jan (micaelaishot123)

Race #6525

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Official speed 122.55 wpm (84.60 seconds elapsed during race)
Without ending ping 122.71 wpm (113 ms delay sending score to TypeRacer’s server)
Timerless 123.09 wpm (260 ms elapsed before first character typed; 84.23 seconds elapsed during race)
Timerless minus one 122.95 wpm, ignoring the first character typed
Race Start December 31, 2023 3:08:50am UTC
Race Finish December 31, 2023 3:10:15am UTC
Outcome No win (2 of 5)
Opponents 1. chqnges (144.34 wpm)
4. johnathandoeherty (84.55 wpm)
Accuracy 96.2%
Points 330.89
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 u sunds understand how a chcange in one quantity is related to a change in another. How odoes the speed of a falling object change as a function of time? How does the level of water in a barrel change as a fucntionfunction of the amount of liquid poured into it/ W? Wes see change orccuriring in nearly evrytheverything we observec in the world and universe,a nd and power morful modern instrumcents help us see more and more. In this section we introduce the idea s of average and instanteoaneous rates of change, and show that wthey arec lse closely related to the slop of e of a curve at a point _pP on the curve. We give preceideise developments of these important concepts in the next chapter, but for now we use an informal approach yosso you will see hwo thehow they lead neaaturally to the main idea of this chapter, the limit. The idea of a limit plays a foundational role thorugroughout calculuus.s.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 260 128 96 69 125 123 77 81 64 202 90 37 103 49 85 44 173 148 48 84 105 66 59 68 79
Character e l p s u s u n d -s -u -n -d - s u n d e r s t
Milliseconds 63 107 179 72 16 73 112 0 80 50 85 320 0 0 0 352 120 88 97 44 33 122 84 64 89
Character a n d h o w a c h c -c a n g e i n o n e
Milliseconds 40 131 44 108 54 67 43 87 143 28 151 343 82 227 72 102 46 43 42 55 41 104 47 52 42
Character q u a n t i t y i s r e l a t e d t o a
Milliseconds 119 122 91 290 125 37 105 80 42 80 61 58 76 62 59 66 43 72 108 51 63 88 54 52 81
Character c h a n g e i n a n o t h e r . H o w o
Milliseconds 78 60 80 57 113 31 46 52 64 35 97 71 57 53 43 103 47 43 85 46 126 67 48 98 115
Character -o d o e s t h e s p e e d o f a f a l l
Milliseconds 276 82 102 43 29 50 68 72 44 93 70 46 86 113 46 74 53 41 85 37 114 257 96 87 173
Character i n g o b j e c t c h a n g e a s a f u
Milliseconds 32 84 0 97 49 60 25 58 34 155 66 96 52 50 110 44 57 57 94 43 57 61 89 58 101
Character n c t i o n o f t i m e ? H o w d o e s
Milliseconds 42 9 155 34 12 44 81 66 91 42 100 22 51 41 158 74 173 146 71 83 51 80 74 57 26
Character t h e l e v e l o f w a t e r i n a b
Milliseconds 101 75 74 32 73 74 80 69 137 99 84 67 65 91 70 75 95 65 59 39 46 107 85 68 42
Character a r r e l c h a n g e a s a f u c n t i o
Milliseconds 76 104 150 90 90 55 87 65 104 67 58 59 97 118 53 54 88 67 59 89 51 0 164 31 12
Character n -f -u -c -n -t -i -o -n f u n c t i o n o f t h e
Milliseconds 47 264 0 0 0 0 0 0 0 160 83 32 47 145 42 7 36 94 52 59 75 79 61 94 50
Character a m o u n t o f l i q u i d p o u r e d i
Milliseconds 84 45 90 53 56 21 82 65 52 65 69 55 36 126 33 59 91 37 181 55 72 326 65 52 69
Character n t o i t / W -W - -/ ? W e s - -s s e e
Milliseconds 33 61 74 130 90 53 150 62 101 255 136 129 176 38 84 162 229 89 239 132 39 81 47 109 58
Character c h a n g e o r -r c c u r i -i r i n g i n n
Milliseconds 96 87 46 100 43 44 64 147 93 250 42 132 141 52 115 256 75 55 29 39 69 50 40 128 71
Character e a r l y e v r y t h -e -v -r -y -t -h e v e r y t h
Milliseconds 123 35 63 93 51 96 50 60 112 56 84 112 208 0 0 0 0 0 254 59 85 42 59 62 110
Character i n g w e o b s e r v e c -c i n t h e w
Milliseconds 121 65 57 60 87 42 40 87 39 78 279 167 157 120 59 293 141 44 57 84 43 91 36 91 60
Character o r l d a n d u n i v e r s e , a n d -n -d
Milliseconds 50 74 98 82 35 93 45 88 47 75 47 48 19 31 62 137 34 93 93 15 125 22 91 252 0
Character - - -a a n d p o w e r m o r -r -o -m - f u l
