Long (phamlong0711)

Race #4577

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Official speed 71.32 wpm (145.37 seconds elapsed during race)
Without ending ping 71.49 wpm (342 ms delay sending score to TypeRacer’s server)
Timerless 71.58 wpm (192 ms elapsed before first character typed; 144.84 seconds elapsed during race)
Timerless minus one 71.50 wpm, ignoring the first character typed
Race Start October 14, 2023 1:56:11pm UTC
Race Finish October 14, 2023 1:58:37pm UTC
Outcome No win (2 of 4)
Opponents 4. hoenchioma (68.63 wpm)
Accuracy 97.5%
Points 192.56
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 undertsstyand and how a change in one quantity is related to a change inm a another. How does the speed of a falling object change as a function ioif f 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 mordern instruments help us see more and more. In this section we introduce the ideas of average nad and instantagneoeous rates of change, and sohhow that they are closely related to the slope of a curve at a point P on the curve. We give prescise eddevelopments of these important concepstts in the netxt xt chapter, but for now we use an infrormal approachj h so you will see how they lead naturally to the man idin idea of this chapeter, the limit,. The idea of a limit plays a foundational role trhrtououghtout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 192 419 111 409 306 193 189 110 58 128 124 60 130 77 165 74 186 185 74 85 131 56 86 59 158
Character e l p s u s u n d e r t s -s -t s t y a n d -
Milliseconds 75 101 95 74 148 236 112 104 297 93 165 196 81 234 83 489 160 64 56 17 70 58 110 133 309
Character -d -n -a -y a n d h o w a c h a n g e i n o
Milliseconds 137 185 152 184 168 132 127 156 366 76 104 67 139 120 121 118 69 122 100 45 87 225 208 137 256
Character n e q u a n t i t y i s r e l a t e d t o
Milliseconds 136 135 104 242 115 119 246 361 104 156 184 99 190 149 108 181 58 152 119 88 62 171 135 84 108
Character a c h a n g e i n m a -a - -m a n o t h e
Milliseconds 81 200 118 117 103 87 409 101 66 192 271 191 6 16 176 322 177 168 65 174 73 137 136 133 99
Character r . H o w d o e s t h e s p e e d o f
Milliseconds 61 218 74 272 157 98 100 127 94 98 95 112 111 94 69 99 209 149 181 148 152 115 334 105 105
Character a f a l l i n g o b j e c t c h a n g e a
Milliseconds 87 122 132 80 78 203 186 51 77 92 154 119 127 81 56 218 83 154 97 89 144 184 80 176 129
Character s a f u n c t i o n i -i o i f - -f -i f t
Milliseconds 135 161 110 120 47 153 194 61 176 82 79 62 130 474 317 122 0 86 40 1363 171 189 106 81 124
Character i m e ? H o w d o e s t h e l e v e l o
Milliseconds 57 194 68 371 270 199 133 126 94 414 98 121 80 91 116 111 83 105 190 104 128 87 219 284 344
Character f w a t e r i n a b a r r e l c h a n g
Milliseconds 112 89 176 127 164 190 96 119 174 128 42 123 102 231 161 456 153 105 277 208 185 110 81 121 109
Character e a s a f u n c t i o n o f t h e a m
Milliseconds 34 338 135 89 109 105 112 160 111 171 49 183 67 77 92 99 110 137 96 415 90 88 80 152 95
Character o u n t o f l i q u i d p o u r e d i n t
Milliseconds 105 168 198 89 96 138 118 89 366 306 226 196 62 332 206 292 406 207 96 128 198 96 154 112 97
Character o i t ? W e s e e c h a n g e o c c u r
Milliseconds 94 88 159 202 377 192 111 209 207 98 173 163 67 99 80 87 140 82 66 306 320 86 153 160 102
Character r i n g i n n e a r l y e v e r y t h i n g
Milliseconds 492 119 95 131 83 164 144 182 337 80 85 87 397 96 128 280 161 124 98 112 200 89 104 157 71
Character w e o b s e r v e i n t h e w o r l d
Milliseconds 114 223 83 134 259 74 372 81 59 271 192 197 302 121 87 61 142 53 104 142 138 98 118 75 143
Character a n d u n i v e r s e , a n d p o w e r f u
Milliseconds 142 96 112 66 272 111 143 162 194 82 229 56 366 105 320 143 90 75 291 184 101 84 41 197 160
Character l m o r -r d e r n i n s t r u m e n t s h e
Milliseconds 240 88 233 104 151 346 68 156 89 199 176 473 76 163 103 439 153 365 92 90 74 106 144 336 96
Character l p u s s e e m o r e a n d m o r e .
