I1 (bbstarfish)

Race #818

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Official speed 63.87 wpm (162.33 seconds elapsed during race)
Without ending ping 63.98 wpm (270 ms delay sending score to TypeRacer’s server)
Timerless 64.20 wpm (554 ms elapsed before first character typed; 161.51 seconds elapsed during race)
Timerless minus one 64.12 wpm, ignoring the first character typed
Race Start October 15, 2023 8:28:48pm UTC
Race Finish October 15, 2023 8:31:30pm UTC
Outcome No win (4 of 5)
Opponents 2. candlelearner (68.12 wpm)
3. firesforsale (66.59 wpm)
Accuracy 97.2%
Points 172.44
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 understnand how a change in one quantity is reallated to a change in another. How does the speed of a falling object change as a function of time? How dowes the level of water in a barrel change as una function of the amount of liquid poured into it? We see change occurring in nearly everythintg we observie in the wold rld and universe, and pwerowerful modern instruments help us see more and more. In this ecsection we introduce the ideas of average and instantaneiouous rates of change, and shwoow that they are lclosely related to the splpoeopope of a cureveve at a ponint P on the curve. We give precise developments of these important concepts in the netxt chapter, but for now we use an infroormal approach so you will se howe how they elead naturally to the main idea of this chapter, the limit. The iedea of a limit polalays a foundationsal role thorroughtout callculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 554 134 184 451 106 210 166 82 120 231 217 84 185 140 437 78 139 220 117 165 101 103 64 161 175
Character e l p s u s u n d e r s t n -n a n d h o w
Milliseconds 147 131 166 165 85 160 100 124 154 198 98 152 95 221 136 159 622 99 167 185 139 209 118 83 82
Character a c h a n g e i n o n e q u a n t i t y
Milliseconds 136 118 159 97 126 116 176 108 132 134 326 199 153 104 135 111 554 124 407 299 172 100 107 155 244
Character i s r e a l -l -a l a t e d t o a c h a n g
Milliseconds 175 100 95 152 84 138 179 411 143 235 143 170 170 173 106 200 120 136 161 216 186 88 142 105 125
Character e i n a n o t h e r . H o w d o e s t h
Milliseconds 81 115 118 139 105 107 108 106 184 125 164 65 313 105 285 98 96 133 151 62 170 208 158 274 116
Character e s p e e d o f a f a l l i n g o b j e
Milliseconds 86 515 160 125 112 146 222 114 187 114 119 135 133 192 158 111 120 127 151 133 76 268 241 241 156
Character c t c h a n g e a s a f u n c t i o n o
Milliseconds 176 199 126 260 98 134 148 146 100 167 185 196 116 71 364 190 101 268 73 233 42 35 107 171 319
Character f t i m e ? H o w d o w -w e s t h e l e
Milliseconds 74 127 156 76 151 94 498 140 365 80 101 105 130 106 164 479 86 170 81 174 94 86 101 192 81
Character v e l o f w a t e r i n a b a r r e l
Milliseconds 148 98 129 114 160 64 122 119 135 132 215 203 175 200 145 117 124 89 566 200 134 141 189 154 150
Character c h a n g e a s u n -n -u a f u n c t i o n
Milliseconds 194 118 68 170 101 72 173 128 194 121 319 190 353 106 136 119 302 103 247 269 225 54 72 110 155
Character o f t h e a m o u n t o f l i q u i d p
Milliseconds 162 86 100 167 92 74 109 145 129 132 111 216 122 80 136 122 94 187 53 247 144 368 141 277 546
Character o u r e d i n t o i t ? W e s e e c h a
Milliseconds 154 272 286 312 175 150 159 151 149 94 404 219 104 362 145 353 110 170 284 148 120 149 167 105 98
Character n g e o c c u r r i n g i n n e a r l y e
Milliseconds 163 154 54 140 241 127 141 191 268 156 117 132 107 113 134 131 117 242 105 102 157 162 180 113 215
Character v e r y t h i n t -t g w e o b s e r v i -i e
Milliseconds 152 103 119 80 235 93 99 172 534 429 85 230 201 108 150 258 109 428 137 96 288 236 505 75 150
Character i n t h e w o l d - -d -l r l d a n d u n
Milliseconds 110 124 113 121 95 103 67 164 68 226 149 165 321 123 126 131 120 139 120 109 55 98 68 176 317
Character i v e r s e , a n d p w e r -r -e -w o w e r f u
Milliseconds 136 136 321 96 184 164 419 84 204 104 88 99 224 192 91 130 437 130 161 217 86 146 97 295 99
Character l m o d e r n i n s t r u m e n t s h e l p
