JGB 🇭🇹 (jgb000)

Race #19608

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Official speed 88.01 wpm (117.80 seconds elapsed during race)
Without ending ping 88.19 wpm (241 ms delay sending score to TypeRacer’s server)
Timerless 88.28 wpm (116 ms elapsed before first character typed; 117.45 seconds elapsed during race)
Timerless minus one 88.18 wpm, ignoring the first character typed
Race Start April 21, 2024 12:16:28am UTC
Race Finish April 21, 2024 12:18:26am UTC
Outcome Win (1 of 5)
Opponents 2. aulaman (81.74 wpm)
4. paratentacle (75.20 wpm)
Accuracy 97.4%
Points 237.63
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 tha tt helps us understand how a change in tonone quantity is related to a chang ie ain another. How does the speed of a falling object change as a function of time? How does the level of water in a barerel change as a function of the maamount of liquid poured into it ? We see change occurinring in naearly aeverything we observe in the wolrd anrlrld and universe, and powerful modern instrumens ts ts help us see more and more. In this section owe we introduce the ideas aoof average and instrananantanouioueous rates of change, and show that they are closely related to the slope of a cruurve at a point P aon ton the curve. We gie prve precise deveoplopments of these important concepts on in the next chapter, but for now we use an informal appreoaaochoach so you will see how theyl lead natuarally 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 -t
Milliseconds 116 113 565 350 100 201 216 64 81 105 15 113 121 100 73 112 132 176 42 116 83 52 116 14 504
Character - t h e l p s u s u n d e r s t a n d h o
Milliseconds 134 92 78 77 81 73 116 170 98 194 269 134 187 178 34 132 37 113 84 84 67 114 86 98 65
Character w a c h a n g e i n t o n -n -o -t o n e q
Milliseconds 85 89 98 97 299 101 55 80 64 100 73 77 84 135 114 134 82 241 127 137 188 38 53 101 148
Character u a n t i t y i s r e l a t e d t o a c
Milliseconds 86 233 4 145 102 95 137 133 137 78 84 246 106 99 101 69 79 186 34 97 67 64 69 115 122
Character h a n g i -i - e a -a i n a n o t h e r . H
Milliseconds 63 38 98 46 169 100 316 134 100 65 123 364 186 48 48 48 135 117 117 80 64 72 199 117 273
Character o w d o e s t h e s p e e d o f a f a
Milliseconds 106 105 56 149 107 120 35 150 84 171 83 112 120 112 68 135 180 68 88 79 36 62 119 99 100
Character l l i n g o b j e c t c h a n g e a s a
Milliseconds 67 150 131 89 30 67 100 68 120 44 277 91 104 285 94 86 81 83 105 95 102 98 83 85 116
Character f u n c t i o n o f t i m e ? H o w d o e
Milliseconds 101 160 156 62 104 55 40 122 99 85 47 85 85 50 98 40 242 101 383 153 81 89 111 90 79
Character s t h e l e v e l o f w a t e r i n a
Milliseconds 48 101 99 67 19 97 67 54 167 62 118 49 150 56 62 98 138 64 99 101 49 224 93 100 53
Character b a r e -e r e l c h a n g e a s a f u n
Milliseconds 124 60 140 127 96 538 39 72 135 134 218 97 48 68 67 84 84 98 88 62 101 102 133 110 142
Character c t i o n o f t h e m a -a -m a m o u n t o
Milliseconds 59 110 50 67 111 182 128 156 84 135 47 101 82 206 112 210 140 82 103 113 102 171 47 68 80
Character f l i q u i d p o u r e d i n t o i t -
Milliseconds 67 106 143 84 116 101 84 101 132 584 133 97 119 99 172 45 101 50 83 50 81 119 100 294 459
Character ? W e s e e c h a n g e o c c u r i n -n -i
Milliseconds 222 75 210 74 104 83 95 153 65 170 63 49 101 64 90 80 193 124 173 71 88 117 83 278 142
Character r i n g i n n a -a e a r l y a -a e v e r y t
Milliseconds 117 113 83 84 68 380 42 82 182 135 301 100 46 81 87 129 186 313 330 33 153 67 89 12 132
Character h i n g w e o b s e r v e i n t h e w o
Milliseconds 55 59 73 132 21 128 68 83 203 96 134 72 61 183 82 87 98 64 69 99 17 82 34 51 65
Character l r d a n -n -a - -d -r r l -l -r -l r l d a n d u
Milliseconds 152 70 41 90 81 33 274 151 145 133 132 150 167 236 154 127 47 179 97 94 64 69 85 67 131
Character n i v e r s e , a n d p o w e r f u l m o d
Milliseconds 166 101 100 133 66 105 95 178 92 64 100 99 83 135 274 62 64 67 207 92 81 104 181 104 97
Character e r n i n s t r u m e n s - -s t -t s - -s t s
