20to30wpm (10to20wpm)

Race #2951

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Official speed 122.92 wpm (84.35 seconds elapsed during race)
Without ending ping 123.13 wpm (146 ms delay sending score to TypeRacer’s server)
Timerless 123.58 wpm (304 ms elapsed before first character typed; 83.90 seconds elapsed during race)
Timerless minus one 123.44 wpm, ignoring the first character typed
Race Start January 15, 2024 1:01:00am UTC
Race Finish January 15, 2024 1:02:25am UTC
Outcome No win (2 of 2)
Opponents 1. dawittymidget (138.12 wpm)
Accuracy 97.1%
Points 331.89
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 Calcuulus is a tool that helps uns understand how a change in one qualntity is related to a change in another. How does the speed of a falling object change as a function of time? How edoes the level of water nia in a b arrarrel change as a function of the amount of liquid opoured into it? We se e change occuring in ring in nearly everything we observe nitin the world and universe, and pweowerful modern instruments help us see more and more. In this section we ointroduce the ideas of average and instantaneous rates of achchange, and show that they are closely related to the slope of a ciurve at a point P on the curve. We give proecise devlelopments of these ijpmportant concepts ni thein the next chapter, b ut ut forn ow now we use an informal papapproach so you will see how they lead naturlally to the main oidea of this chapter, the limit. The idea of a limit plays a dofofoundational roole throughout calculus.
Timing
Character C a l c u u -u l u s i s a t o o l t h a t
Milliseconds 304 180 72 122 96 123 217 175 29 88 42 73 58 70 88 100 32 73 97 123 57 95 71 52 71
Character h e l p s u n -n s u n d e r s t a n d h o
Milliseconds 66 39 122 76 152 20 163 123 61 192 81 70 66 33 28 130 69 85 71 89 45 208 64 213 37
Character w a c h a n g e i n o n e q u a l -l n t
Milliseconds 84 77 86 71 92 36 119 12 64 118 42 73 31 94 188 58 94 95 85 137 81 137 215 116 58
Character i t y i s r e l a t e d t o a c h a n g
Milliseconds 73 57 128 91 38 91 72 31 92 44 117 38 61 157 38 65 69 62 87 106 236 38 145 12 211
Character e i n a n o t h e r . H o w d o e s t h
Milliseconds 59 69 71 33 63 122 73 97 88 97 57 66 106 62 125 132 51 133 120 73 53 65 41 64 72
Character e s p e e d o f a f a l l i n g o b j e
Milliseconds 62 36 60 79 88 121 153 69 97 88 64 91 75 56 96 70 128 31 61 67 39 40 94 68 88
Character c t c h a n g e a s a f u n c t i o n o
Milliseconds 61 130 68 148 68 88 44 59 64 69 92 91 43 215 101 148 70 61 28 160 39 38 58 32 82
Character f t i m e ? H o w e -e d o e s t h e l e
Milliseconds 82 45 93 68 32 56 147 55 155 131 81 104 89 223 52 72 86 62 9 70 65 62 42 70 55
Character v e l o f w a t e r n i a - -a -i -n i n a
Milliseconds 72 88 44 91 102 90 34 88 63 72 63 96 36 75 5 146 101 161 124 94 123 173 60 93 29
Character b a r r -r -r -a - a r r e l c h a n g e a s
Milliseconds 133 97 0 119 66 98 164 122 125 92 16 68 129 58 77 92 92 35 92 41 63 35 69 63 90
Character a f u n c t i o n o f t h e a m o u n t
Milliseconds 77 144 73 89 100 33 60 130 36 67 28 103 37 87 73 61 65 61 41 92 13 99 59 35 63
Character o f l i q u i d o -o p o u r e d i n t o
Milliseconds 71 72 55 69 46 59 146 73 97 203 65 72 217 145 61 124 89 62 125 67 5 35 101 42 261
Character i t ? W e s e - e c h a n g e o c c u r
Milliseconds 98 58 137 84 89 131 69 59 244 297 418 139 65 93 157 143 42 124 59 68 131 288 239 126 90
Character i n g i n - -n -i - -g -n -i r i n g i n n e a
Milliseconds 70 61 33 67 6 70 97 103 95 123 123 123 93 95 197 70 60 63 68 100 61 96 126 116 89
Character r l y e v e r y t h i n g w e o b s e r v e
Milliseconds 7 110 91 60 61 97 93 62 130 122 33 39 125 66 61 94 34 97 73 92 89 65 63 129 60
Character n i t -t -i -n i n t h e w o r l d a n d u
Milliseconds 68 72 5 209 163 94 94 146 29 31 68 73 28 69 60 81 59 67 57 75 52 46 94 36 39
Character n i v e r s e , a n d p w e -e -w o w e r f u l
