apackwolf (apackwolf)

Race #3926

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Official speed 131.15 wpm (79.05 seconds elapsed during race)
Without ending ping 131.71 wpm (337 ms delay sending score to TypeRacer’s server)
Timerless 132.21 wpm (299 ms elapsed before first character typed; 78.42 seconds elapsed during race)
Timerless minus one 132.06 wpm, ignoring the first character typed
Race Start January 15, 2024 4:15:58am UTC
Race Finish January 15, 2024 4:17:17am UTC
Outcome No win (2 of 5)
Opponents 1. pavlova_conditioning (132.16 wpm)
3. wxlx (107.65 wpm)
Accuracy 98.0%
Points 354.11
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 quantitiy is realted related to a change in another. How does the speed of a falling aoiobjeobject change as a fuonctfunction of time? How does the level of water in a barrel change as a funciton ontion of the amount ofl i liquid poured into it? We see change occuring inrirring nin nearly everything we observe in the world adn und universe, and powerful modern instruments help us see more and more. In this section we introduce the ideas of average and instanteaneous rartes ottes of change, and show that they are closely related to the slope of a curve at a point P on the curve. WE ge give prerecise 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 play sa fos 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 299 138 87 92 95 109 72 68 71 157 94 79 65 86 24 101 116 132 57 55 57 51 46 39 49
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 74 58 48 89 25 83 71 33 94 51 54 133 49 76 86 20 81 71 70 41 73 0 93 80 97
Character c h a n g e i n o n e q u a n t i t i -i y
Milliseconds 90 77 57 85 39 47 38 42 46 81 36 70 33 50 132 98 60 90 137 84 80 133 314 131 69
Character i s r e a l t e d -r -e -a -l -t -e -d - r e l a t e
Milliseconds 89 48 129 59 53 73 0 86 54 119 71 223 0 0 0 0 0 0 0 160 86 106 38 55 58
Character d t o a c h a n g e i n a n o t h e r .
Milliseconds 124 65 87 128 60 97 77 117 65 69 73 86 52 33 41 50 60 46 75 60 41 74 40 52 65
Character H o w d o e s t h e s p e e d o f a
Milliseconds 29 117 109 42 119 70 91 48 41 55 58 99 16 222 49 205 77 124 136 42 89 69 146 116 127
Character f a l l i n g a o -o -a i o b j e -e -i -o -b -j o b j
Milliseconds 64 53 78 142 46 32 31 51 53 177 221 105 161 0 42 148 47 199 90 0 0 0 180 67 344
Character e c t c h a n g e a s a f u o n c t -f -u -o
Milliseconds 97 102 121 67 164 105 48 96 37 41 87 15 82 96 28 104 33 89 27 17 42 131 215 0 0
Character -n -c -t f u n c t i o n o f t i m e ? H o w
Milliseconds 0 0 0 232 89 54 39 125 41 45 43 44 83 76 162 142 83 45 51 162 60 153 140 45 139
Character d o e s t h e l e v e l o f w a t e r i
Milliseconds 40 93 28 52 63 29 124 66 85 71 28 91 52 53 81 100 87 163 42 66 53 77 58 36 63
Character n a b a r r e l c h a n g e a s a f u
Milliseconds 51 72 32 103 29 91 74 135 57 68 42 73 104 39 109 38 39 72 43 64 82 52 87 43 98
Character n c i t o n o n -o -n - -n -o -t -i t i o n o f t
Milliseconds 32 62 129 0 43 116 0 63 13 265 0 375 119 123 122 124 100 82 25 41 81 77 94 39 98
Character h e a m o u n t o f l i -i - -l l i q u i d
Milliseconds 47 53 75 147 100 80 65 120 48 87 43 103 98 88 107 238 112 132 135 89 60 104 84 66 44
Character p o u r e d i n t o i t ? W e s e e c
Milliseconds 113 23 44 54 33 78 85 60 44 40 85 104 161 144 71 161 75 109 152 98 72 41 125 91 65
Character h a n g e o c c u r i n g i n -i -n - -g -n -i -r r
Milliseconds 100 36 104 40 48 89 52 59 131 115 73 80 50 30 39 70 51 299 0 190 116 140 107 118 66
Character i -i -r r r i n g n -n i n n e a r l y e v e r
Milliseconds 117 225 110 69 343 139 56 51 77 85 239 205 54 92 100 73 73 34 123 52 56 59 92 60 68
Character y t h i n g w e o b s e r v e i n t h e
Milliseconds 72 89 92 72 73 23 98 42 50 101 52 49 75 35 36 125 48 43 41 39 66 47 117 50 104
Character w o r l d a d n u -u - -n -d n d u n i v e r s
