(altrocality)

Race #47625

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Official speed 154.05 wpm (67.30 seconds elapsed during race)
Without ending ping 155.27 wpm (296 ms delay sending score to TypeRacer’s server)
Timerless 156.08 wpm (351 ms elapsed before first character typed; 66.66 seconds elapsed during race)
Timerless minus one 155.90 wpm, ignoring the first character typed
Race Start February 3, 2024 10:44:03am UTC
Race Finish February 3, 2024 10:45:10am UTC
Outcome Win (1 of 3)
Accuracy 98.4%
Points 415.95
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 ac hange 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 odoes the level of water in ab arr barrel change as a function of the amount of liquid poured into it? we seWe 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 nheythathey are closely related to the slope of ac ur curve taat a point P o nthe n 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 wheythey lead naturally to the main idea of this 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 351 76 79 38 74 65 84 92 43 84 66 50 83 75 56 86 131 20 54 79 43 31 83 30 100
Character e l p s u s u n d e r s t a n d h o w a c
Milliseconds 45 111 56 108 50 106 69 67 78 63 32 84 28 63 61 74 67 41 48 81 47 67 72 86 75
Character h a n g e a -c - -h -a -n -g -e - -a c h a n g e
Milliseconds 19 49 70 62 51 33 67 131 406 0 0 0 0 0 0 0 0 134 111 60 49 84 31 37 40
Character i n o n e q u a n t i t y i s r e l a t e
Milliseconds 70 34 62 60 139 103 69 80 74 77 36 37 64 84 117 46 106 49 37 107 68 89 64 79 67
Character d t o a c h a n g e i n a n o t h e r .
Milliseconds 67 32 83 66 75 109 39 68 76 33 110 48 15 80 34 61 51 52 83 77 99 0 66 75 58
Character H o w d o e s t h e s p e e d o f a
Milliseconds 25 100 69 88 29 90 17 42 91 40 93 30 36 59 52 50 50 131 55 60 69 76 39 101 83
Character f a l l i n g o b j e c t c h a n g e a s
Milliseconds 99 87 80 108 99 74 20 53 50 97 85 39 109 59 58 140 67 98 78 49 35 58 63 67 84
Character a f u n c t i o n o f t i m e ? H o w o
Milliseconds 75 83 52 57 109 41 64 33 46 51 49 71 79 69 131 73 77 69 73 80 78 84 65 42 60
Character d -o o e s t h e l e v e l o f w a t e r
Milliseconds 83 393 144 38 78 80 58 32 59 34 92 44 129 19 102 19 79 65 55 113 65 68 57 69 24
Character i n a b a r r -b - -a -r -r b a r r e l c h a
Milliseconds 110 30 65 69 92 0 104 89 127 266 0 0 0 0 82 54 53 99 118 75 71 46 84 65 52
Character n g e a s a f u n c t i o n o f t h e
Milliseconds 67 54 33 50 62 37 96 65 94 43 85 100 14 52 48 54 62 34 75 63 46 82 65 22 47
Character a m o u n t o f l i q u i d p o u r e d i
Milliseconds 90 120 73 24 46 45 26 84 76 36 81 65 102 65 76 62 65 67 88 79 46 83 57 54 40
Character n t o i t ? w e s e $W -e - -s -e e s e e c
Milliseconds 68 59 98 68 57 72 148 29 118 54 49 85 51 414 0 0 0 0 96 72 71 62 138 25 49
Character h a n g e o c c u r r i n g i n n e a r l y
Milliseconds 66 74 78 63 36 74 47 52 110 87 99 121 91 69 25 56 68 49 66 102 75 25 84 83 83
Character e v e r y t h i n g w e o b s e r v e i n
Milliseconds 53 80 77 83 60 97 67 53 63 56 45 49 100 90 69 59 83 52 68 114 141 41 66 72 51
Character t h e w o r l d a n d u n i v e r s e ,
Milliseconds 63 80 19 43 50 62 79 69 47 66 17 77 72 41 10 117 83 92 92 82 92 26 54 51 64
Character a n d p o w e r f u l m o d e r n i n s t r
Milliseconds 97 0 34 56 44 71 65 68 94 62 61 49 96 56 80 56 123 27 68 55 77 92 85 104 117
Character u m e n t s h e l p u s s e e m o r e a
Milliseconds 111 83 83 254 32 89 92 88 62 97 67 60 97 79 73 93 70 136 46 64 59 75 61 45 51
