👺Wainie san (wxia)

Race #4087

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Official speed 105.08 wpm (98.67 seconds elapsed during race)
Without ending ping 105.54 wpm (427 ms delay sending score to TypeRacer’s server)
Timerless 106.03 wpm (461 ms elapsed before first character typed; 97.78 seconds elapsed during race)
Timerless minus one 105.91 wpm, ignoring the first character typed
Race Start October 6, 2023 4:58:11pm UTC
Race Finish October 6, 2023 4:59:49pm UTC
Outcome No win (3 of 5)
Opponents 1. jesterc (127.47 wpm)
2. aelius_qwerty2 (126.69 wpm)
Accuracy 97.9%
Points 283.71
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 help suss us understand how a change in one quantity is realtedrelated toa a change in another. How does the speed of a falling object change as a function of time? How does the level of water ina a a abbarrel change a s s a function of the amount of liquid poured into it? We see change occurring in nearly everything we observe in the world andu universe, and powerful modern instruments help us see more and more. In this ectisection we ointroduce the ideas of eaveraege and instantaneous rates of chaanangnge, and show taht tthat they are closely realtedrelated to the slop\e e of a curve at a point P on the curve. We give precise developments of these important concepts in the next chapter, but fornow w 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.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 461 111 137 264 104 82 132 65 74 106 77 108 44 72 69 90 115 120 102 81 64 42 94 38 171
Character e l p s u s -s -u -s - s u s u n d e r s t a n
Milliseconds 120 81 111 112 0 120 72 272 97 111 120 87 67 118 104 79 112 136 22 140 94 113 127 99 60
Character d h o w a c h a n g e i n o n e q u a
Milliseconds 107 40 110 50 39 54 83 45 97 99 84 90 208 112 41 103 54 59 95 89 86 64 110 59 112
Character n t i t y i s r e a l t e d -d -r -e -a -l -t -e r e
Milliseconds 72 159 89 71 113 96 134 80 74 65 102 105 32 127 113 129 152 93 0 0 0 0 0 289 121
Character l a t e d t o a - - -a a c h a n g e i
Milliseconds 120 54 122 120 112 62 98 98 52 48 122 312 96 111 136 57 111 73 87 41 112 46 99 70 81
Character n a n o t h e r . H o w d o e s t h e s
Milliseconds 48 71 50 117 56 74 88 22 47 99 96 183 128 71 98 56 104 39 96 63 89 74 62 55 82
Character p e e d o f a f a l l i n g o b j e c t
Milliseconds 53 89 113 136 345 136 41 103 40 72 70 105 377 105 160 29 90 71 104 130 111 80 120 135 65
Character c h a n g e a s a f u n c t i o n o f t
Milliseconds 83 61 40 134 51 118 177 48 183 160 33 79 97 96 135 81 104 54 106 41 110 217 86 67 72
Character i m e ? H o w d o e s t h e l e v e l o
Milliseconds 88 134 23 250 135 185 70 91 79 80 80 58 101 42 319 72 69 91 69 34 121 103 57 87 112
Character f w a t e r i n a a -a - - - -a a a b
Milliseconds 41 96 72 134 97 113 71 64 130 47 209 112 134 23 217 104 113 144 279 104 120 16 145 0 232
Character -b -a b a r r e l c h a n g e a s - -s - s
Milliseconds 225 95 177 111 103 136 129 88 96 64 71 26 117 42 112 119 15 115 182 146 174 106 87 97 80
Character a f u n c t i o n o f t h e a m o u n t
Milliseconds 52 70 108 97 152 47 121 21 114 46 68 134 97 56 199 105 22 114 0 162 111 103 136 104 7
Character o f l i q u i d p o u r e d i n t o i t ?
