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Race #12124

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Official speed 62.23 wpm (166.61 seconds elapsed during race)
Without ending ping 62.37 wpm (379 ms delay sending score to TypeRacer’s server)
Timerless 62.92 wpm (1,442 ms elapsed before first character typed; 164.79 seconds elapsed during race)
Timerless minus one 62.84 wpm, ignoring the first character typed
Race Start December 4, 2024 1:47:57pm UTC
Race Finish December 4, 2024 1:50:44pm UTC
Outcome No win (4 of 5)
Opponents 1. str4tos (91.71 wpm)
2. samy_mohsen (84.43 wpm)
3. andystarr (70.37 wpm)
Accuracy 94.7%
Points 168.02
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 totol that haelpes us undrerstand how a change in one quantity is realilated to a chnage ange oin another. Hoew does the speed on af a falling object change as a functinon of time? How does the level of water ina b a barrle el rel change saas a function of the amount of liquid poured into tittiit? We see change uoccurring in nearely ly everything we observe i the nin the world iand unvieriversem,l and and ooiwopowerful modern insturrutmemments heolp us see more and mreore. In this section we introduce the ideas nof average and isnstantaneous reates of change, and show that thye aey are colosely related ot thto the slpe ope of tha curve ata . a point P on the curve,. We give precise developments of these important concepts in the next chanperpeter, but for now we use an informal approach so you will see how they lead naturally to the main idea of this chnpaper, ter, the ilimit. The idea of a limit plays a foundeaational rola te thourouhgghout calcuslus.
Timing
Character C a l c u l u s i s a t o t -t o l t h a t
Milliseconds 1442 100 171 153 235 163 147 117 85 52 99 67 77 76 164 154 93 410 402 195 194 235 77 115 7
Character h a -a e l p e -e s u s u n d r -r e r s t a n
Milliseconds 51 52 178 531 58 133 141 107 415 100 87 111 98 171 866 138 51 260 354 65 88 149 83 77 70
Character d h o w a c h a n g e i n o n e q u a
Milliseconds 102 137 127 43 68 83 151 122 137 46 106 64 110 98 93 231 136 95 65 122 94 73 247 52 553
Character n t i t y i s r e a l i -i -l -a l a t e d t o
Milliseconds 189 715 157 289 81 47 153 129 32 150 42 80 78 68 309 106 86 465 68 133 55 165 61 170 66
Character a c h n a g e - -e -g -a -n a n g e o -o i n
Milliseconds 61 76 109 136 134 150 19 111 108 178 185 105 218 262 132 185 112 105 60 119 83 291 169 137 53
Character a n o t h e r . H o e -e w d o e s t h e s
Milliseconds 114 91 65 109 42 119 50 230 66 181 103 271 276 57 125 255 131 55 127 103 110 38 90 96 216
Character p e e d o n a -a - -n f a f a l l i n g o
Milliseconds 98 135 97 487 77 71 229 62 110 361 106 195 123 160 73 82 555 113 113 108 162 104 145 32 285
Character b j e c t c h a n g e a s a f u n c t i n
Milliseconds 150 184 47 201 169 55 411 77 123 32 60 119 123 254 133 95 35 93 136 81 154 111 187 5 310
Character -n o n o f t i m e ? H o w d o e s t h e
Milliseconds 404 152 117 109 38 102 98 249 102 119 64 252 81 196 187 149 103 166 99 67 119 96 74 78 59
Character l e v e l o f w a t e r i n a b - -b -
Milliseconds 91 82 66 203 47 135 22 256 133 73 335 137 141 123 91 51 76 147 86 24 207 8 309 102 198
Character -a a b a r r l e - -e -l -r e l - -l -e r e l
Milliseconds 231 186 164 249 219 83 182 133 89 27 173 295 218 81 101 170 109 49 262 221 368 104 249 87 43
Character c h a n g e s a -a -s a s a f u n c t i o n
Milliseconds 189 99 103 31 84 94 138 534 131 203 199 116 134 66 68 85 182 89 158 63 173 31 39 129 67
Character o f t h e a m o u n t o f l i q u i d p
Milliseconds 98 184 92 109 45 60 76 351 63 44 219 240 331 170 67 154 26 136 80 127 244 64 119 116 455
Character o u r e d i n t o t i t -t -i -t t i -i -t i t ?