Milliseconds 68 115 32 115 48 54 88 100 15 135 82 227 117 118 109 154 98 55 89 159 87 75 70 107 70
Character e , a n d p o w e r f u l m o d e r n i n
Milliseconds 30 48 71 72 113 73 85 48 54 48 22 42 130 57 78 57 76 34 66 112 20 65 50 67 70
Character s t r u m e n t s h e l p u s s e e m o r
Milliseconds 51 97 68 41 120 45 113 25 39 56 77 106 54 61 71 93 69 82 88 58 135 76 54 52 0
Character e a n d m o r e . I n t h i s s e c t i
Milliseconds 48 161 101 97 65 35 64 40 26 36 98 36 146 99 91 58 175 41 52 106 59 63 114 162 28
Character o n w e i n t r o d u c e t h e i d e a s
Milliseconds 42 38 74 27 37 100 140 32 147 76 81 97 82 58 59 54 67 92 14 104 61 50 102 34 94
Character o f a v e r a g e a n d i n s t a n t e -e
Milliseconds 48 51 81 46 100 90 69 82 95 57 17 65 96 90 114 71 75 61 64 102 77 148 63 60 445
Character a n e o u s r a r t e s o -o - -s -e -t t -t -r t e
Milliseconds 74 124 91 89 50 56 68 96 78 76 0 49 46 74 47 282 133 134 126 133 104 176 143 34 16
Character s o f c h a n g e , a n d s h o w t h a
Milliseconds 65 76 51 74 59 115 49 61 83 32 77 45 67 61 65 83 97 127 58 49 41 52 37 99 71
Character t t h e y a r e c l o s e l y r e l a t e
Milliseconds 51 50 91 43 92 51 33 106 139 64 57 94 103 125 50 33 75 64 59 111 0 144 0 360 219
Character d t o t h e s l o p e o f a c u r v e
Milliseconds 143 31 104 26 73 78 66 53 94 68 34 149 100 130 87 82 58 78 23 102 34 149 28 148 39
Character a t a p o i n t P o n t h e c u r v
Milliseconds 58 69 64 74 69 72 32 68 41 32 22 51 158 167 64 42 81 50 104 54 61 101 75 80 150
Character e . W E g -g - -E e g i v e p r e -e -r r e c
Milliseconds 21 49 41 101 70 154 163 142 115 134 75 83 76 66 74 30 66 34 83 87 140 134 126 58 311
Character i s e d e v e l o p m e n t s o f t h e s e
Milliseconds 188 57 42 51 112 122 83 61 34 150 21 166 82 80 42 58 64 103 88 98 61 75 72 66 106
Character i m p o r t a n t c o n c e p t s i n t h
Milliseconds 47 51 77 62 55 80 137 62 54 56 73 105 16 58 72 77 18 92 59 26 62 45 48 67 87
Character e n e x t c h a p t e r , b u t f o r n
Milliseconds 49 76 46 68 150 89 59 109 85 74 137 36 83 62 60 45 105 59 51 54 98 50 65 35 33
Character o w w e u s e a n i n f o r m a l a p p
Milliseconds 54 29 56 101 38 62 56 63 33 73 64 62 63 46 63 56 115 129 118 118 133 99 156 137 123
Character r o a c h s o y o u w i l l s e e h o w
Milliseconds 109 94 46 100 26 71 115 35 66 55 73 55 36 48 58 120 126 43 50 64 132 30 46 60 21
Character t h e y l e a d n a t u r a l l y t o t
Milliseconds 64 41 63 90 56 28 122 33 41 94 29 55 62 60 86 47 53 53 101 64 34 51 59 51 46
Character h e m a i n i d e a o f t h i s c h a p
Milliseconds 79 57 46 69 82 60 47 45 90 25 108 54 63 63 58 58 68 52 38 38 52 82 64 60 17
Character t e r , t h e l i m i t - . T h e i d e
Milliseconds 205 82 73 75 42 203 132 56 51 92 84 66 77 49 150 323 173 53 53 101 55 59 64 51 94
Character a o f a l i m i t p l a y s a f o -f -o
Milliseconds 31 80 59 89 51 21 94 111 67 87 71 50 72 44 128 40 121 57 10 115 38 104 25 373 0
Character - -a -s - s a f o u n d a t i o n a l r o l e
Milliseconds 158 139 125 125 90 50 87 42 193 81 52 119 24 138 53 99 30 60 100 79 72 66 88 128 37
Character t h r o u g h o u t c a l c u l u s .
Milliseconds 71 75 83 84 33 44 88 48 83 54 48 68 103 49 43 95 64 107 54 61 61
WPM Timing
Seconds WPM
1.58 113.85
3.16 144.2
4.74 161.91
6.32 144.2
7.91 129.02
9.49 137.88
11.07 137.7
12.65 132.82
14.23 123.12
15.81 120.68
17.39 122.13
18.97 125.23
20.55 128.44
22.14 126.31
23.72 123.97
25.3 120.96
26.88 123.22
28.46 123.97
30.04 118.24
31.62 114.6
33.2 116.38
34.78 119.71
36.37 116.49
37.95 119.22
39.53 121.44
41.11 123.19
42.69 124.25
44.27 125.77
45.85 125.88
47.43 123.97
49.01 122.66
50.59 124.52
52.18 124.43
53.76 125.01
55.34 126.21
56.92 125.65
58.5 124.31
60.08 124.83
61.66 125.91
63.24 126.94
64.82 128.84
66.41 128.66
67.99 129.91
69.57 131.44
71.15 132.74
72.73 131.83
74.31 132.58
75.89 130.61
77.47 130.88
79.05 131.15