Ben (b5mith)

Race #1388

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Official speed 69.45 wpm (149.29 seconds elapsed during race)
Without ending ping 69.59 wpm (295 ms delay sending score to TypeRacer’s server)
Timerless 69.78 wpm (406 ms elapsed before first character typed; 148.59 seconds elapsed during race)
Timerless minus one 69.70 wpm, ignoring the first character typed
Race Start October 1, 2023 1:33:21am UTC
Race Finish October 1, 2023 1:35:50am UTC
Outcome No win (3 of 5)
Opponents 1. dalinar_ (82.55 wpm)
Accuracy 98.0%
Points 187.52
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 Calsulculus is ta 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 cchahange as a function fo of time? How does the level of water in a barrel change as a function of the amount ofl liquid ouprououred into it? We see change occurreinging in nearly everything we observe in the world and universe, and pwerowerful modern instruments help us see more and more. In this esection we introduce the ideas of average and instantaneous rates of change, and show that they are closely related to the slpope of ta curve at a point P on the curve. We bvgive precise developments of these important concepts in the next schapter, but for now we use an informal approach so you will see how they lead natualrally to the main idea of this chapter, the limit. The idea of a limit plays a foundational role through out calculues.
Timing
Character C a l s u l -l -u -s c u l u s i s t -t a t o o
Milliseconds 406 200 168 256 96 272 274 126 149 321 380 336 196 184 131 153 112 85 131 322 106 137 234 73 146
Character l t h a t h e l p s u s u n d e r s t a n
Milliseconds 146 122 135 132 31 55 89 168 104 168 160 160 90 246 136 111 234 232 110 145 96 224 46 77 190
Character d h o w a c h a n g e i n o n e q u a
Milliseconds 138 126 135 88 108 129 156 95 192 111 121 105 143 72 151 179 101 80 153 404 148 158 536 187 119
Character n t i t y i s r e l a t e d t o a c h a
Milliseconds 281 247 121 155 170 431 203 125 131 367 69 163 165 220 95 216 119 177 47 123 123 79 221 108 99
Character n g e i n a n o t h e r . H o w d o e s
Milliseconds 136 121 57 129 139 58 129 127 154 131 165 113 60 56 170 124 319 302 127 145 135 87 106 79 101
Character t h e s p e e d o f a f a l l i n g o b
Milliseconds 195 137 127 62 211 127 172 199 221 159 177 75 122 118 110 304 63 196 152 145 242 67 77 171 165
Character j e c t c c h a -a -h -c h a n g e a s a f u
Milliseconds 356 260 273 192 222 374 131 153 195 302 127 139 193 100 185 268 69 163 179 79 178 62 102 168 134
Character n c t i o n f o - -o -f o f t i m e ? H o w
Milliseconds 216 84 119 89 81 80 159 213 0 141 366 145 153 253 66 111 141 67 182 57 198 195 470 137 146
Character d o e s t h e l e v e l o f w a t e r
Milliseconds 135 208 80 122 49 110 180 100 121 66 196 136 129 65 120 112 142 105 22 223 98 257 127 56 130
Character i n a b a r r e l c h a n g e a s a f
Milliseconds 120 106 120 116 82 171 221 287 143 62 336 283 306 106 112 211 234 39 283 217 26 177 97 87 329
Character u n c t i o n o f t h e a m o u n t o f l
Milliseconds 231 260 189 143 82 94 60 170 156 128 52 138 100 117 43 221 156 153 98 456 203 154 165 91 179
Character -l l i q u i d o u -u -o p r o u -u -o -r o u r e d
Milliseconds 402 152 128 212 333 134 243 385 139 176 152 446 506 239 731 96 61 457 145 303 246 83 299 167 202
Character i n t o i t ? W e s e e c h a n g e o
Milliseconds 115 184 144 113 77 122 312 126 219 183 249 182 71 163 183 137 126 186 87 113 96 107 51 128 117
Character c c u r r e i n g -g -n -i -e i n g i n n e a r l
Milliseconds 182 134 128 145 151 40 122 188 52 254 136 163 159 238 233 41 110 80 89 119 240 66 87 216 120
Character y e v e r y t h i n g w e o b s e r v e i
Milliseconds 167 82 147 136 68 140 144 147 132 19 266 41 142 121 49 150 204 148 319 97 96 237 272 155 129
Character n t h e w o r l d a n d u n i v e r s e ,
Milliseconds 137 112 96 112 95 47 183 74 121 134 154 158 88 145 88 95 176 208 146 166 130 175 264 63 214
