Jag (type4825)

Race #168

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Official speed 71.33 wpm (145.35 seconds elapsed during race)
Without ending ping 71.44 wpm (225 ms delay sending score to TypeRacer’s server)
Timerless 72.07 wpm (1,274 ms elapsed before first character typed; 143.85 seconds elapsed during race)
Timerless minus one 71.99 wpm, ignoring the first character typed
Race Start September 16, 2024 5:10:09am UTC
Race Finish September 16, 2024 5:12:34am UTC
Outcome No win (2 of 2)
Opponents 1. venerator (73.61 wpm)
Accuracy 97.5%
Points 192.59
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 Calkcuylus is a tools tha that helps us understand how a change in ione quantity is related to cha 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 instrucments help us see more na and mroe ore. In this section we introduce the ideas of average and instantaneous rates of change, and show that they are closely related to the sloe poe e of a curve at a poin tt P on the curve. We give precise developments of these importante concepts in the next chapeter, but for now we use an informal apporroach so weyou will see how they lead naturally to the main idea o ff this chapter, the limit. The idea of a limit plays a foundational role throughout calculaus.
Timing
Character C a l k -k c u y -y l u s i s a t o o l s t
Milliseconds 1274 537 130 3 560 500 187 2 579 758 460 179 268 160 61 137 114 158 177 62 126 158 122 62 213
Character h a -a -h -t - -s t h a t h e l p s u s u n d
Milliseconds 83 71 594 155 128 118 127 414 428 123 59 83 116 307 142 91 228 66 157 183 67 131 327 177 17
Character e r s t a n d h o w a c h a n g e i n i
Milliseconds 176 66 140 111 70 98 65 188 128 105 66 113 253 147 182 117 52 102 64 123 163 201 198 251 201
Character -i o n e q u a n t i t y i s r e l a t e d
Milliseconds 410 224 99 96 81 399 94 129 83 344 61 83 175 168 231 52 108 200 78 146 119 115 68 180 218
Character t o c h -h -c a c h a n g e i n a n o t h e
Milliseconds 33 190 408 195 146 337 159 123 138 188 120 71 100 53 128 109 110 110 25 178 116 114 88 118 70
Character r . H o w d o e s t h e s p e e d o f
Milliseconds 95 125 108 326 68 98 86 193 81 139 83 83 151 66 70 101 112 109 97 134 134 172 143 96 77
Character a f a l l i n g o b j e c t c h a n g e a
Milliseconds 295 145 92 149 47 138 151 17 91 58 246 112 117 93 166 195 77 169 107 63 80 60 121 86 140
Character s a f u n c t i o n o f t i m e ? H o w
Milliseconds 129 129 130 173 153 290 167 54 177 32 99 78 88 156 93 35 235 64 143 77 223 208 242 117 134
Character d o e s t h e l e v e l o f w a t e r
Milliseconds 174 148 98 96 72 100 165 78 69 71 454 94 159 117 104 101 265 71 97 161 176 85 123 96 53
Character i n a b a r r e l c h a n g e a s a f
Milliseconds 182 102 14 191 24 334 172 63 148 82 111 220 234 115 69 77 52 115 108 125 136 103 218 72 393
Character u n c t i o n o f t h e a m o u n t o f
Milliseconds 162 154 46 158 54 83 55 94 150 68 42 290 123 88 130 169 97 149 84 321 194 134 204 80 56
Character l i q u i d p o u r e d i n t o i t ? W e
Milliseconds 331 174 205 102 135 126 258 250 207 197 136 140 192 157 126 70 104 117 308 250 76 235 209 373 208
Character s e e c h a n g e o c c u r r i n g i n
Milliseconds 167 190 167 129 44 262 117 73 102 62 112 72 284 127 115 185 122 128 113 86 76 143 167 75 107
Character n e a r l y e v e r y t h i n g w e o b s e
Milliseconds 370 109 94 38 140 231 95 191 182 140 35 62 204 165 146 131 43 83 137 92 90 361 119 175 193
Character r v e i n t h e w o r l d a n d u n i v
Milliseconds 108 160 170 0 253 94 49 159 81 56 61 205 96 108 57 116 138 128 11 92 125 247 197 152 94
Character e r s e , - -, - , a n d p o w e r f u l
Milliseconds 175 76 135 124 103 123 153 399 121 132 308 137 185 97 83 76 375 171 92 100 26 210 52 180 55
Character m o d e r n i n s t r u c -c m e n t s h e l p
Milliseconds 452 294 142 198 113 145 124 198 124 56 133 134 108 153 480 216 109 105 89 345 172 221 318 95 262
Character u s s e e m o r e n a - -a -n a n d m r
Milliseconds 134 176 110 116 261 152 118 105 178 143 37 86 11 287 0 195 407 114 129 169 99 71 99 156 127
Character o e - -e -o -r o r e . I n t h i s s e c t i
Milliseconds 0 64 207 349 109 121 130 239 57 72 181 233 267 113 62 288 79 109 24 98 196 111 197 166 85
Character o n w e i n t r o d u c e t h e i d e a s
Milliseconds 89 59 47 137 58 152 230 89 120 124 87 139 100 110 154 66 204 115 99 10 323 79 160 73 181
Character o f a v e r a g e a n d i n s t a n t a n
Milliseconds 158 348 95 67 561 265 160 107 128 132 115 68 264 146 8 113 320 226 169 201 217 160 64 493 688
Character e o u s r a t e s o f c h a n g e , a n d
Milliseconds 223 225 117 72 144 268 125 112 100 80 129 178 110 113 240 92 92 90 18 116 153 63 205 63 72
Character s h o w t h a t t h e y a r e c l o s e
Milliseconds 95 182 175 94 126 79 203 95 83 85 30 340 99 98 127 19 280 64 92 17 312 95 138 53 71
Character l y r e l a t e d t o t h e s l o e - -e
Milliseconds 149 232 97 318 113 28 514 115 72 174 188 208 56 103 184 102 61 112 169 371 183 376 235 643 150
Character p o e - -e -o e o f a c u r v e a t a
Milliseconds 403 324 168 239 482 142 264 120 148 143 107 104 448 114 185 149 82 178 123 69 355 70 145 498 186
Character p o i n t -t - t P o n t h e c u r v e .
