. (moody_k)

Race #1243

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Official speed 61.04 wpm (169.86 seconds elapsed during race)
Without ending ping 61.20 wpm (450 ms delay sending score to TypeRacer’s server)
Timerless 61.44 wpm (669 ms elapsed before first character typed; 168.74 seconds elapsed during race)
Timerless minus one 61.37 wpm, ignoring the first character typed
Race Start August 19, 2023 3:54:17am UTC
Race Finish August 19, 2023 3:57:07am UTC
Outcome No win (3 of 5)
Opponents 2. madara989 (67.86 wpm)
Accuracy 94.9%
Points 164.80
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 oen ne quantity is related to a change in anotehrher. How does the speed of a falling object cahgnchange as a funcionttion of time? HOw ow does the ellevel of water in a barrel channge as a function of hte the amount of liquid poruured into it? WE e see change occurring in ejnearnearly efveryeeverything we obseverrve in the world and universe, and powerful omodern in testrumments help us ssee ee more and more. iNIn this section we interoduce the ideas of average and instantanoueous rates of change, and show that wehtthey are colloselly y related to the slope of a coursve at a point P on the curve. We give precise developments of thseesese important concepts in the necsxxt chapter, but for now we use oan informal approach so you will see hhow they lead unatureally to the main idea of this ahcahngahapter, the limit. The idea of a limit plays a foruundeational orole thorurough ouout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 669 173 434 376 203 173 473 87 126 169 94 123 94 91 237 47 156 128 171 338 33 29 93 205 230
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 129 200 219 186 140 266 156 161 178 198 68 157 58 182 103 114 228 82 167 275 66 63 156 61 116
Character c h a n g e i n o e n - -n -e n e q u a n t
Milliseconds 196 62 94 31 97 76 110 211 116 64 154 109 0 162 368 175 90 441 106 126 636 133 278 347 435
Character i t y i s r e l a t e d t o a c h a n g
Milliseconds 404 122 110 335 180 105 92 139 47 407 105 284 96 152 93 137 17 127 139 140 202 67 77 45 117
Character e i n a n o t e h r -r -h -e h e r . H o w d
Milliseconds 85 78 171 63 88 191 95 61 129 111 27 124 293 162 126 160 33 112 293 123 349 52 108 175 249
Character o e s t h e s p e e d o f a f a l l i n
Milliseconds 157 108 105 124 187 16 62 94 291 164 200 159 171 59 187 76 154 160 77 257 115 132 147 77 102
Character g o b j e c t c a h g n -n -c -a -h -g c h a n g e
Milliseconds 39 186 674 153 323 312 188 190 91 456 76 16 143 0 300 184 0 0 0 373 110 105 0 134 135
Character a s a f u n c i o n t -t -n -o -i t i o n o f
Milliseconds 0 332 164 146 147 82 222 255 177 167 98 8 101 10 343 171 180 159 96 141 46 85 210 234 80
Character t i m e ? H O w - -w -O o w d o e s t h e
Milliseconds 107 156 48 86 113 536 151 430 79 148 113 237 173 134 157 82 173 157 204 126 71 184 148 42 62
Character e l -l -e l e v e l o f w a t e r i n a
Milliseconds 46 418 107 261 102 253 39 134 108 273 165 184 62 127 227 99 186 187 62 170 108 62 78 143 125
Character b a r r e l c h a n n -n g e a s a f u n c
Milliseconds 235 279 188 111 307 132 226 420 124 16 174 668 279 94 46 99 151 202 243 115 79 171 405 186 108
Character t i o n o f h t e - -e -h -t t h e a m o u n
Milliseconds 220 64 0 151 201 167 99 78 155 31 60 97 291 162 155 0 211 61 47 144 348 130 126 186 217
Character t o f l i q u i d p o r u -u -r u r e d i n
Milliseconds 114 118 161 77 90 546 334 239 77 451 111 109 320 802 128 58 349 144 154 99 147 100 185 327 81
Character t o i t ? W E - -E e s e e c h a n g e
Milliseconds 105 109 63 156 93 384 162 156 93 155 401 139 62 159 131 157 161 99 265 47 61 99 57 102 53
Character o c c u r r i n g i n e -e j n e a r -r -j -n -e -a
Milliseconds 652 194 197 183 289 118 168 142 28 160 120 47 78 267 268 132 37 44 62 61 311 158 0 0 0
Character n e a r l y e f v e r y -y -e -f -v -e -r e e -e v e r
Milliseconds 327 94 79 124 187 150 147 240 102 31 62 128 75 219 158 0 0 0 0 470 244 298 140 134 115
Character y t h i n g w e o b s e v e r -r -e -v r v e i
Milliseconds 190 291 299 83 107 43 217 150 86 107 356 219 372 92 287 131 123 171 254 151 79 353 134 171 155
Character n t h e w o r l d a n d u n i v e r s e ,
Milliseconds 109 46 171 78 17 155 328 47 106 149 163 50 167 47 48 108 397 183 123 132 39 291 297 108 186
Character a n d p o w e r f u l o -o m o d e r n i n
