of 2)
Accuracy 98.0%
Points 376.97
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 quantit yis rey is related to a change in another. hHow does the speed of a falling objet ct change as a function of time? How does the leve ofl 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 obvserve 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 instatantaneous rates ofc h change, and show that they are closely related to the slope of a curve at a tppoint P on the curve. We give pecisprecise developments of these important concepts in the next chapte,r butr, but for now we use an informal approach as yoso you will see how they lead naturalloy ty to the main idea of this chapte,r the lr, the lmit. limit. The idaea 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 408 248 59 82 75 98 84 84 72 45 37 93 51 89 93 35 112 156 160 105 89 45 48 35 68
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 67 22 37 128 22 60 62 57 46 38 45 152 35 98 62 88 77 88 38 44 48 35 52 83 67
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 54 36 83 45 47 28 45 37 75 47 100 19 59 68 54 84 88 63 86 46 104 106 7 100 82
Character r e -r -e -y -i -s - - y i s r e l a t e d t o
Milliseconds 35 75 40 207 0 144 0 0 0 166 291 97 83 75 55 66 29 98 59 67 38 105 54 74 22
Character a c h a n g e i n a n o t h e r . h -h H
Milliseconds 70 73 76 36 76 90 44 29 31 67 30 60 61 29 53 67 39 59 60 46 44 31 211 329 143
Character o w d o e s t h e s p e e d o f a f a
Milliseconds 166 42 121 54 67 51 37 47 73 30 30 120 47 89 37 122 126 68 44 31 82 59 99 37 39
Character l l i n g o b j e t - -t c t c h a n g e a
Milliseconds 44 111 61 60 74 61 44 62 133 53 196 60 345 112 67 172 98 78 42 82 54 39 20 83 56
Character s a f u n c t i o n o f t i m e ? H o w
Milliseconds 64 53 67 75 59 91 44 60 129 37 30 45 73 64 35 76 44 53 68 8 193 60 150 150 38
Character d o e s t h e l e v e o f -f -o - l o f
Milliseconds 93 43 81 60 23 68 59 48 43 40 80 29 108 13 97 9 118 218 120 136 166 90 29 29 67
Character w a t e r i n a b a r r e l c h a n g e
Milliseconds 10 103 52 84 82 11 26 83 53 75 48 93 45 46 104 77 21 98 75 55 94 45 62 21 82
Character a s a f u n c t i o n o f t h e a m o u
Milliseconds 69 52 104 114 82 127 69 59 54 127 24 5 39 66 61 37 75 45 55 43 40 155 52 142 22
Character n t o f l i q u i d p o u r e d i n t o
Milliseconds 121 44 76 39 88 45 84 43 84 97 68 67 76 98 99 72 46 51 130 36 83 28 71 66 59
Character i t ? W e s e e c h a n g e o c c u r r i
Milliseconds 82 36 190 34 133 140 113 81 60 91 68 74 30 97 39 52 39 74 134 233 128 247 143 188 126
Character n g i n n e a r l y e v e r y t h i n g w
Milliseconds 62 58 61 30 60 97 76 36 83 53 36 60 48 21 112 90 53 24 82 21 52 94 42 60 83
Character e o b v -v s e r v e i n t h e w o r l d
Milliseconds 22 104 73 268 5 381 166 53 22 143 52 45 90 26 50 52 47 28 54 21 46 80 76 23 55
Character a n d u n i v e r s e , a n d p o w e r f u
Milliseconds 56 45 61 24 66 134 24 30 66 99 90 51 84 45 92 51 59 68 90 115 68 26 60 113 23
Character l m o d e r n i n s t r u m e n t s h e l p
Milliseconds 30 82 68 22 84 111 23 39 68 82 58 69 59 115 20 167 58 90 36 53 93 95 127 108 20
Character u s s e e m o r e a n d m o r e . I n
Milliseconds 142 98 37 397 99 61 111 30 53 40 42 30 38 107 4 79 11 61 31 61 5 106 97 38 121
Character t h i s s e c t i o n w e i n t r o d u c
Milliseconds 73 83 46 37 82 53 90 44 109 134 19 24 30 53 91 28 90 143 60 67 120 53 96 69 44
Character e t h e i d e a s o f a v e r a g e a n