Milliseconds 174 185 138 82 203 66 217 125 159 126 82 50 107 167 209 86 183 188 66 412 88 201 32 284 184
Character W e s e e c h a n g e u -u o c c u r r i n g
Milliseconds 188 360 203 132 193 135 127 135 88 72 68 100 99 78 319 353 151 136 170 43 258 515 143 104 107
Character i n n e a r e l y - -y -l -e l y e v e r y t
Milliseconds 68 138 135 87 277 96 87 68 71 68 144 51 323 124 192 444 273 145 59 141 183 62 88 42 744
Character h i n g w e o b s e r v e i t h e - -e -h
Milliseconds 99 15 134 81 98 90 100 113 382 132 223 99 49 300 282 241 140 219 63 51 63 94 278 99 102
Character -t - -i n -n i n t h e w o r l d i -i a n d u
Milliseconds 93 125 131 542 310 197 145 74 87 25 63 87 104 136 114 165 150 67 131 277 126 35 154 116 110
Character n v i e r -r -e -i -v i v e r s e m -m , l a n d -
Milliseconds 171 66 6 183 120 223 111 222 119 331 116 172 39 141 113 166 373 33 23 168 107 82 128 53 359
Character -d -n -a - -l a n d o o i w -w -i -o -o o -o p o w e r
Milliseconds 210 217 104 130 398 168 117 43 118 17 136 101 63 20 275 96 215 167 352 419 191 122 97 52 28
Character f u l m o d e r n i n s t u r -r -u r u t m -m -t
Milliseconds 258 65 158 104 221 42 228 164 83 130 61 239 218 119 129 165 158 301 111 721 131 150 129 358 194
Character e m -m -e m e n t s h e o -o l p u s s e e m
Milliseconds 151 85 280 120 188 59 168 94 156 189 458 122 165 598 169 143 127 110 99 83 304 194 107 95 89
Character o r e a n d m r e -e -r o r e . I n t h i s
Milliseconds 68 69 72 87 251 117 100 49 102 131 63 348 163 231 102 94 446 70 384 299 84 193 52 37 99
Character s e c t i o n w e i n t r o d u c e t h e
Milliseconds 96 158 66 205 194 71 57 184 75 94 85 105 437 111 105 114 112 258 123 118 54 99 298 114 171
Character i d e a s n -n o f a v e r a g e a n d i
Milliseconds 127 141 148 171 89 147 87 221 399 169 47 121 135 199 118 124 176 65 113 108 228 100 82 65 169
Character s -s n s t a n t a n e o u s r e -e a t e s o f
Milliseconds 453 366 151 57 116 138 171 434 214 166 373 132 90 138 66 430 71 378 70 85 83 199 103 96 137
Character c h a n g e , a n d s h o w t h a t t h
Milliseconds 82 158 93 104 47 44 83 137 154 128 19 140 22 154 101 48 91 194 83 71 67 45 63 140 21
Character y e a -a - -e -y e y a r e c o -o l o s e l y
Milliseconds 160 32 32 192 202 308 234 120 298 138 55 82 60 68 95 234 171 432 181 139 53 106 51 133 68
Character r e l a t e d o t t h -h -t - -t -o t o t h e
Milliseconds 150 53 128 137 109 70 187 59 209 0 117 147 35 254 156 155 203 115 450 79 89 59 56 88 80
Character s l p e - -e -p o p e o f t h -h -t a c u r v
Milliseconds 205 129 150 145 140 327 105 579 193 58 184 205 112 146 88 148 96 278 97 199 283 697 161 117 489
Character e a t a . - -. -a a p o i n t P o n t