Milliseconds 160 191 121 100 157 32 551 91 153 164 286 254 227 107 65 159 66 76 101 316 152 70 169 110 165
Character W e g i v e p r e c i s e d e v e l o p m
Milliseconds 39 401 111 515 231 78 87 133 22 302 76 80 177 75 186 165 184 207 186 159 125 56 184 215 211
Character e n t s o f t h e s e i m p o r t a n t e -e
Milliseconds 57 156 30 139 84 214 171 212 148 110 93 33 84 664 352 148 286 82 516 176 110 190 154 93 444
Character c o n c e p t s i n t h e n e x t c h a
Milliseconds 163 344 101 97 118 194 153 90 100 147 180 74 73 143 101 305 157 377 55 172 196 65 228 142 108
Character p e -e t e r , b u t f o r n o w w e u s
Milliseconds 220 400 458 68 109 100 304 225 338 56 139 123 176 52 89 105 197 99 16 127 206 102 184 511 83
Character e a n i n f o r m a l a p p o r -r -o r o a c
Milliseconds 146 157 287 100 79 517 161 134 86 90 87 137 127 94 218 212 124 236 72 432 108 163 131 118 190
Character h s o w e -e -w y o u w i l l s e e h o w
Milliseconds 119 166 224 90 81 156 89 308 100 267 150 91 24 210 143 124 134 19 134 138 162 152 135 97 51
Character t h e y l e a d n a t u r a l l y t o t
Milliseconds 110 258 93 141 126 66 218 65 71 118 113 211 78 168 153 78 92 87 119 213 27 217 61 128 199
Character h e m a i n i d e a o f -f - f t h i s
Milliseconds 95 100 118 130 86 76 95 77 198 66 143 99 91 88 188 102 399 121 185 161 203 70 111 25 118
Character c h a p t e r , t h e l i m i t . T h e i
Milliseconds 195 104 77 86 162 88 117 176 106 160 78 78 81 227 173 122 128 177 363 187 393 243 77 95 239
Character d e a o f a l i m i t p l a y s a f o
Milliseconds 58 144 105 103 143 105 162 194 101 133 147 129 139 113 125 329 207 77 177 343 232 236 127 130 128
Character u n d a t i o n a l r o l e t h r o u g h o u
Milliseconds 87 158 64 177 85 138 100 130 144 150 125 195 78 155 53 114 190 110 73 505 83 128 107 286 120
Character t c a l c u l a -a u s .
Milliseconds 86 146 183 317 168 222 63 221 187 306 210 81 134
WPM Timing
Seconds WPM
2.91 12.38
5.81 24.77
8.72 26.14
11.63 39.21
14.54 48.71
17.44 50.91
20.35 51.89
23.26 58.31
26.16 63.29
29.07 66.05
31.98 68.67
34.88 70.52
37.79 72.4
40.7 73.42
43.61 73.2
46.51 72.75
49.42 74.06
52.33 74.76
55.23 76.26
58.14 74.71
61.05 74.7
63.96 73.93
66.86 73.58
69.77 72.24
72.68 73.31
75.58 73.35
78.49 73.38
81.4 72.83
84.3 73.88
87.21 74.16
90.12 73.77
93.03 71.59
95.93 71.43
98.84 70.9
101.75 70.88
104.65 71.32
107.56 71.07
110.47 70.61
113.38 70.7
116.28 70.48
119.19 70.38
122.1 70.08
125 70.08
127.91 70.74
130.82 70.82
133.72 71.34
136.63 71.4
139.54 71.38
142.45 71.69
145.35 71.33