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Race #748

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Official speed 130.61 wpm (79.38 seconds elapsed during race)
Without ending ping 130.77 wpm (95 ms delay sending score to TypeRacer’s server)
Timerless 131.33 wpm (340 ms elapsed before first character typed; 78.95 seconds elapsed during race)
Timerless minus one 131.18 wpm, ignoring the first character typed
Race Start December 15, 2023 4:20:05pm UTC
Race Finish December 15, 2023 4:21:24pm UTC
Outcome No win (2 of 4)
Opponents 1. smurfaccount1337 (134.88 wpm)
3. poem (129.04 wpm)
Accuracy 98.2%
Points 352.64
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 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 barrlelel change as a function of the amount of liquid poured into it? We see chang oce occurring in nearly evertything we observe in the world and universe, and powerful modern instruments help us seee more and more. In this section we introdue the 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 corurve. We give precise developments of these important concepts in the next chapter, but for now we use an informal approach so you wil l see how they lead naturally ot ehto the mainidea omain idae of thidae of tidea of this cpahapter, the limit. The idea of a limit plays a foundationall role trhougthroughout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 340 71 51 165 107 282 144 47 105 82 51 46 124 45 102 48 136 156 57 71 69 36 43 63 54
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 63 136 31 86 30 128 38 68 79 57 32 109 93 168 150 81 79 89 83 83 116 29 34 77 87
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 103 44 47 80 97 40 24 45 82 25 130 53 24 43 126 291 114 72 189 48 89 180 113 71 81
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 29 98 40 43 53 75 30 70 48 86 0 82 27 82 92 42 54 80 98 37 0 82 79 0 72
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 68 113 70 26 104 75 27 77 125 94 46 84 91 33 93 58 47 91 57 36 50 65 84 81 98
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 87 43 53 66 49 67 56 85 51 66 124 176 0 68 0 112 75 47 68 162 156 44 178 103 39
Character n g e a s a f u n c t i o n o f t i m e
Milliseconds 462 101 31 50 108 13 74 85 78 100 41 63 73 147 40 141 24 45 73 95 29 120 0 117 50
Character ? H o w d o e s t h e l e v e l o f w
Milliseconds 192 89 155 123 0 56 84 50 109 67 26 93 26 75 0 93 89 226 57 53 57 120 42 38 52
Character a t e r i n a b a r r l e l -l -e -l e l c h
Milliseconds 102 40 107 39 22 71 61 24 55 95 75 78 17 123 73 74 211 192 85 87 94 66 68 92 49
Character a n g e a s a f u n c t i o n o f t h e
Milliseconds 45 85 54 41 49 116 23 66 50 67 93 89 66 139 290 60 136 42 52 69 80 43 172 0 79
Character a m o u n t o f l i q u i d p o u r e d
Milliseconds 21 100 45 109 68 128 37 40 52 85 41 98 47 91 98 123 70 74 99 40 178 62 39 76 22
Character i n t o i t ? W e s e e c h a n g o c -c
Milliseconds 81 67 62 86 38 106 91 222 83 129 64 81 117 40 108 50 105 32 54 93 50 85 64 107 272
Character -o - e o c c u r r i n g i n n e a r l y e
Milliseconds 107 99 85 68 89 69 117 106 81 106 84 59 85 47 69 35 51 99 26 71 78 78 101 17 132
Character v e r t -t y t h i n g w e o b s e r v e i n
Milliseconds 40 71 43 180 272 81 123 35 79 58 38 42 91 49 62 63 95 72 53 58 232 45 77 86 52
Character t h e w o r l d a n d u n i v e r s e ,
Milliseconds 34 79 66 30 55 78 101 67 75 85 41 83 25 70 22 113 78 83 106 123 53 138 85 65 22
Character a n d p o w e r f u l m o d e r n i n s t r
Milliseconds 70 80 24 47 107 60 26 49 27 166 42 156 57 100 223 194 329 56 33 36 208 130 94 50 73
Character u m e n t s h e l p u s s e e e - -e m o
Milliseconds 96 90 51 56 82 68 69 87 55 128 25 49 166 16 52 82 77 166 146 33 250 104 61 115 146
Character r e a n d m o r e . I n t h i s s e c t
Milliseconds 0 0 45 92 34 73 0 123 92 67 31 83 44 169 60 58 62 70 40 19 75 93 56 197 154
