(altrocality)

Race #41676

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Official speed 137.15 wpm (75.60 seconds elapsed during race)
Without ending ping 137.75 wpm (330 ms delay sending score to TypeRacer’s server)
Timerless 137.91 wpm (87 ms elapsed before first character typed; 75.18 seconds elapsed during race)
Timerless minus one 137.75 wpm, ignoring the first character typed
Race Start December 18, 2023 11:30:09am UTC
Race Finish December 18, 2023 11:31:25am UTC
Outcome Win (1 of 4)
Opponents 2. kewlbum (118.03 wpm)
3. someone_who_needs_help (111.28 wpm)
Accuracy 98.0%
Points 370.30
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 alcCalculus is at oa tool theat helps us understand how a chance inhange in one quantity is related to a change in another. HOw ow does the speed of a falling object change as a function of time? How does the level of water in ab arr barrel change as a function of the amount of liquid poured into it? We see change occurring in nearly everything tewe observe in the world and universe, and powerful modern instruments help us see more and more. In this section we introduce the ideas o f average and instantaneous rates of change, and show that they are closery reloseryly related to the slope of a curve at a point P on the curev. ve. We give precise developments of tehse ihese important concenspts in the next chapter, but for now we use an informar l approach so you will see how they lead naturally to the main idea of this chapter, the imlimit. The idea of a limit plays a foundational role throughout calculus.
Timing
Character a l c -a -l -c C a l c u l u s i s a t o -a -t -
Milliseconds 87 51 55 483 0 0 222 175 112 32 60 128 147 88 71 89 55 81 66 109 0 104 547 0 0
Character -o a t o o l t h e -e a t h e l p s u s u
Milliseconds 0 109 90 66 84 133 39 53 80 44 63 306 123 93 68 64 69 97 55 104 68 67 62 85 60
Character n d e r s t a n d h o w a c h a n c e i n
Milliseconds 67 39 62 317 86 89 140 25 62 72 90 68 94 60 71 99 29 54 68 42 51 68 48 60 55
Character -h -a -n -c -e - -i -n h a n g e i n o n e q u a n
Milliseconds 351 0 0 0 0 0 0 0 54 51 87 62 34 44 60 43 80 69 95 47 59 88 81 66 49
Character t i t y i s r e l a t e d t o a c h a n
Milliseconds 47 95 51 107 60 89 37 62 119 40 103 81 65 80 61 69 50 76 74 159 111 123 61 79 86
Character g e i n a n o t h e r . H O w - -w -O o w
Milliseconds 51 36 61 36 48 74 46 97 69 90 41 25 95 63 32 100 83 91 93 334 105 122 116 73 60
Character d o e s t h e s p e e d o f a f a l l i
Milliseconds 73 60 73 84 37 151 30 34 56 75 70 70 127 50 58 62 87 67 81 90 27 96 75 126 75
Character n g o b j e c t c h a n g e a s a f u n
Milliseconds 89 42 58 36 114 116 17 73 44 36 236 71 91 90 43 43 59 55 77 77 74 90 14 94 116
Character c t i o n o f t i m e ? H o w d o e s t
Milliseconds 52 68 48 34 58 80 48 63 27 105 84 70 81 104 48 116 73 82 43 93 24 58 92 60 90
Character h e l e v e l o f w a t e r i n a b a
Milliseconds 50 22 65 112 52 143 39 124 26 103 21 60 83 72 67 95 70 107 45 81 70 60 84 0 131
Character r r -b - -a -r -r b a r r e l c h a n g e a s
Milliseconds 90 99 306 0 0 0 0 89 55 78 86 131 66 91 43 68 55 66 93 44 28 67 47 56 88
Character a f u n c t i o n o f t h e a m o u n t
Milliseconds 75 80 17 110 57 40 76 50 55 29 99 52 43 81 47 66 35 63 72 107 72 47 74 25 57
Character o f l i q u i d p o u r e d i n t o i t ?