Milliseconds 31 59 68 30 60 38 77 28 127 7 122 29 39 125 61 104 93 4 745 111 60 30 49 40 42
Character d i n s t a t a -a -t n t a n e o u s r a t e s
Milliseconds 57 62 36 67 47 104 111 420 105 242 111 142 23 152 133 30 149 61 45 67 54 118 76 30 24
Character o f c h -h - -c c h a n g e , a n d s h o
Milliseconds 73 30 75 8 45 83 262 120 123 50 31 84 93 58 41 25 164 96 67 43 48 67 75 45 15
Character w t h a t t h e y a r e c l o s e l y r
Milliseconds 67 75 45 54 44 62 20 98 67 60 106 45 53 29 30 60 112 45 121 37 22 180 116 34 150
Character e l a t e d t o t h e s l o p e o f a
Milliseconds 31 97 75 63 27 127 38 68 39 67 28 68 38 52 115 27 138 102 120 69 51 60 47 120 43
Character c u r v e a t a t p -t -p p o i n t P o n
Milliseconds 83 84 51 137 28 39 84 82 5 150 22 490 83 245 0 307 24 59 60 23 100 133 156 54 97
Character t h e c u r v e . W e g i v e p e c i s
Milliseconds 22 60 67 15 78 67 88 46 149 37 38 45 114 118 60 90 84 59 24 36 30 142 128 90 45
Character -p -e -c -i -s p r e c i s e d e v e l o p m e n t s
Milliseconds 210 0 0 0 0 173 67 38 106 83 52 51 98 52 135 83 38 59 149 54 121 51 107 36 67
Character o f t h e s e i m p o r t a n t c o n c e
Milliseconds 76 22 59 68 60 31 51 114 37 63 79 60 31 90 59 114 59 29 68 82 90 45 39 67 30
Character p t s i n t h e n e x t c h a p t e , r
Milliseconds 59 90 60 38 23 55 66 28 71 36 51 63 19 233 52 91 127 113 89 82 83 98 47 5 38
Character b u t -t -u -b - -r -, r , b u t f o r n o w w
Milliseconds 126 54 61 389 165 164 144 149 122 67 134 48 109 76 52 68 105 30 121 141 68 31 104 63 162
Character e u s e a n i n f o r m a l a p p r o a c
Milliseconds 67 71 82 72 30 75 60 75 67 61 45 52 173 142 8 211 29 84 111 123 134 126 82 83 44
Character h a s y o -y -o -a -s - s o y o u w i l l s
Milliseconds 63 20 98 22 77 68 5 272 0 105 0 0 125 39 59 22 98 30 23 82 52 122 89 6 99
Character e e h o w t h e y l e a d n a t u r a l l
Milliseconds 38 96 70 43 37 55 35 83 31 96 39 99 156 81 46 89 23 45 67 52 82 61 31 60 112
Character o y t -t - -y -o y t o t h e m a i n i d e
Milliseconds 7 26 72 100 206 145 141 143 157 23 67 45 38 52 76 52 37 75 60 69 54 96 44 30 120
Character a o f t h i s c h a p t e , r t h e l -l
Milliseconds 9 83 20 61 59 121 44 38 97 30 91 24 110 60 98 91 59 7 41 118 44 75 15 83 218
Character -t -h -e - - -r -, r , t h e l m i t . - -. -l -m -i
Milliseconds 141 0 0 0 155 145 151 105 84 35 69 62 50 29 71 95 68 74 106 74 262 128 136 0 0
Character -t l i m i t . T h e i d a -a e a o f a l
Milliseconds 0 218 58 68 90 97 93 51 104 105 98 24 59 44 173 314 144 74 97 47 74 67 203 137 111
Character i m i t p l a y s a f o u n d a t i o n a l
Milliseconds 36 46 97 121 36 55 58 60 90 60 82 45 105 38 82 23 127 53 97 53 37 24 60 96 30
Character r o l e t h r o u g h o u t c a l c u l u s
Milliseconds 99 59 46 126 49 34 86 48 161 0 0 56 61 75 83 38 43 115 52 52 81 9 123 66 88
Character .
Milliseconds 91
WPM Timing
Seconds WPM
1.49 105.04
2.97 133.32
4.46 156.21
5.94 143.42
7.43 135.74
8.91 145.44
10.4 143.13
11.88 145.44
13.37 140.95
14.85 143.82
16.34 142.5
17.82 144.09
19.31 146.06
20.79 148.9
22.28 149.75
23.76 148.47
25.25 147.34
26.73 147.23
28.22 149.26
29.7 150.69
31.19 151.59
32.67 150.58
34.16 152.81
35.64 153.85
37.13 151.58
38.61 148.86
40.1 148.43
41.58 147.75
43.07 148.78
44.56 149.48
46.04 149.35
47.53 146.95
49.01 147.64
50.5 146.15
51.98 147.05
53.47 148.36
54.95 146.31
56.44 144.16
57.92 144.61
59.41 144.02
60.89 143.27
62.38 144.28
63.86 142.81
65.35 143.78
66.83 140.95
68.32 138.94
69.8 138.22
71.29 138.37
72.77 139.34
74.26 139.62