Character i o n w e i n t r o d u e t h e -t -h -e - -i
Milliseconds 30 155 14 42 32 54 70 80 58 40 42 81 87 87 173 53 93 42 34 47 256 0 0 0 96
Character -n -t -r -o -d -u -e - i n t r o d u c e t h e i d e
Milliseconds 0 0 0 0 0 0 0 0 313 63 249 46 80 117 97 117 41 64 98 28 47 44 80 78 128
Character a s o f a v e r a g e a n d i n s t a n t
Milliseconds 58 28 51 58 80 50 97 173 120 68 86 91 57 44 30 124 65 26 96 35 57 113 74 54 98
Character a n e o u s r a t e s o f c h a n g e , a
Milliseconds 445 85 156 217 28 51 128 232 96 75 71 65 72 27 77 82 81 51 33 112 55 23 89 24 55
Character n d s h o w t h a t t h e y a r e c l o
Milliseconds 80 44 69 38 65 96 35 70 60 53 50 40 39 83 39 49 90 42 51 40 32 33 180 14 156
Character s e l y r e l a t e d t o t h e s l o p e
Milliseconds 52 32 93 86 46 148 27 42 81 71 18 77 0 117 0 54 55 64 20 32 112 51 133 128 62
Character o f a c u r v e a t a p o i n t P
Milliseconds 18 82 68 50 64 65 93 101 73 189 45 54 137 38 30 102 52 146 67 157 124 46 39 133 87
Character o n t h e c o r -r -o u r v e . W e g i v e
Milliseconds 97 70 43 44 92 53 46 151 40 103 184 99 169 45 162 50 53 49 154 73 43 133 65 142 64
Character p r e c i s e d e v e l o p m e n t s o f
Milliseconds 40 195 111 46 186 53 84 53 47 121 75 156 33 50 156 24 177 40 98 48 91 33 49 74 67
Character t h e s e i m p o r t a n t c o n c e p t s
Milliseconds 101 8 98 122 57 64 85 84 150 33 63 34 70 13 88 29 172 121 85 101 61 69 126 128 110
Character i n t h e n e x t c h a p t e r , b u t
Milliseconds 78 57 47 108 63 59 24 95 47 152 141 25 141 15 95 73 98 84 61 59 25 152 76 24 71
Character f o r n o w w e u s e a n i n f o r m a
Milliseconds 65 74 104 0 69 130 39 65 172 69 41 158 62 34 42 105 51 47 172 97 124 97 65 67 175
Character l a p p r o a c h s o y o u w i l - l
Milliseconds 104 67 153 0 150 104 73 103 72 49 47 71 76 66 251 79 51 37 36 89 146 181 289 185 58
Character s e e h o w t h e y l e a d n a t u r a l
Milliseconds 69 41 141 40 94 95 27 44 64 65 42 94 36 144 38 62 113 37 142 70 56 45 105 24 47
Character l y o t e h -e -h -o -t - t o t h e m a i n i
Milliseconds 125 71 18 125 0 75 36 97 289 0 107 0 0 140 22 43 50 67 34 26 130 49 83 63 108
Character d e a o -o -m -a -i -n -i -d -e -a - m a i n i d a e
Milliseconds 72 81 25 23 25 268 117 0 0 0 0 0 0 0 0 330 48 106 42 29 122 67 143 0 0
Character o f t h -t -h -o -f - -i -d -a -e - i d a e o f t -t
Milliseconds 19 78 63 83 46 266 0 73 0 0 114 0 0 0 0 144 53 113 0 0 60 75 51 114 197
Character -o -f - -i -d -a -e - i d e a o f t h i s c p a -a
Milliseconds 94 0 0 109 0 0 0 0 209 81 70 35 39 97 114 76 165 27 18 58 104 42 100 35 386
Character -p h a p t e r , t h e l i m i t . T h e i
Milliseconds 100 100 211 129 107 97 57 90 15 98 77 39 34 209 111 163 101 52 144 40 64 84 45 38 83
Character d e a o f a l i m i t p l a y s a f o
Milliseconds 104 55 82 26 63 95 32 80 73 97 53 166 93 48 61 85 44 29 144 47 72 45 109 78 182
Character u n d a t i o n a l -l l r o l e t r h o u g -t
Milliseconds 57 140 34 57 111 28 153 14 332 68 165 449 68 90 55 90 54 40 194 56 23 126 50 38 243
Character -r -h -o -u -g t h r o u g h o u t c a l c u l u s .
Milliseconds 0 0 0 0 0 203 55 27 111 19 71 67 83 65 0 65 112 17 49 102 80 196 198 34 141
WPM Timing
Seconds WPM
1.59 90.7
3.18 128.49
4.76 133.53
6.35 134.16
7.94 145.12
9.53 149.91
11.11 153.33
12.7 147.39
14.29 147.81
15.88 148.15
17.46 147.05
19.05 146.76
20.64 147.1
22.23 147.93
23.81 146.13
25.4 142.67
26.99 141.83
28.58 143.61
30.16 144.41
31.75 142.48
33.34 143.25
34.93 141.55
36.52 142.3
38.1 138.26
39.69 137.56
41.28 138.38
42.87 136.61
44.45 137.94
46.04 139.7
47.63 141.59
49.22 141.42
50.8 140.3
52.39 139.95
53.98 140.28
55.57 140.59
57.15 140.88
58.74 141.36
60.33 141.02
61.92 140.12
63.51 140.4
65.09 139.37
66.68 136.95
68.27 134.47
69.86 132.96
71.44 131.85
73.03 132.11
74.62 132.84
76.21 131.8
77.79 130.19
79.38 130.61