Milliseconds 112 89 43 117 100 83 120 40 64 96 137 135 121 72 136 111 40 352 81 95 62 106 185 32 463
Character W e s e e c h a n g e o c c u r r i n g
Milliseconds 184 176 183 265 65 128 119 41 103 80 26 119 62 113 57 151 88 104 128 96 121 134 42 71 49
Character i n n e a r l y e v e r y t h i n g w e o
Milliseconds 87 72 58 190 64 113 97 73 123 27 143 140 108 47 90 120 112 40 137 0 94 66 79 136 103
Character b s e r v e i n t h e w o r l d a n d u -u
Milliseconds 73 255 137 70 160 478 117 113 90 30 91 45 75 86 88 111 52 113 43 88 95 96 81 143 478
Character u n i v e r s e , a n d p o w e r f u l m
Milliseconds 138 120 135 40 552 151 105 112 145 77 68 33 126 33 65 96 143 0 78 93 116 111 38 81 112
Character o d e r n i n s t r u m e n t s h e l p u s
Milliseconds 88 49 135 23 121 63 89 89 95 136 112 72 146 62 72 62 91 46 136 97 64 112 97 95 39
Character s e e m o r e a n d m o r e . I n t h
Milliseconds 114 54 128 122 135 200 88 32 96 130 112 63 79 49 80 54 45 111 44 100 157 153 80 80 45
Character i s e c t i -i -t -c -e s e c t i o n w e o -o i
Milliseconds 52 32 78 97 160 137 116 159 93 122 123 66 123 132 98 88 111 49 88 207 97 222 145 392 158
Character n t r o d u c e t h e i d e a s o f e -e a
Milliseconds 58 70 137 47 113 114 53 113 89 88 95 24 72 129 10 149 145 498 118 95 80 97 74 312 31
Character v e r a e -e g e a n d i n s t a n t a n e o u
Milliseconds 111 119 137 111 225 281 127 78 58 96 62 99 45 73 65 41 129 86 112 91 117 183 210 158 88
Character s r a t e s o f c h a a n -n -a a n g -g -n -a n
Milliseconds 89 72 62 96 103 124 111 74 141 115 40 121 59 89 54 41 576 90 71 113 72 216 95 112 168
Character g e , a n d s h o w t a h t t -t -t -a -h -t -
Milliseconds 55 97 63 99 44 124 48 78 82 87 21 90 48 89 89 22 73 87 57 273 87 0 0 0 0
Character t h a t t h e y a r e c l o s e l y r e a
Milliseconds 160 72 49 53 97 73 87 22 140 136 57 89 114 70 88 87 117 22 94 430 98 87 94 117 108
Character l t e d -r -e -a -l -t -e -d r e l a t e d t o t h e
Milliseconds 0 111 112 136 233 0 0 0 0 0 0 207 119 82 53 115 218 51 70 138 0 92 71 122 60
Character s l o p \ e - -e -\ e o f a c u r v e a
Milliseconds 81 100 68 120 139 0 0 208 160 111 112 0 55 129 49 95 39 98 56 144 40 129 102 81 178
Character t a p o i n t P o n t h e c u r v e .
Milliseconds 109 96 113 63 329 175 160 33 88 88 159 120 135 115 70 41 97 42 71 70 111 39 138 103 43
Character W e g i v e p r e c i s e d e v e l o p m
Milliseconds 94 151 137 248 96 75 70 110 39 113 54 130 160 74 72 135 95 105 319 160 97 88 143 129 141
Character e n t s o f t h e s e i m p o r t a n t c
Milliseconds 91 95 56 98 30 152 185 80 87 88 48 153 106 85 153 159 184 123 42 155 73 111 72 50 103
Character o n c e p t s i n t h e n e x t c h a p t
Milliseconds 97 94 66 139 86 68 121 50 222 120 81 81 62 97 56 102 55 130 136 28 127 69 74 71 88
Character e r , b u t f o r n o w w -w - -w -o -n n o w
Milliseconds 103 55 90 72 88 64 54 84 81 63 87 118 41 96 38 123 199 95 120 127 113 146 111 39 55
Character w e u s e a n i n f o r m a l a p p r o
Milliseconds 91 70 105 72 119 49 111 24 113 63 111 56 154 87 120 47 97 62 84 94 74 86 97 143 112
Character a c h s o y o u w i l l s e e h o w t
Milliseconds 65 160 95 89 40 104 104 41 52 67 71 65 58 110 127 23 67 327 144 151 121 49 54 73 111
Character h e y l e a d n a t u r a l l y t o t h e
Milliseconds 70 70 156 85 86 55 86 114 89 111 38 123 108 49 108 69 98 60 47 130 54 90 91 38 80
Character m a i n i d e a o f t h i s c h a p t e
Milliseconds 46 114 111 89 54 56 138 96 137 121 86 120 88 71 83 69 34 52 84 86 199 97 89 95 96
Character r , t h e l i m i t . T h e i d e a o f
Milliseconds 81 47 82 87 72 54 76 94 151 106 86 88 96 91 181 129 54 47 114 19 134 121 110 98 61
Character a l i m i t p l a y s a f o u n d a t i
Milliseconds 75 39 71 145 135 113 103 75 51 107 113 33 157 135 116 68 48 129 54 130 120 24 128 121 143
Character o n a l r o l e t h r o u g h o u t c a l c
Milliseconds 105 119 41 136 112 208 111 120 65 45 130 112 120 41 72 87 81 61 98 89 64 113 118 17 319
Character u l u s .
Milliseconds 121 112 94 90 95
WPM Timing
Seconds WPM
1.97 91.22
3.95 85.13
5.92 99.32
7.89 107.94
9.87 96.08
11.84 93.24
13.81 101.64
15.79 101.86
17.76 104.73
19.73 106.42
21.71 106.69
23.68 104.9
25.65 100.1
27.63 99.47
29.6 100.94
31.57 102.24
33.55 100.16
35.52 102.03
37.49 103.7
39.47 103.07
41.44 102.51
43.41 102.55
45.39 103.91
47.36 104.9
49.33 104.11
51.31 102.68
53.28 102.93
55.25 101.42
57.23 101.91
59.2 101.35
61.17 100.83
63.15 100.53
65.12 98.95
67.09 99.26
69.07 99.55
71.04 99.83
73.01 100.25
74.99 100.18
76.96 100.57
78.93 101.25
80.91 100.86
82.88 101.35
84.85 102.25
86.83 102.55
88.8 103.51
90.77 104.17
92.75 104.67
94.72 105.02
96.69 105.36
98.67 105.08