Matthias (matthiasfiveonetwo)

Race #33

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Official speed 97.89 wpm (105.91 seconds elapsed during race)
Without ending ping 98.10 wpm (229 ms delay sending score to TypeRacer’s server)
Timerless 98.40 wpm (323 ms elapsed before first character typed; 105.36 seconds elapsed during race)
Timerless minus one 98.29 wpm, ignoring the first character typed
Race Start July 4, 2024 6:02:26am UTC
Race Finish July 4, 2024 6:04:12am UTC
Outcome Win (1 of 3)
Opponents 2. cerberus17 (95.90 wpm)
Accuracy 96.3%
Points 264.30
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 inan another. Howe does the speed of a falling object change as a function of time? hHow does the leve ll of water in a barerel change as a function of the amount of liquide p prooured into it? AWeWe see change occurring in nearly eavverything we observe in the world and universe, and powerful modern instruments help us lssee more and more. In this esection we interrorotroduce the ideas of ageverage and isnnstangtaneous rates of change, and show that hty=they are closely reltated to the slop eoe of a curve at a point P on the curvbee. We give precidse developments of these important conscepts in the next chapter, but ofr for now we use an informaol apporoach so you will see how they lead noaturally to the main ideacf o of this chgapter, the limit. The idea of a limit plays a foundational role throughout calculu.s s.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 323 158 113 128 142 113 112 104 75 67 121 83 84 104 284 98 127 142 107 51 91 37 59 61 105
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 67 109 94 89 53 67 121 75 105 141 92 126 75 91 112 97 37 106 52 76 74 55 95 71 80
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 66 100 112 29 96 121 7 135 86 95 77 74 75 97 405 232 99 126 128 89 99 67 97 67 85
Character r e l a t e d t o a c h a n g e i n a n
Milliseconds 96 225 142 97 83 68 141 120 76 112 61 97 92 88 91 58 105 53 97 106 89 70 67 158 97
Character -n -a a n o t h e r . H o w e - -e d o e s
Milliseconds 188 119 113 134 84 90 35 91 38 83 126 99 112 75 37 181 59 262 120 158 143 82 84 104 59
Character t h e s p e e d o f a f a l l i n g o b
Milliseconds 99 29 97 53 121 82 231 144 134 62 97 75 83 104 46 118 143 92 110 113 53 89 53 60 120
Character j e c t c h a n g e a s a f u n c t i o n
Milliseconds 150 62 111 172 83 97 83 67 104 75 113 83 120 150 108 66 70 75 80 148 107 194 37 60 30
Character o f t i m e ? h -h H o w d o e s t h e
Milliseconds 99 84 64 106 97 83 68 45 240 150 187 412 158 68 81 121 105 91 82 118 63 52 88 62 89
Character l e v e l -l - l o f w a t e r i n a b
Milliseconds 59 107 105 104 120 76 246 104 191 74 89 83 83 112 105 92 103 76 50 69 68 112 30 91 133
Character a r e -e r e l c h a n g e a s a f u n c t
Milliseconds 76 172 173 329 121 89 120 308 130 125 82 122 44 113 105 51 91 127 98 74 188 114 148 143 187
Character i o n o f t h e a m o u n t o f l i q u
Milliseconds 68 61 13 93 81 75 67 97 76 52 60 127 113 134 46 150 128 113 83 73 68 46 119 157 137
Character i d e p -p - -e p r o -o -r o u r e d i n t o
Milliseconds 88 181 7 61 105 239 127 129 113 105 179 30 232 129 180 75 51 174 126 62 81 52 112 62 96
Character i t ? A W e -e -W -A W e s e e c h a n g e o
Milliseconds 97 75 242 141 158 21 167 225 128 142 158 211 0 569 126 128 67 91 76 57 84 83 105 75 112
Character c c u r r i n g i n n e a r l y e a v -v -a v
Milliseconds 68 149 158 97 136 141 47 88 38 99 58 105 136 14 121 67 78 141 81 90 76 74 255 112 105
Character e r y t h i n g w e o b s e r v e i n t h
Milliseconds 113 77 96 104 84 97 68 44 63 117 112 91 53 113 194 149 150 189 119 113 68 60 104 46 82
Character e w o r l d a n d u n i v e r s e , a n d
Milliseconds 30 113 38 164 90 166 67 126 91 75 75 46 98 148 54 112 104 76 112 128 84 117 84 75 82
Character p o w e r f u l m o d e r n i n s t r u m e
Milliseconds 16 111 83 104 69 81 152 73 107 81 203 128 83 149 61 96 75 75 70 67 118 151 111 145 118
Character n t s h e l p u s l s -s -l s e e m o r e
