Rafa (devrafa)

Race #71

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Official speed 59.88 wpm (173.15 seconds elapsed during race)
Without ending ping 59.98 wpm (281 ms delay sending score to TypeRacer’s server)
Timerless 60.07 wpm (259 ms elapsed before first character typed; 172.61 seconds elapsed during race)
Timerless minus one 60.00 wpm, ignoring the first character typed
Race Start February 5, 2025 5:46:44am UTC
Race Finish February 5, 2025 5:49:37am UTC
Outcome No win (3 of 4)
Opponents 1. xocodeine (81.03 wpm)
Accuracy 95.2%
Points 161.68
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 duunderstand how a hchange in one wqquantity is reallated to a change in another. How does to sthe speed of a falling object change ass a a function of time? How does the level of water in anb batrrrel chanbe ge as a function of the amouhnnt oif f kuqluiquid poured inotto its?? We see change ocucurring in nearly everything we observe in the world iand uinniverse, and peowrferful modern instruments hlepjhejelhelp uis us see more and more. In this section we introducte the ideas pof of average an id intastantaneous reatrated os of caahnange, and show that hethey are closely realtrelated to the slope of a curvbe at a point P ON on the curve. We give prescise developments of these important cocncepts in the nect nect xt chapterm, , but for now we use an informal approach so youw will see how they tlead naturally to the maun main idea of hthis chapter, the limit. The idead of a limit plays a foundational role thorroughout clacclaalculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 259 556 255 267 282 211 242 160 81 94 79 79 102 123 135 121 155 151 94 68 128 47 61 83 67
Character e l p s u s d u -u -d u n d e r s t a n d h o
Milliseconds 143 492 243 125 96 154 100 115 255 225 288 114 206 188 71 194 98 160 131 70 132 83 62 96 82
Character w a h -h c h a n g e i n o n e w q -q -w q
Milliseconds 78 61 149 74 237 370 121 272 82 135 71 106 97 95 132 96 61 95 93 69 367 63 340 135 68
Character u a n t i t y i s r e a l -l -a l a t e d t o
Milliseconds 115 126 299 148 109 103 75 172 133 189 78 216 87 65 229 336 156 214 81 364 131 175 55 184 69
Character a c h a n g e i n a n o t h e r . H o w
Milliseconds 100 125 174 196 82 467 129 122 110 142 110 134 266 114 245 123 133 80 76 26 244 96 186 106 144
Character d o e s t o s -s t -t - -o h e s p e e d o
Milliseconds 93 134 72 104 91 55 148 105 81 199 426 223 279 150 144 175 260 164 179 116 229 121 138 50 281
Character f a f a l l i n g o b j e c t c h a n g e
Milliseconds 63 59 118 90 131 135 86 183 110 130 51 111 92 118 95 134 185 174 70 153 122 83 134 81 80
Character a s s a -a - -s a f u n c t i o n o f t
Milliseconds 140 210 11 109 158 102 504 315 185 118 99 248 425 165 186 69 183 53 80 83 68 251 82 65 181
Character i m e ? H o w d o e s t h e l e v e l o
Milliseconds 46 176 104 236 122 294 108 155 111 107 130 83 66 54 173 101 96 100 91 95 156 98 140 120 148
Character f w a t e r i n a n -n b -b b a t r -r -t r r