Milliseconds 131 49 68 108 128 82 67 101 120 80 159 58 102 129 102 278 138 113 334 70 231 233 136 86 59
Character h e l p u s s e e m o r e a n d m o r
Milliseconds 54 83 52 116 83 241 148 81 66 154 12 214 40 93 101 52 63 62 283 92 114 14 137 133 113
Character e . I n t h i s s e c t i o n o w e - -e
Milliseconds 120 150 65 219 84 104 99 59 83 32 84 123 35 223 124 67 99 80 86 108 71 36 155 132 139
Character -w -o w e i n t r o d u c e t h e i d e a s
Milliseconds 144 136 113 86 114 151 55 179 142 108 133 165 102 165 67 133 65 48 88 102 98 133 82 122 129
Character a o -o -a o f a v e r a g e a n d i n s t r a
Milliseconds 82 116 229 140 226 58 98 62 153 153 52 110 101 103 67 229 105 80 56 92 55 78 100 133 235
Character n -n -a a n -n -a -r a n t a n o u -u -o i o u -u -o -i e o
Milliseconds 87 466 136 120 126 276 142 134 54 130 47 83 264 174 97 252 116 469 148 97 287 132 137 96 147
Character u s r a t e s o f c h a n g e , a n d s
Milliseconds 59 111 111 210 129 85 96 151 226 173 68 66 147 89 64 83 50 80 277 77 322 135 83 80 95
Character h o w t h a t t h e y a r e c l o s e l y
Milliseconds 103 32 50 117 99 84 39 83 75 103 48 90 64 85 97 103 79 63 187 55 147 65 8 143 151
Character r e l a t e d t o t h e s l o p e o f
Milliseconds 64 138 81 96 103 67 84 184 33 81 103 48 65 92 39 65 277 190 167 123 117 85 115 82 67
Character a c r u -u -r u r v e a t a p o i n t P
Milliseconds 64 119 133 119 81 422 135 242 46 204 326 192 188 212 101 78 138 140 96 46 57 107 20 286 98
Character a o n t -t - -n -o -a o n t h e c u r v e . W
Milliseconds 135 63 84 86 84 258 126 145 136 138 213 50 64 49 87 43 39 202 83 63 190 61 199 70 434
Character e g i e p r -r -p - -e v e p r e c i s e d e
Milliseconds 115 100 141 73 196 73 151 81 292 130 147 134 80 85 67 130 51 70 184 118 97 79 121 283 155
Character v e o p -p -o l o p m e n t s o f t h e s e i
Milliseconds 78 145 111 129 255 160 268 165 82 222 81 98 40 115 78 119 46 60 111 117 0 167 115 102 99
Character m p o r t a n t c o n c e p t s o n - -n -o i
Milliseconds 102 81 31 63 153 67 66 85 72 178 85 89 55 154 85 82 134 83 116 80 121 224 132 134 199
Character n t h e n e x t c h a p t e r , b u t f
Milliseconds 48 47 72 112 0 67 115 67 338 96 65 212 72 135 64 153 115 84 167 131 202 99 83 36 148
Character o r n o w w e u s e a n i n f o r m a l
Milliseconds 0 117 84 130 85 46 103 102 82 101 331 103 64 88 114 134 240 94 64 386 115 52 77 69 183
Character a p p r e o a -a -o -e a o c h -h -c -o -a o a c h s
Milliseconds 118 151 84 165 56 58 154 86 301 117 146 266 16 205 113 354 130 133 71 393 68 135 69 98 264
Character o y o u w i l l s e e h o w t h e y l
Milliseconds 118 87 117 96 72 63 81 101 106 135 37 75 76 162 42 135 29 55 131 101 87 43 104 185 38
Character - -l l e a d n a t u a -a r a l l y t o t h
Milliseconds 264 163 101 99 46 84 136 83 353 114 116 183 473 345 65 53 114 134 150 150 167 80 137 77 71
Character e m a i n i d e a o f t h i s c h a p t
Milliseconds 65 39 116 69 116 41 100 91 48 132 38 117 133 79 50 99 108 41 86 72 259 71 101 78 118
Character e r , t h e l i m i t . T h e i d e a o
Milliseconds 116 69 151 115 84 82 32 84 135 119 113 101 100 118 84 196 137 15 68 114 65 120 116 153 148
Character f a l i m i t p l a y s a f o u n d a t
Milliseconds 63 70 81 119 721 60 101 105 83 75 106 148 62 139 100 63 135 85 67 80 85 139 57 66 72
Character i o n a l r o l e t h r o u g h o u t c a l
Milliseconds 79 52 102 90 130 98 61 120 153 64 100 160 75 88 32 63 160 73 132 82 85 82 302 101 54
Character c u l u s .
Milliseconds 350 195 111 456 85 185
WPM Timing
Seconds WPM
2.36 76.4
4.71 76.4
7.07 84.89
9.42 84.04
11.78 89.64
14.14 85.74
16.49 88.77
18.85 92.31
21.2 95.07
23.56 97.79
25.92 98.62
28.27 98.89
30.63 97.55
32.99 97.13
35.34 96.09
37.7 95.18
40.05 93.47
42.41 94.51
44.77 91.95
47.12 92.44
49.48 93.37
51.83 90.52
54.19 91.68
56.55 92.53
58.9 91.27
61.26 91.09
63.61 90.17
65.97 87.86
68.33 86.76
70.68 87.77
73.04 89.05
75.4 89.61
77.75 88.44
80.11 87.48
82.46 87.31
84.82 86.73
87.18 86.45
89.53 87.39
91.89 87.11
94.24 87.6
96.6 87.83
98.96 85.86
101.31 86.35
103.67 86.35
106.02 86.02
108.38 86.92
110.74 87.45
113.09 87.64
115.45 88.45
117.8 88.01