Milliseconds 91 7 172 136 75 112 45 119 76 99 104 91 90 103 159 112 128 113 133 83 75 68 45 83 51
Character a n d m o r e . I n t h i s e -e s e c t i
Milliseconds 68 99 148 69 90 75 37 90 90 126 137 59 112 32 83 65 69 126 75 263 53 97 128 187 38
Character o n w e i n t e r -r -e -t r o -o -r r o -o -r t r o
Milliseconds 45 39 96 53 134 91 91 43 91 134 61 210 112 112 114 120 313 128 293 143 360 126 174 135 179
Character d u c e t h e i d e a s o f a g e -e -g v e
Milliseconds 136 134 61 142 89 83 24 89 46 90 67 134 91 97 105 67 76 81 91 105 112 338 119 204 134
Character r a g e a n d i s n -n -s n s t a n g -g t a n e
Milliseconds 91 126 113 120 91 90 39 94 61 105 46 45 247 121 412 97 119 91 90 106 389 98 105 113 233
Character o u s r a t e s o f c h a n g e , a n d
Milliseconds 111 98 134 128 225 135 82 129 120 44 99 37 58 279 83 89 91 59 112 137 96 91 74 69 44
Character s h o w t h a t h t y = -= -y -t -h t h e y a r
Milliseconds 127 61 83 60 52 52 120 83 113 44 186 62 171 180 128 128 134 136 151 67 97 83 113 82 67
Character e c l o s e l y r e l t -t a t e d t o t h
Milliseconds 96 76 106 97 127 74 113 46 149 61 75 82 150 106 301 74 81 107 133 76 97 83 29 99 89
Character e s l o p e o -o -e - e o f a c u r v e
Milliseconds 45 83 105 83 134 99 51 61 104 286 119 136 112 52 91 89 61 99 65 136 163 78 201 166 83
Character a t a p o i n t P o n t h e c u r v b
Milliseconds 81 104 99 97 75 241 21 83 60 37 158 142 143 90 82 121 22 99 78 38 122 392 82 212 0
Character e -e -b e . W e g i v e p r e c i d -d s e d
Milliseconds 193 217 119 242 111 143 180 166 126 142 99 75 127 53 113 82 396 143 158 83 276 98 98 61 125
Character e v e l o p m e n t s o f t h e s e i m p o
Milliseconds 168 140 84 120 150 68 120 96 105 54 157 97 63 58 50 99 22 105 135 129 0 112 82 112 83
Character r t a n t c o n s -s c e p t s i n t h e n
Milliseconds 113 127 113 81 112 151 112 99 67 112 234 90 118 91 97 120 62 51 67 98 52 83 97 69 59
Character e x t c h a p t e r , b u t o f r - -r -f -o
Milliseconds 112 174 180 67 113 51 77 171 127 127 60 86 80 241 164 104 23 143 22 165 45 271 134 143 143
Character f o r n o w w e u s e a n i n f o r m a
Milliseconds 188 119 83 98 97 83 51 127 85 142 120 43 107 120 81 69 75 119 165 60 98 150 76 96 98
Character o -o l a p p o -o r o a c h s o y o u w i l
Milliseconds 180 315 180 97 53 143 134 149 272 149 75 97 91 105 91 88 75 91 112 105 46 74 105 83 112
Character l s e e h o w t h e y l e a d n o -o a t
Milliseconds 134 92 67 104 150 91 83 67 89 32 66 121 97 90 114 74 75 44 120 112 69 89 302 118 98
Character u r a l l y t o t h e m a i n i d e a c f
Milliseconds 90 68 111 76 112 158 128 112 90 82 8 126 38 113 90 113 91 52 97 209 85 164 60 120 14
Character o -o - -f -c o f t h i s c h g -g a p t e r ,
Milliseconds 54 91 185 128 128 127 136 142 38 104 83 59 67 113 90 263 97 0 444 180 149 151 121 66 75
Character t h e l i m i t . T h e i d e a o f a
Milliseconds 84 96 21 120 32 104 134 122 97 82 120 120 151 30 120 59 75 105 142 75 90 112 54 150 82
Character l i m i t p l a y s a f o u n d a t i o n
Milliseconds 75 98 150 105 91 172 157 21 130 96 75 158 149 113 59 92 83 50 128 84 126 106 52 67 38
Character a l r o l e t h r o u g h o u t c a l c u l
Milliseconds 165 120 60 180 68 151 80 83 91 67 76 74 46 51 107 88 61 30 97 75 98 59 151 128 112
Character u . s - -s -. s .
Milliseconds 113 203 22 286 246 136 316 103 89
WPM Timing
Seconds WPM
2.12 90.64
4.24 110.47
6.35 120.85
8.47 114.71
10.59 111.03
12.71 107.63
14.83 110.06
16.95 111.88
19.06 111.41
21.18 109.9
23.3 109.69
25.42 107.16
27.54 108.51
29.66 106.02
31.77 104.23
33.89 100.2
36.01 101.64
38.13 101.97
40.25 102.57
42.37 103.95
44.48 104.4
46.6 103.77
48.72 105.42
50.84 104.09
52.96 100.61
55.08 100.88
57.19 99.66
59.31 98.73
61.43 99.43
63.55 98.19
65.67 98.5
67.79 98.25
69.9 98.36
72.02 98.64
74.14 97.92
76.26 97.25
78.38 98.14
80.5 98.39
82.61 98.34
84.73 97.58
86.85 97.41
88.97 97.38
91.09 98.02
93.21 98.36
95.32 97.69
97.44 97.41
99.56 97.99
101.68 98.19
103.8 99.19
105.91 97.89