Character n d m o r e . I n t h i s s e c t i o n
Milliseconds 43 52 53 105 42 82 66 140 29 98 52 46 111 8 83 37 101 62 68 69 62 34 40 64 36
Character w e i n t r o d u c e t h e i d e a s o f
Milliseconds 103 49 57 52 83 19 120 81 84 79 100 56 75 60 32 60 57 78 52 104 42 107 31 86 95
Character a v e r a g e a n d i n s t a n t a n e o u
Milliseconds 33 119 88 78 84 86 70 60 74 39 52 23 59 76 72 62 89 91 68 59 106 194 159 184 82
Character s r a t e s o f c h a n g e , a n d s h
Milliseconds 42 81 76 76 56 67 60 68 73 56 53 98 35 50 101 65 27 59 39 66 44 31 70 37 61
Character o w t h a t n h e y $t -h -e -y h a -t -h -a t h e y
Milliseconds 60 83 46 96 40 33 108 2 8 161 20 65 336 0 0 0 44 87 427 0 0 149 18 7 63
Character a r e c l o s e l y r e l a t e d t o t
Milliseconds 80 18 82 89 45 60 65 58 93 49 101 55 51 35 81 77 58 99 52 73 92 59 92 49 142
Character h e s l o p e o f a c u r -c - -u -r c u r
Milliseconds 73 86 24 77 151 107 118 56 84 73 79 66 58 82 11 116 67 431 0 0 0 400 173 67 67
Character v e t a -a -t a t a p o i n t P o n t h
Milliseconds 162 53 52 101 150 174 106 37 107 51 54 99 14 75 79 44 24 61 200 109 114 112 6 174 53
Character e - -n -t -h -e - n t h e c u r v e . W e g
Milliseconds 49 14 376 0 0 0 0 0 60 40 83 16 63 34 72 113 62 157 28 131 35 82 66 67 115
Character i v e p r e c i s e d e v e l o p m e n t s
Milliseconds 29 89 51 52 68 73 94 66 133 117 69 28 56 92 85 50 123 61 57 36 90 267 43 112 117
Character o f t h e s e i m p o r t a n t c o n c e p
Milliseconds 78 57 59 66 43 16 76 66 38 54 45 138 74 9 64 88 60 48 80 94 49 99 77 48 93
Character t s i n t h e n e x t c h a p t e r , b
Milliseconds 117 91 118 58 62 62 65 44 47 45 56 54 105 52 66 81 38 47 50 83 58 85 66 42 59
Character u t f o r n o w w e u s e a n i n f o
Milliseconds 41 84 42 75 74 27 88 77 66 67 44 105 44 43 56 92 73 63 56 58 76 57 83 50 67
Character r m a l a p p r o a c h s o y o u w i l l
Milliseconds 83 114 57 83 49 67 111 151 118 67 82 49 24 61 77 65 49 50 69 74 33 116 116 87 104
Character s e e h o w w h e y $t -h -e -y h e y l e a d
Milliseconds 49 61 76 141 33 72 62 92 24 88 70 111 63 270 0 0 0 25 76 96 0 74 54 66 41
Character n a t u r a l l y t o t h e m a i n i d
Milliseconds 50 83 51 99 58 92 92 80 110 51 39 77 72 61 32 34 67 52 48 39 56 44 84 69 86
Character e a o f t h i s c h a p t e r , t h e l
Milliseconds 55 3 83 89 44 66 66 37 53 60 39 93 43 19 63 110 44 107 49 70 39 32 59 52 63
Character i m i t . T h e i d e a o f a l i m i t
Milliseconds 67 84 86 67 71 60 68 130 35 69 103 95 66 35 52 131 59 41 76 107 34 74 83 84 75
Character p l a y s a f o u n d a t i o n a l r o l
Milliseconds 54 63 90 67 136 48 208 92 118 29 95 50 24 43 84 57 74 54 70 80 69 62 70 64 100
Character e t h r o u g h o u t c a l c u l u s .
Milliseconds 58 44 81 32 78 90 50 43 56 92 67 41 101 84 99 72 27 72 78 92 62 84
WPM Timing
Seconds WPM
1.35 133.72
2.69 151.55
4.04 145.61
5.38 135.95
6.73 140.86
8.08 148.58
9.42 157.92
10.77 157.13
12.11 158.49
13.46 159.58
14.81 155.61
16.15 155.27
17.5 152.24
18.84 156.01
20.19 157.5
21.54 156.01
22.88 154.7
24.23 155.02
25.58 155.78
26.92 157.79
28.27 159.2
29.61 158.04
30.96 157.37
32.31 158.61
33.65 159.4
35 159.78
36.34 159.81
37.69 159.51
39.04 160.16
40.38 157.5
41.73 157.88
43.07 156.85
44.42 153.17
45.77 152.34
47.11 149.52
48.46 150.07
49.8 149.87
51.15 150.38
52.5 150.87
53.84 152
55.19 152.64
56.53 152.83
57.88 152.8
59.23 152.36
60.57 153.34
61.92 154.46
63.26 154.59
64.61 154.34
65.96 155.01
67.3 154.05