Milliseconds 138 98 62 31 93 268 102 134 101 79 270 122 125 164 354 298 174 50 156 237 76 140 162 119 46
Character t e -e -t - s t r u m m -m e n t s h e l p u s
Milliseconds 77 178 118 215 158 144 28 108 327 574 229 86 480 112 91 110 198 127 343 76 185 155 123 158 124
Character s s e e - -e -e -s e e m o r e a n d m o r
Milliseconds 94 278 272 61 121 136 217 155 186 138 40 172 134 178 133 144 58 138 158 48 16 123 147 78 67
Character e . i N -N -i I n t h i s s e c t i o n w e
Milliseconds 81 202 194 120 77 281 146 276 340 172 154 17 108 93 95 186 61 298 201 48 0 63 148 148 80
Character i n t e -e r o d u c e t h e i d e a s o f
Milliseconds 91 172 60 190 159 370 92 107 235 141 171 189 107 266 20 55 125 182 116 150 120 195 172 162 79
Character a v e r a g e a n d i n s t a n t a n o u -u
Milliseconds 130 229 268 126 95 201 198 83 237 363 80 96 132 255 92 290 227 151 205 809 91 219 198 206 242
Character -o e o u s r a t e s o f c h a n g e , a n
Milliseconds 159 124 139 47 186 170 339 100 118 144 158 159 197 17 437 252 76 34 93 76 81 358 154 125 46
Character d s h o w t h a t w e h t -t -h -w -e t h e y
Milliseconds 48 61 279 77 47 125 78 159 28 62 105 33 238 12 49 83 185 137 175 0 216 55 46 110 93
Character a r e c o l -l -o l o s e l l y - -y -l y r e l
Milliseconds 154 90 111 72 287 59 434 192 113 193 148 111 286 157 171 34 107 394 169 185 218 150 240 49 247
Character a t e d t o t h e s l o p e o f a c o
Milliseconds 111 109 102 203 128 143 61 108 80 45 65 29 389 122 630 136 205 153 213 101 108 78 108 260 128
Character -o u r s -s v e a t a p o i n t P o n t
Milliseconds 318 144 92 285 233 47 62 159 196 125 141 109 112 214 65 115 106 31 169 607 86 271 94 139 116
Character h e c u r v e . W e g i v e p r e c i s e
Milliseconds 67 11 107 385 182 74 578 123 217 157 344 101 179 297 62 62 78 108 329 137 515 235 198 350 120
Character d e v e l o p m e n t s o f t h s e e s -s -e
Milliseconds 94 255 197 107 80 184 214 49 285 133 468 108 232 130 150 45 105 405 34 141 16 61 140 243 158
Character -e -s e s e i m p o r t a n t c o n c e p t s
Milliseconds 191 162 106 108 121 235 202 78 145 120 79 202 110 201 169 121 268 32 64 474 214 132 131 234 185
Character i n t h e n e c s -s x -x -c x t c h a p t e r
Milliseconds 138 104 54 155 62 16 105 298 82 187 149 198 136 39 193 237 193 146 386 93 326 132 168 108 137
Character , b u t f o r n o w w e u s e o -o a n
Milliseconds 155 126 155 92 63 132 180 32 485 120 216 94 62 123 125 63 107 266 108 94 123 136 297 64 136
Character i n f o r m a l a p p r o a c h s o y o u
Milliseconds 136 195 78 273 85 94 156 99 179 147 209 121 133 244 144 248 202 94 140 315 111 73 187 118 72
Character w i l l s e e h -h h o w t h e y l e a d
Milliseconds 107 279 48 214 161 109 221 107 203 155 301 339 592 139 140 126 340 0 78 96 92 140 78 72 117
Character u -u n a t u r e -e a l l y t o t h e m a i
Milliseconds 138 171 655 198 142 124 143 121 77 431 66 139 172 138 146 139 73 78 171 31 46 91 175 107 93
Character n i d e a o f t h i s a h -h -a c a h n g -g
Milliseconds 62 126 281 123 171 130 306 168 32 134 114 47 402 115 78 468 26 241 145 65 96 0 168 79 242
Character -n -h -a a -a h a p t e r , t h e l i m i t . T
Milliseconds 136 188 166 218 291 254 87 229 191 130 79 179 119 137 45 62 31 506 66 135 351 140 179 178 224
Character h e i d e a o f a l i m i t p l a y s
Milliseconds 101 93 112 661 72 137 109 154 124 16 139 77 94 311 62 245 264 127 120 308 161 61 110 172 139
Character a f o r u -u -r u n d e -e a t i o n a l o -o r o
Milliseconds 138 109 187 15 138 285 195 147 124 186 144 168 284 305 111 92 16 95 264 116 132 214 315 97 93
Character l e t h o r u -u -r -o r o u g h o u -u -o - o u t
Milliseconds 167 279 167 197 32 153 79 0 336 160 156 115 84 47 372 115 225 159 58 265 157 114 175 71 108
Character c a l c u l u s .
Milliseconds 173 252 89 66 748 143 219 367 107 389
WPM Timing
Seconds WPM
3.4 49.45
6.79 61.82
10.19 71.83
13.59 60.93
16.99 65.7
20.38 65.94
23.78 69.13
27.18 64.91
30.57 63.98
33.97 62.88
37.37 62.3
40.77 63.58
44.16 62.77
47.56 62.57
50.96 61.93
54.35 61.38
57.75 61.3
61.15 60.84
64.55 59.12
67.94 58.46
71.34 59.88
74.74 60.37
78.13 59.59
81.53 59.17
84.93 59.49
88.33 60.32
91.72 60.97
95.12 60.81
98.52 60.54
101.91 61.11
105.31 60.85
108.71 61.04
112.1 60.91
115.5 61.4
118.9 61.26
122.3 61.42
125.69 61.2
129.09 61.45
132.49 61.5
135.88 61.82
139.28 62.12
142.68 61.99
146.08 61.86
149.47 62.46
152.87 61.62
156.27 61.74
159.66 62.23
163.06 61.82
166.46 61.35
169.86 61.04