Milliseconds 68 63 93 119 94 92 124 131 119 25 73 61 76 6 85 66 169 95 491 85 32 68 155 38 39
Character m o d e r n i n s t r u m e n t s h e l p
Milliseconds 92 70 62 61 153 33 103 94 68 59 60 41 125 127 123 59 42 58 126 184 152 117 74 123 62
Character u s s e e m o r e a n d m o r e . I n
Milliseconds 96 54 76 60 67 124 96 41 60 60 67 40 64 39 60 71 70 36 54 69 75 31 164 125 59
Character t h i s s e c t i o n w e o -o i n t r o d u
Milliseconds 94 38 40 52 48 92 67 96 154 37 37 59 35 69 34 99 101 243 89 60 60 126 42 115 41
Character c e t h e i d e a s o f a v e r a g e a
Milliseconds 93 119 39 93 40 93 37 102 53 99 88 66 43 101 60 65 92 66 152 36 122 40 60 71 59
Character n d i n s t a n t a n e o u s r a t e s o f
Milliseconds 74 59 70 42 33 120 66 88 107 91 290 103 202 102 59 92 39 62 61 71 63 91 10 108 55
Character a c h -h -c -a c h a n g e , a n d s h o w t
Milliseconds 40 86 71 96 194 122 95 80 66 58 107 30 92 134 119 55 73 59 39 63 105 37 89 8 94
Character h a t t h e y a r e c l o s e l y r e l a
Milliseconds 129 25 71 101 60 157 89 66 66 54 69 35 70 95 70 65 51 68 78 56 67 89 62 108 77
Character t e d t o t h e s l o p e o f a c i -i
Milliseconds 76 28 129 37 64 70 62 65 39 61 68 29 49 68 123 52 100 100 55 68 26 76 92 77 214
Character u r v e a t a p o i n t P o n t h e
Milliseconds 116 29 185 58 74 59 100 62 91 69 74 33 123 34 61 69 103 354 71 58 63 64 36 59 77
Character c u r v e . W e g i v e p r o -o e c i s e
Milliseconds 56 75 90 124 59 107 88 123 128 71 120 99 91 27 71 102 88 102 184 51 63 104 115 34 70
Character d e v l -l e l o p m e n t s o f t h e s e i
Milliseconds 151 151 64 79 441 81 68 98 62 63 93 70 92 114 100 74 82 73 58 36 209 123 60 69 161
Character j p -p -j m p o r t a n t c o n c e p t s n i
Milliseconds 31 101 187 93 144 36 34 58 100 85 45 64 70 121 68 63 95 59 75 93 85 41 72 5 65
Character t h e -e -h -t - -i -n i n t h e n e x t c h a p
Milliseconds 33 67 29 174 95 122 121 125 94 145 58 65 64 99 58 131 95 56 156 68 67 92 98 57 74
Character t e r , b u t - -t -u - u t f o r n o w
Milliseconds 91 93 62 72 95 124 0 65 93 65 221 121 94 95 143 30 66 97 101 25 132 31 42 88 70
Character - -w -o - -n n o w w e u s e a n i n f o r
Milliseconds 161 96 122 122 96 83 98 6 87 70 90 61 100 129 88 32 71 57 46 97 98 29 64 104 89
Character m a l p a p -p -a -p a p p r o a c h s o y o u
Milliseconds 72 112 44 60 105 19 110 216 92 124 45 83 93 51 107 111 8 189 123 88 43 93 34 41 60
Character w i l l s e e h o w t h e y l e a d n
Milliseconds 69 62 70 3 103 59 60 37 157 65 95 65 23 42 96 69 90 70 67 69 84 62 96 42 68
Character a t u r l -l a l l y t o t h e m a i n o -o
Milliseconds 85 42 131 56 129 219 44 109 95 30 65 90 101 30 63 99 58 69 72 86 70 37 95 70 217
Character i d e a o f t h i s c h a p t e r , t h e
Milliseconds 115 25 127 89 9 106 56 40 97 34 67 60 40 123 184 90 75 56 90 96 40 65 66 71 85
Character l i m i t . T h e i d e a o f a l i m
Milliseconds 41 103 180 59 63 61 103 57 131 72 54 77 39 86 123 60 43 102 145 96 60 101 36 66 66
Character i t p l a y s a d o -o f o -o -f -d f o u n d a
Milliseconds 58 90 69 70 92 85 364 85 41 149 100 91 101 157 112 100 189 95 93 110 100 32 32 58 97
Character t i o n a l r o o -o l e t h r o u g h o u t
Milliseconds 43 98 38 31 94 44 90 62 193 121 302 144 54 41 93 71 90 73 31 94 36 100 32 29 103
Character c a l c u l u s .
Milliseconds 151 117 164 114 72 210 60 178 77
WPM Timing
Seconds WPM
1.69 85.36
3.37 110.26
5.06 116.19
6.75 119.15
8.43 123.77
10.12 124.49
11.81 127.03
13.5 130.71
15.18 132.78
16.87 132.31
18.56 132.57
20.24 125.08
21.93 126.95
23.62 131.09
25.3 129.46
26.99 125.82
28.68 123.02
30.37 118.16
32.05 119.81
33.74 118.79
35.43 121.27
37.11 119.63
38.8 120.93
40.49 121.52
42.17 123.49
43.86 123.94
45.55 125.41
47.23 125.5
48.92 124.36
50.61 125.91
52.3 127.58
53.98 127.6
55.67 127.83
57.36 127.41
59.04 126.42
60.73 125.87
62.42 125.35
64.1 124.67
65.79 123.48
67.48 122.17
69.16 122.14
70.85 122.45
72.54 123.41
74.23 123.68
75.91 123.77
77.6 124.33
79.29 124.41
80.97 123.3
82.66 123.11
84.35 122.92