Milliseconds 215 122 310 105 185 161 114 235 156 179 167 110 143 200 94 256 154 95 128 207 113 137 117 131 144
Character u s s e e m o r e a n d m o r e . I n
Milliseconds 135 200 88 142 201 200 136 98 250 172 132 117 159 168 94 124 98 183 99 86 53 233 58 243 132
Character t h i s e c -c -e s e c t i o n w e i n t r
Milliseconds 180 151 84 123 115 111 338 218 273 109 69 150 242 238 69 53 79 187 133 116 140 127 114 136 163
Character o d u c e t h e i d e a s o f a v e r a g
Milliseconds 144 144 130 136 184 106 140 68 100 109 141 128 165 89 176 152 116 103 102 327 140 181 102 190 145
Character e a n d i n s t a n t a n e i o u -u -o -i o u s
Milliseconds 100 140 199 113 99 118 113 123 94 152 93 149 153 385 113 616 265 94 107 332 109 151 184 73 143
Character r a t e s o f c h a n g e , a n d s h w
Milliseconds 280 165 111 155 131 218 106 156 105 120 349 120 58 187 110 6 329 38 196 108 93 100 260 117 132
Character o -o -w o w t h a t t h e y a r e l -l c l o
Milliseconds 164 344 88 178 38 128 98 61 95 83 130 126 48 90 147 263 97 185 66 113 308 481 218 115 134
Character s e l y r e l a t e d t o t h e s p -p l p
Milliseconds 61 155 429 407 198 219 89 292 130 167 274 195 110 133 51 73 118 89 76 107 139 465 421 201 195
Character o e -e -o o p -p -o -p o p e o f a c u r e v e -e
Milliseconds 0 271 356 107 221 188 223 105 134 373 144 188 177 183 80 100 105 103 159 143 124 74 237 132 263
Character -v -e v e a t a p o n -n i n t P o n t h
Milliseconds 131 131 157 183 125 107 169 374 75 328 334 111 275 470 219 75 184 138 307 197 146 137 110 125 93
Character e c u r v e . W e g i v e p r e c i s e
Milliseconds 61 110 386 158 160 306 137 339 99 552 215 185 331 149 102 75 153 191 125 111 271 105 329 140 129
Character d e v e l o p m e n t s o f t h e s e i m p
Milliseconds 213 175 161 103 169 159 108 266 121 119 111 190 119 155 79 104 113 84 121 294 137 137 196 186 148
Character o r t a n t c o n c e p t s i n t h e n e
Milliseconds 171 98 175 187 103 113 89 191 97 106 268 169 203 147 181 151 129 121 111 128 87 88 103 178 89
Character t -t x t c h a p t e r , b u t f o r n o w
Milliseconds 418 502 105 225 136 317 128 0 585 247 147 102 628 69 286 137 205 153 141 107 92 113 154 77 69
Character w e u s e a n i n f r o -o -r o r m a l a
Milliseconds 150 165 113 119 182 66 159 275 107 120 590 305 116 180 173 346 272 505 225 353 115 275 109 107 230
Character p p r o a c h s o y o u w i l l s e h o
Milliseconds 112 133 152 97 351 201 133 222 137 90 82 215 137 33 134 132 117 151 129 120 113 183 111 123 91
Character w -w -o -h - e h o w t h e y e -e l e a d n a
Milliseconds 95 317 104 131 181 190 127 242 87 104 116 386 88 111 102 79 267 368 243 118 141 183 142 256 117
Character t u r a l l y t o t h e m a i n i d e a
Milliseconds 150 140 844 151 183 117 206 58 204 82 62 136 115 94 122 230 92 108 183 139 276 134 189 98 161
Character o f t h i s c h a p t e r , t h e l i m i
Milliseconds 117 106 86 129 37 114 86 116 284 129 105 173 167 154 84 255 49 287 73 175 115 162 49 258 151
Character t . T h e i e -e d e a o f a l i m i t
Milliseconds 180 216 84 452 199 99 148 237 712 414 76 160 87 291 123 94 101 108 77 294 311 202 146 154 125
Character p o l a -a -l -o l a y s a f o u n d a t i o n s
Milliseconds 238 18 166 101 371 94 117 300 193 125 376 193 415 115 153 139 43 235 83 583 152 111 68 62 345
Character -s a l r o l e t h o r -r -o r o u g h t -t o u t
Milliseconds 547 69 166 124 308 82 190 77 119 242 74 129 186 298 103 139 126 86 134 117 83 449 224 57 119
Character c a l -l l c u l u s .
Milliseconds 122 274 166 343 414 561 219 129 468 149 147 157
WPM Timing
Seconds WPM
3.25 51.75
6.49 70.23
9.74 69
12.99 66.53
16.23 65.05
19.48 68.38
22.73 69.17
25.97 69.77
29.22 70.64
32.47 70.23
35.71 70.56
38.96 69.92
42.21 70.8
45.45 69.96
48.7 69.24
51.95 69.77
55.19 69.79
58.44 68.38
61.69 68.48
64.93 67.64
68.18 67.24
71.43 67.88
74.67 68.78
77.92 68.53
81.16 69.19
84.41 68.81
87.66 68.58
90.9 68.91
94.15 68.32
97.4 68.01
100.64 66.89
103.89 66.18
107.14 65.97
110.38 65.66
113.63 65.9
116.88 66.43
120.12 66.23
123.37 65.95
126.62 66.15
129.86 65.51
133.11 65.54
136.36 65.21
139.6 65.24
142.85 65.69
146.1 65.79
149.34 65.41
152.59 64.88
155.84 64.61
159.08 64.49
162.33 63.87