Milliseconds 56 97 88 183 96 105 247 240 160 73 104 94 42 48 115 352 94 78 101 131 40 100 53 149 51
Character I n t h i s s e c t i o n w e i n t r o d
Milliseconds 225 232 149 139 94 89 119 120 152 50 168 190 70 83 103 104 205 24 223 198 115 286 67 115 263
Character u c e t h e i d e a s o f a v e r a g e
Milliseconds 169 113 71 148 188 111 74 135 287 63 196 74 147 164 174 136 108 315 167 176 100 256 125 58 134
Character n a d -n -a -d - a n d i n s t a n t a g -g n e -e
Milliseconds 266 93 121 113 390 0 0 0 146 136 87 123 150 104 150 63 155 150 463 298 240 582 122 215 345
Character o -o e o u s r a t e s o f c h a n g e , a
Milliseconds 157 453 123 83 199 115 131 210 90 168 65 150 151 224 86 98 128 104 80 129 106 37 146 83 72
Character n d s o h -h -o h o w t h a t t h e y a r e
Milliseconds 132 68 106 170 160 21 411 167 28 52 135 88 128 130 71 83 86 113 77 89 88 93 117 44 100
Character c l o s e l y r e l a t e d t o t h e s
Milliseconds 87 145 134 177 28 88 220 79 152 280 154 184 110 96 77 190 140 88 120 48 92 126 61 97 137
Character l o p e o f a c u r v e a t a p o i n
Milliseconds 112 233 247 100 102 184 110 96 169 169 135 258 61 249 105 128 126 138 118 167 126 227 89 232 235
Character t P o n t h e c u r v e . W e g i v e
Milliseconds 129 182 358 248 249 91 99 104 137 47 128 216 312 304 215 74 133 56 202 135 146 170 76 130 57
Character p r e s -s c i s e e d -d -e d e v e l o p m e n
Milliseconds 105 174 119 151 346 319 98 69 218 88 169 288 144 221 183 23 157 102 95 74 183 137 368 72 118
Character t s o f t h e s e i m p o r t a n t c o n
Milliseconds 58 88 159 208 79 104 81 99 103 194 44 138 223 175 146 67 117 143 152 127 87 414 197 142 61
Character c e p s t -t -s t s i n t h e n e t x t - -t
Milliseconds 340 234 132 233 96 386 154 44 97 75 135 207 86 71 113 86 88 123 87 106 162 119 28 297 185
Character -x -t x t c h a p t e r , b u t f o r n o w
Milliseconds 159 157 78 54 120 97 97 207 134 396 124 81 158 50 103 122 127 87 385 102 93 91 130 90 102
Character w e u s e a n i n f r -r o r m a l a p p
Milliseconds 108 190 221 169 216 96 65 118 155 126 120 295 80 433 374 392 116 109 111 297 148 244 135 187 173
Character r o a c h j - -j -h - h s o y o u w i l l
Milliseconds 153 322 177 180 153 9 61 378 188 166 49 452 122 86 91 94 87 219 102 155 67 162 104 191 168
Character s e e h o w t h e y l e a d n a t u r a
Milliseconds 139 98 70 183 68 124 95 92 84 87 170 33 129 117 658 104 76 131 161 279 74 88 133 135 109
Character l l y t o t h e m a n i d -d -i - -n i n i
Milliseconds 182 152 112 117 260 88 73 57 130 54 105 146 103 88 63 143 130 322 186 157 171 407 104 110 296
Character d e a o f t h i s c h a p e -e t e r , t h
Milliseconds 157 271 366 155 350 112 79 110 87 78 116 134 104 490 141 124 221 330 96 143 50 104 67 115 104
Character e l i m i t , -, . T h e i d e a o f a
Milliseconds 74 103 297 182 189 100 94 273 428 212 121 42 109 81 121 159 95 201 76 283 176 81 111 88 127
Character l i m i t p l a y s a f o u n d a t i o n a
Milliseconds 169 175 184 116 133 103 163 120 103 90 174 113 131 169 121 377 111 200 179 115 163 111 75 143 151
Character l r o l e t r -r h r t o u -u -o -t o u g h t -t o
Milliseconds 127 113 200 78 188 80 129 173 244 381 54 126 0 115 218 292 176 165 108 329 217 362 152 391 148
Character u t c a l c u l u s .
Milliseconds 205 87 129 383 76 70 179 130 263 395 84 164
WPM Timing
Seconds WPM
2.91 66.04
5.81 78.42
8.72 60.53
11.63 67.07
14.54 70.99
17.44 68.1
20.35 71.93
23.26 74.81
26.17 77.04
29.07 70.58
31.98 71.29
34.89 72.23
37.8 72.07
40.7 73.7
43.61 72.37
46.52 72.74
49.43 73.08
52.33 73.37
55.24 73.42
58.15 74.09
61.06 73.9
63.96 73.35
66.87 74.11
69.78 75.15
72.69 75.45
75.59 74.61
78.5 73.68
81.41 72.82
84.32 73.3
87.22 74.15
90.13 74.82
93.04 74.68
95.95 74.67
98.85 74.17
101.76 74.53
104.67 74.41
107.58 73.73
110.48 73.86
113.39 73.87
116.3 73.26
119.21 72.68
122.11 73.01
125.02 73.14
127.93 72.23
130.84 72.37
133.74 72.23
136.65 72.54
139.56 72.66
142.47 71.68
145.37 71.32