Milliseconds 60 57 59 44 97 94 85 80 61 67 50 93 96 84 75 76 43 57 98 40 19 112 51 65 162
Character W e s e e c h a n g e o c c u r r i n g
Milliseconds 45 90 85 53 72 65 134 57 41 59 67 84 64 25 60 82 71 119 95 101 117 82 91 32 48
Character i n n e a r l y e v e r y t h i n g t e -t -e
Milliseconds 78 51 71 79 78 48 57 67 68 49 85 72 109 85 69 65 74 91 36 64 87 158 117 346 0
Character w e o b s e r v e i n t h e w o r l d a
Milliseconds 150 49 79 47 43 35 122 101 164 40 63 135 84 63 125 9 49 58 59 72 72 49 50 31 76
Character n d u n i v e r s e , a n d p o w e r f u l
Milliseconds 77 40 17 124 59 102 83 82 60 66 43 73 49 57 78 45 30 117 89 69 118 89 50 110 48
Character m o d e r n i n s t r u m e n t s h e l p
Milliseconds 127 118 80 89 86 50 75 5 111 139 43 119 92 125 94 95 116 51 61 108 99 52 89 44 73
Character u s s e e m o r e a n d m o r e . I n
Milliseconds 87 63 39 106 34 129 32 82 51 84 44 60 28 95 17 48 118 40 109 53 132 33 109 62 46
Character t h i s s e c t i o n w e i n t r o d u c e
Milliseconds 124 10 99 61 62 93 52 83 66 27 72 34 65 76 52 73 68 74 27 118 59 106 71 130 87
Character t h e i d e a s o - f a v e r a g e a
Milliseconds 60 78 56 33 67 55 100 95 36 85 31 91 150 390 128 46 47 106 34 112 44 83 57 60 50
Character n d i n s t a n t a n e o u s r a t e s o f
Milliseconds 67 40 54 81 74 17 87 97 67 55 87 91 100 117 66 53 79 68 56 109 52 128 67 87 51
Character c h a n g e , a n d s h o w t h a t t h
Milliseconds 61 78 48 80 85 51 87 18 75 60 347 43 149 95 32 59 107 49 96 51 36 76 61 90 37
Character e y a r e c l o s e r y r e -l -o -s -e -r -y - -r
Milliseconds 39 72 36 60 55 84 43 29 68 68 74 72 87 102 28 57 79 460 0 0 0 0 0 0 0
Character -e l o s e r y -y -r l y r e l a t e d t o t h
Milliseconds 0 91 74 117 69 81 222 213 109 158 54 56 40 87 96 66 83 66 78 71 72 64 66 33 60
Character e s l o p e o f a c u r v e a t a p
Milliseconds 56 71 7 156 66 85 49 60 78 51 92 51 85 50 100 108 168 47 101 111 73 83 69 109 31
Character o i n t P o n t h e c u r e v . - -. -v -e
Milliseconds 67 87 53 42 58 113 98 136 107 48 99 26 49 49 71 131 67 186 0 151 81 286 121 139 146
Character v e . W e g i v e p r e c i s e d e v e l
Milliseconds 208 55 135 57 84 69 69 85 63 72 58 51 44 79 98 30 157 143 106 44 65 74 92 57 94
Character o p m e n t s o f t e h s e i -e -h -s -e - -i h
Milliseconds 51 66 68 70 78 25 43 110 41 82 81 51 51 8 100 34 81 64 434 0 0 0 0 0 34
Character e s e i m p o r t a n t c o n c e n s -s -n p t
Milliseconds 94 73 77 53 57 65 119 31 65 49 70 106 21 67 489 91 62 411 111 238 45 295 100 72 87
Character s i n t h e n e x t c h a p t e r , b u
Milliseconds 63 41 95 51 79 53 26 64 64 150 132 138 107 60 112 52 43 44 89 84 103 66 64 57 58
Character t f o r n o w w e u s e a n i n f o r
Milliseconds 85 49 90 50 70 40 135 99 117 43 90 99 53 71 99 73 55 83 71 79 50 84 58 83 42
Character m a r - -r l a p p r o a c h s o y o u w
Milliseconds 112 82 79 81 240 106 158 59 73 110 143 84 113 71 27 45 67 92 92 55 71 63 87 24 138
Character i l l s e e h o w t h e y l e a d n a t
Milliseconds 121 109 107 17 100 49 141 36 75 65 58 51 116 50 39 62 57 49 94 54 86 42 89 56 105
Character u r a l l y t o t h e m a i n i d e a o
Milliseconds 67 86 70 99 123 55 49 100 45 72 57 29 64 57 44 76 72 30 90 72 94 65 43 58 101
Character f t h i s c h a p t e r , t h e i m -m -i l
Milliseconds 32 122 53 58 52 49 55 80 49 41 47 94 66 84 53 74 72 29 40 68 123 124 275 98 164
Character i m i t . T h e i d e a o f a l i m i t
Milliseconds 88 75 117 100 54 62 77 84 89 41 69 90 59 17 91 118 59 83 47 117 13 80 101 71 65
Character p l a y s a f o u n d a t i o n a l r o l
Milliseconds 69 49 103 99 42 140 67 85 108 19 110 44 32 38 69 89 84 50 67 99 67 77 54 76 110
Character e t h r o u g h o u t c a l c u l u s .
Milliseconds 75 43 210 55 52 105 60 55 66 72 63 100 93 101 71 111 36 74 74 116 75 79
WPM Timing
Seconds WPM
1.51 47.62
3.02 55.56
4.54 76.72
6.05 91.27
7.56 93.66
9.07 105.83
10.58 113.38
12.1 109.13
13.61 115.53
15.12 119.05
16.63 124.83
18.14 128.31
19.65 127.6
21.17 128.69
22.68 133.34
24.19 135.42
25.7 137.26
27.21 138.46
28.73 136.18
30.24 137.71
31.75 139.46
33.26 139.26
34.77 140.1
36.29 141.54
37.8 142.86
39.31 141.64
40.82 142.57
42.33 143.43
43.85 143.96
45.36 140.48
46.87 139.02
48.38 140.14
49.89 139.98
51.41 137.96
52.92 137.65
54.43 138.46
55.94 137.07
57.45 135.35
58.96 134.32
60.48 135.13
61.99 135.51
63.5 134.36
65.01 134.74
66.52 135.47
68.04 136.69
69.55 136.48
71.06 136.62
72.57 137.08
74.08 137.52
75.6 137.15