Character a n d p w e r -r -e -w o w e r f u l m o d e r
Milliseconds 152 162 146 103 73 174 205 100 105 399 138 158 200 73 65 59 199 130 234 127 175 81 191 192 68
Character n i n s t r u m e n t s h e l p u s s e e
Milliseconds 338 155 157 171 104 128 249 665 446 145 127 109 155 208 234 78 125 115 112 168 105 120 368 208 128
Character m o r e a n d m o r e . I n t h i s e
Milliseconds 95 149 64 125 46 97 95 144 59 80 190 46 153 68 137 128 331 198 163 24 202 98 204 263 305
Character -e s e c t i o n w e i n t r o d u c e t h e
Milliseconds 364 58 78 211 208 88 63 105 158 123 72 127 200 176 145 140 476 439 153 175 358 175 147 72 96
Character i d e a s o f a v e r a g e a n d i n s
Milliseconds 84 173 164 188 92 154 146 154 111 119 271 195 210 50 217 228 70 110 162 150 90 82 165 180 144
Character t a n t a n e o u s r a t e s o f c h a n g
Milliseconds 139 105 479 330 30 268 234 686 93 321 157 226 55 197 90 73 280 217 112 88 216 59 148 114 118
Character e , a n d s h o w t h a t t h e y a r e
Milliseconds 59 161 76 276 141 103 76 149 108 69 67 115 163 125 30 76 111 166 109 125 95 96 146 127 63
Character c l o s e l y r e l a t e d t o t h e s
Milliseconds 115 158 90 152 138 304 172 181 190 173 67 103 117 166 75 416 166 154 64 81 142 112 97 46 184
Character l p -p o p e o f t -t a c u r v e a t a
Milliseconds 185 313 473 208 104 239 379 309 73 55 152 387 117 199 432 137 121 367 78 160 187 207 148 48 118
Character p o i n t P o n t h e c u r v e . W e
Milliseconds 238 121 374 338 46 255 344 156 151 143 112 144 98 102 40 219 165 89 295 75 178 123 224 192 108
Character b v -v -b g i v e p r e c i s e d e v e l o p m
Milliseconds 267 63 353 197 147 194 151 40 195 501 112 57 326 166 215 89 199 275 178 190 40 169 207 185 487
Character e n t s o f t h e s e i m p o r t a n t c
Milliseconds 110 103 141 63 151 162 95 93 78 98 162 201 55 154 111 176 92 159 336 329 99 265 153 133 257
Character o n c e p t s i n t h e n e x t s -s c h a
Milliseconds 79 154 118 262 159 165 201 188 353 137 108 131 56 167 0 201 49 241 81 103 425 362 293 120 114
Character p t e r , b u t f o r n o w w e u s e
Milliseconds 101 407 153 55 145 104 184 103 109 59 161 98 63 112 189 69 132 182 364 54 139 182 96 82 119
Character a n i n f o r m a l a p p r o a c h s o y
Milliseconds 243 126 120 114 179 154 114 80 167 94 157 161 138 154 100 251 399 177 301 194 144 218 91 97 294
Character o u w i l l s e e h o w t h e y l e a d
Milliseconds 84 97 95 208 94 165 110 112 139 180 170 69 141 54 87 130 102 139 59 153 123 175 102 73 176
Character n a t u a l -l -a r a l l y t o t h e m a i
Milliseconds 143 161 119 170 155 156 171 309 128 110 64 131 132 159 120 203 65 119 126 89 140 0 203 98 112
Character n i d e a o f t h i s c h a p t e r , t
Milliseconds 143 98 247 207 149 51 158 165 135 15 145 111 98 148 137 190 109 155 27 681 200 78 210 98 262
Character h e l i m i t . T h e i d e a o f a l
Milliseconds 103 128 32 169 81 239 95 184 139 158 233 134 92 90 115 128 145 94 170 159 73 86 163 110 207
Character i m i t p l a y s a f o u n d a t i o n a l
Milliseconds 90 303 114 212 146 152 192 103 161 161 160 100 117 176 118 88 208 252 88 179 98 80 75 380 249
Character r o l e t h r o u g h - o u t c a l c u l
Milliseconds 206 242 101 250 92 112 212 87 153 84 89 227 199 267 390 222 83 143 148 300 87 126 137 146 220
Character u e -e s .
Milliseconds 375 306 331 82 134
WPM Timing
Seconds WPM
2.99 24.11
5.97 50.24
8.96 61.63
11.94 64.31
14.93 63.5
17.91 68.32
20.9 71.2
23.89 71.34
26.87 67.43
29.86 67.52
32.84 67.96
35.83 70.33
38.81 69.87
41.8 70.62
44.79 69.4
47.77 66.06
50.76 64.78
53.74 65.87
56.73 65.36
59.71 66.52
62.7 67.56
65.69 66.86
68.67 67.28
71.66 66.98
74.64 67.68
77.63 67.86
80.62 67.58
83.6 68.04
86.59 67.35
89.57 67.79
92.56 68.97
95.54 69.33
98.53 68.32
101.52 68.09
104.5 68.32
107.49 67.65
110.47 67.78
113.46 68.01
116.44 68.12
119.43 68.02
122.42 68.42
125.4 68.52
128.39 69.07
131.37 69.06
134.36 69.58
137.34 69.64
140.33 69.95
143.32 70.08
146.3 69.8
149.29 69.45