Milliseconds 68 69 220 151 109 149 63 69 91 135 87 71 558 379 67 386 183 277 166 170 132 293 164 149 144
Character e l c h a n b e - -e -b g e a s a f u n c
Milliseconds 122 119 136 207 119 391 134 134 122 115 335 146 187 83 129 108 142 84 142 107 86 143 110 185 70
Character t i o n o f t h e a m o u h n -n -h n t o i
Milliseconds 186 90 73 105 107 129 68 71 112 86 64 73 100 92 94 176 455 119 358 164 185 78 104 72 0
Character f - -f -i f k u q -k -u -q l u -u i q u i d p o u
Milliseconds 79 66 497 158 180 249 465 327 206 120 395 0 0 246 273 545 326 108 299 174 247 108 310 132 210
Character r e d i n o t -t -o t o i t s ? -? -s ? W e s
Milliseconds 225 160 161 44 129 123 170 185 364 162 92 106 456 128 74 184 250 321 154 222 159 217 171 93 154
Character e e c h a n g e o c u -u c u r r i n g i n
Milliseconds 193 116 64 122 111 340 170 104 145 79 292 215 99 543 109 169 110 249 148 126 102 97 90 52 96
Character n e a r l y e v e r y t h i n g w e o b s e
Milliseconds 442 110 84 56 144 146 155 395 156 126 128 152 169 97 84 141 108 147 121 96 100 176 151 292 292
Character r v e i n t h e w o r l d i -i a n d u i
Milliseconds 144 212 124 117 140 167 79 72 118 70 103 116 173 125 331 124 131 226 307 70 158 69 117 110 195
Character n -n -i n i v e r s e , a n d p e -e o w r f -f -r
Milliseconds 148 386 147 217 223 405 236 91 202 94 320 122 130 92 98 58 327 187 440 202 92 121 237 320 153
Character e r f u l m o d e r n i n s t r u m e n t s
Milliseconds 136 123 187 82 262 152 403 127 104 164 105 140 149 366 131 87 157 132 78 180 78 125 51 130 95
Character h l e p -h -l -e -p j h e -j -h -e j e l -j -e -l h e l p
Milliseconds 291 283 121 153 418 0 0 0 263 0 126 426 0 0 239 80 160 439 0 0 217 93 160 238 161
Character u i s -u -i -s - u s s e e m o r e a n d m
Milliseconds 281 33 56 97 371 0 0 0 323 107 119 122 262 118 106 46 110 59 65 86 136 118 66 85 75
Character o r e . I n t h i s s e c t i o n w e i
Milliseconds 133 21 61 182 85 197 122 54 132 93 80 79 98 274 97 186 157 81 70 103 78 126 86 98 153
Character n t r o d u c t -t e t h e i d e a s p o f
Milliseconds 137 80 150 6 687 96 80 408 262 86 95 68 132 54 69 109 167 152 253 220 178 203 0 78 116
Character -p -o -f - o f a v e r a g e a n i -i - d i n
Milliseconds 387 0 0 0 443 142 126 215 154 298 160 118 163 218 101 171 123 129 286 300 137 8 86 174 108
Character t a -a -t s t a n t a n e o u s r e a t -r -e -a -t r
Milliseconds 158 120 506 171 151 135 92 147 210 328 124 378 262 130 152 56 489 133 151 113 392 0 0 0 187
Character a t e d o -o - -d s o f c a a -a -a h n -n a n g
Milliseconds 428 131 131 193 116 123 302 161 189 94 164 143 599 103 215 114 504 284 137 231 184 323 84 126 68
Character e , a n d s h o w t h a t h e -h -e t h e y
Milliseconds 82 175 97 114 103 85 58 276 39 102 73 68 120 104 54 54 80 130 60 527 0 191 93 67 120
Character a r e c l o s e l y r e a l t -r -e -a -l -t r e
Milliseconds 93 278 81 22 139 172 227 201 67 121 119 289 151 224 56 67 145 79 398 0 0 0 0 174 60
Character l a t e d t o t h e s l o p e o f a c