Milliseconds 88 111 254 129 166 13 208 280 99 139 431 135 65 120 144 150 186 81 116 418 133 306 257 69 87
Character h e c u r v e , -, . W e g i v e p r e c i
Milliseconds 50 96 187 163 109 93 189 66 297 350 216 84 114 100 112 217 88 129 32 68 742 81 79 272 132
Character s e d e v e l o p m e n t s o f t h e s e
Milliseconds 105 126 33 220 163 273 213 148 220 112 235 80 132 59 161 114 354 135 34 239 121 53 204 82 60
Character i m p o r t a n t c o n c e p t s i n t h e
Milliseconds 505 136 94 58 460 256 112 34 154 98 217 61 143 144 400 139 112 133 52 106 158 66 54 64 50
Character n e x t c h a n p e r -r -e -p -n p e -e t e r ,
Milliseconds 94 198 59 215 167 69 172 115 83 84 246 113 100 206 234 112 168 388 176 380 90 131 80 59 133
Character b u t f o r n o w w e u s e a n i n f
Milliseconds 161 186 142 106 285 99 71 79 484 29 68 83 130 104 106 153 92 96 71 191 124 34 88 216 142
Character o r m a l a p p r o a c h s o y o u w i l
Milliseconds 104 64 73 98 81 86 240 114 265 328 103 118 168 145 50 251 62 91 365 56 87 75 75 126 144
Character l s e e h o w t h e y l e a d n a t u r
Milliseconds 135 76 43 122 130 118 164 58 123 79 397 78 51 99 57 138 65 98 107 97 178 131 174 85 128
Character a l l y t o t h e m a i n i d e a o f
Milliseconds 73 30 150 156 27 372 79 63 69 48 87 85 120 113 70 168 96 441 110 183 96 152 101 272 126
Character t h i s c h n -n p -p a p e r , - -, -r -e t e r ,
Milliseconds 108 78 47 52 94 139 62 158 472 189 439 131 81 142 59 98 156 249 118 93 107 449 152 50 99
Character t h e i -i l i m i t . T h e i d e a o f
Milliseconds 131 117 50 60 133 237 302 178 124 498 81 109 312 45 291 312 82 72 134 199 263 249 96 98 161
Character a l i m i t p l a y s a f o u n d e a -a
Milliseconds 23 118 43 89 105 159 77 77 115 141 150 99 132 270 113 96 56 234 105 278 136 28 219 316 218
Character -e a t i o n a l r o l a t -t - -a e t h o u -u
Milliseconds 97 483 186 161 121 152 105 112 80 326 108 149 167 166 181 239 300 169 147 132 82 84 392 43 417
Character -o r o u h g -g -h g h o u t c a l c u s -s l u s .
Milliseconds 104 163 149 19 284 282 211 120 151 131 29 123 60 143 213 117 62 161 156 304 434 189 247 115 115
WPM Timing
Seconds WPM
3.33 57.62
6.66 50.42
10 56.42
13.33 61.22
16.66 63.38
19.99 60.02
23.33 64.31
26.66 62.12
29.99 65.22
33.32 66.26
36.65 67.77
39.99 63.92
43.32 63.44
46.65 66.11
49.98 65.78
53.31 65.05
56.65 65.03
59.98 63.62
63.31 63.31
66.64 62.48
69.98 61.74
73.31 59.75
76.64 60.13
79.97 58.07
83.3 58.05
86.64 58.31
89.97 59.49
93.3 59.94
96.63 59.98
99.96 60.62
103.3 61.22
106.63 61.22
109.96 60.35
113.29 59.84
116.63 59.58
119.96 59.82
123.29 60.05
126.62 60.37
129.95 61.22
133.29 60.68
136.62 61.49
139.95 62.08
143.28 63.06
146.61 63.84
149.95 62.9
153.28 62.87
156.61 63.44
159.94 63.17
163.28 62.4
166.61 62.23