Milliseconds 0 198 139 232 78 57 53 93 6 37 37 37 21 86 125 52 66 213 151 151 127 107 84 53 82
Character m o d e r n i n s t r u m c -c e n t s h e l p
Milliseconds 76 25 52 129 49 68 57 93 39 85 69 50 87 21 49 457 251 96 49 47 49 82 81 139 59
Character u s s e e m o r e a n d m o r e . I n
Milliseconds 141 71 55 110 78 67 151 101 48 53 70 34 67 56 35 83 54 41 22 43 24 127 59 147 151
Character t h i s s e c t i o n w e i n t r o d u c
Milliseconds 62 120 44 42 61 56 78 51 59 166 61 13 14 94 53 45 68 178 71 19 47 104 90 186 79
Character e t h e i d e a - s o f a v e r a g e
Milliseconds 44 98 63 105 10 109 61 45 32 8 71 290 75 53 57 49 82 62 103 171 78 93 104 84 80
Character a n d i n s t a n t e o -o -e a n e o u s r a t
Milliseconds 85 93 63 52 68 45 69 59 100 99 96 73 234 210 122 68 75 65 28 66 77 45 80 70 136
Character e s o f c h a n g e , a n d s h o w t h
Milliseconds 50 27 66 75 12 108 68 97 45 120 43 37 80 85 95 94 36 56 416 70 59 29 98 24 130
Character a t w -w t h e y a r e c l s e -e -s -l - -c c
Milliseconds 10 58 102 232 218 56 64 91 50 83 72 73 58 135 52 39 105 45 213 159 140 142 133 130 42
Character l o s e l y r e l a t e d t o t h e s l o
Milliseconds 88 61 58 38 56 125 177 93 53 59 84 72 106 44 100 63 76 49 25 92 29 121 32 51 82
Character p o f - -f -o - e o f a c u r v e a t
Milliseconds 28 98 74 66 83 199 148 137 139 42 185 70 64 90 51 77 51 99 68 162 61 87 95 68 80
Character a p o i n t _ p -p -_ P o n t h e c u r v
Milliseconds 80 129 24 52 165 59 20 94 263 209 292 128 153 119 59 112 163 94 68 77 64 102 116 38 121
Character e . W e g i v e p r e c e i d e -e -d -i -e i s
Milliseconds 63 62 80 125 127 100 63 101 73 57 32 84 61 30 180 325 138 43 46 208 139 136 125 41 61
Character e d e v e l o p m e n t s o f t h e s e i
Milliseconds 424 76 72 49 120 50 57 50 23 146 35 131 22 52 48 88 75 65 93 97 49 103 58 93 38
Character m p o r t a n t c o n c e p t s i n t h e
Milliseconds 55 118 15 61 53 93 85 46 105 63 75 76 54 51 413 46 72 92 43 51 94 42 86 65 53
Character n e x t c h a p t e r , b u t f o r n o w
Milliseconds 79 7 161 108 54 117 73 76 60 57 122 44 42 64 103 49 36 88 51 49 104 63 112 46 106
Character w e u s e a n i n f o r m a l a p p r o
Milliseconds 33 155 46 67 83 97 40 74 106 90 86 55 48 35 109 11 110 121 226 177 66 68 109 48 104
Character a c h y o -o s -s -y s o y o u w i l l s e e
Milliseconds 74 27 70 141 44 64 233 83 157 126 133 71 90 50 39 25 106 0 115 134 141 51 238 112 118
Character h w o t h e -t -h -e -h -w -o - h o w t h e y l
Milliseconds 105 41 36 19 108 40 103 60 176 0 0 118 0 0 0 143 51 20 73 42 56 97 17 77 87
Character e a d n e a -a -e a t u r a l l y t o t h e
Milliseconds 39 22 82 141 58 86 47 272 120 56 46 128 93 59 93 143 27 61 117 61 61 34 90 69 75
Character m a i n i d e a o f t h i s c h a p t e r
Milliseconds 81 85 106 44 104 232 66 54 27 72 67 52 63 87 39 94 42 268 118 89 53 86 9 164 42
Character , t h e l i m i t . T h e i d e a o f
Milliseconds 60 41 62 55 66 38 61 55 83 70 96 83 102 66 78 72 59 56 38 40 24 70 75 54 151
Character a l i m i t p l a y s a f o u n d a t i o
Milliseconds 73 78 66 61 68 64 79 69 63 22 60 38 124 92 72 63 57 39 26 30 281 97 82 47 9
Character n a l r o l e t h o r u g -g -u -r -o r o u g h o
Milliseconds 44 81 55 151 102 82 140 44 59 67 34 94 22 52 142 174 139 139 129 98 85 25 108 57 48
Character u t c a l c u l u u s . -. -s -u s .
Milliseconds 42 60 54 89 72 8 114 67 89 96 144 9 208 258 139 122 66 27
WPM Timing
Seconds WPM
1.69 113.47
3.38 109.93
5.08 104.02
6.77 106.38
8.46 113.47
10.15 125.29
11.84 125.63
13.54 128.54
15.23 134.75
16.92 136.88
18.61 137.97
20.3 135.34
22 137.48
23.69 138.29
25.38 132.38
27.07 129.87
28.76 128.91
30.46 126.08
32.15 124.3
33.84 127.3
35.53 124.95
37.22 122.82
38.92 121.8
40.61 124.11
42.3 125.39
43.99 125.75
45.69 126.34
47.38 126.14
49.07 126.68
50.76 124.58
52.45 123.54
54.15 123
55.84 122.93
57.53 121.4
59.22 121.58
60.91 119.78
62.61 120.18
64.3 120.94
65.99 121.84
67.68 122.87
69.37 123.16
71.07 122.25
72.76 121.22
74.45 120.89
76.14 121.67
77.83 122.57
79.53 123.58
81.22 124.26
82.91 123.46
84.6 122.55