Milliseconds 341 131 94 163 190 64 241 53 115 150 98 101 70 202 118 518 190 92 168 132 113 159 399 110 557
Character u r v b -b e a t a p o i n t P O N -O -N
Milliseconds 160 109 249 0 471 123 117 293 125 151 273 161 196 151 235 179 86 109 1649 208 373 100 144 397 0
Character - o n t h e c u r v e . W e g i v e p r
Milliseconds 0 240 93 115 83 96 78 68 161 103 110 186 103 190 73 345 125 137 284 144 104 161 93 162 97
Character e s -s c i s e d e v e l o p m e n t s o f t
Milliseconds 236 221 428 85 134 91 149 87 173 178 109 80 133 183 157 204 83 130 89 153 103 258 80 80 208
Character h e s e i m p o r t a n t c o c -c n c e p t s
Milliseconds 235 134 200 96 115 106 174 650 306 105 207 249 95 95 114 246 142 301 490 227 67 155 65 152 120
Character i n t h e n e c t -n -e -c -t - n e c t - -t
Milliseconds 108 212 162 65 106 168 19 440 111 65 184 182 80 444 0 0 0 0 284 80 187 238 91 320 160
Character -c x t c h a p t e r m , - -, -m , b u t f o
Milliseconds 184 30 208 99 186 124 94 182 160 148 62 204 0 107 427 161 155 197 129 133 133 102 88 637 94
Character r n o w w e u s e a n i n f o r m a l
Milliseconds 136 209 97 95 98 74 372 90 96 293 122 64 291 527 117 116 104 94 128 131 91 63 150 125 139
Character a p p r o a c h s o y o u w -w w i l l s e
Milliseconds 189 124 201 101 128 343 189 173 132 278 99 397 65 108 98 293 328 81 67 80 199 149 52 93 159
Character e h o w t h e y t -t l e a d n a t u r a l
Milliseconds 132 41 267 108 109 80 167 98 77 126 107 287 469 212 81 43 367 157 288 116 95 120 105 202 107
Character l y t o t h e m a u n -m -a -u -n - m a i n
Milliseconds 162 115 140 242 76 93 521 123 63 95 219 99 96 79 104 401 0 0 0 0 188 109 106 51 107
Character i d e a o f h -h t h i s c h a p t e r , t
Milliseconds 293 122 212 551 298 146 82 135 241 377 91 107 41 77 65 288 533 82 126 147 138 66 172 96 100
Character h e l i m i t . T h e i d e a d -d o f a
Milliseconds 99 50 82 34 126 197 145 101 142 82 212 95 94 66 117 156 228 214 241 446 79 158 68 82 119
Character l i m i t p l a y s a f o u n d a t i o n
Milliseconds 103 132 200 162 157 101 88 186 190 108 240 186 116 241 95 132 185 144 199 81 424 141 107 84 118
Character a l r o l e t h o r -r -o r o u g h o u t c l
Milliseconds 315 105 113 306 74 178 82 95 167 70 93 161 468 164 77 150 137 659 175 106 147 93 104 199 148
Character a c -c -c -l -a c l a -a -l a l c u l u s .
Milliseconds 122 182 296 243 0 0 226 138 116 467 158 69 134 101 113 209 229 120 133
WPM Timing
Seconds WPM
3.46 65.84
6.93 64.11
10.39 73.93
13.85 67.57
17.31 67.92
20.78 68.15
24.24 69.31
27.7 68.44
31.17 69.31
34.63 72.42
38.09 68.99
41.56 68.73
45.02 67.44
48.48 63.86
51.94 63.07
55.41 62.37
58.87 62.58
62.33 63.34
65.8 64.2
69.26 63.41
72.72 62.37
76.18 61.9
79.65 59.96
83.11 61.94
86.57 62.51
90.04 61.98
93.5 61.35
96.96 60.52
100.42 59.51
103.89 59.95
107.35 59.92
110.81 59.99
114.28 59.85
117.74 59.22
121.2 59.31
124.67 59.58
128.13 59.85
131.59 60
135.05 59.09
138.52 58.82
141.98 59.33
145.44 59.32
148.91 59.72
152.37 59.85
155.83 59.53
159.29 60.12
162.76 60.38
166.22 60.57
169.68 60.47
173.15 59.88