Turbo (turbo_ultimatum)

Race #2850

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Official speed 76.87 wpm (134.88 seconds elapsed during race)
Without ending ping 77.11 wpm (426 ms delay sending score to TypeRacer’s server)
Timerless 77.42 wpm (535 ms elapsed before first character typed; 133.92 seconds elapsed during race)
Timerless minus one 77.33 wpm, ignoring the first character typed
Race Start February 16, 2025 11:34:37am UTC
Race Finish February 16, 2025 11:36:52am UTC
Outcome No win (5 of 5)
Opponents 1. predator726 (85.51 wpm)
3. ahnfnsr (80.40 wpm)
Accuracy 95.6%
Points 207.54
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 SCalculus is a tiolo l that helps us understand how a change in one quantity is realtelated t oo a change in another. How does the speed of a falling object change as a function ioof time? How does the level of water ina a b aarrel change as a funciotn ofjhinmcunciton ofuncitonttion of the amount of liquied pd d pourued oniinto it? We see change occurring in nearly everyhtthing owe obeseserve in the wolrld and universe, ansdd powerful modern instrument s help us see more and more. In thise secdttion we introduce the ideas of average and instantaenenneious ous rates of change, and show that they ware closely related to the slope of a curve at a point P on the curve. We give priecise edevelopments of these important conmcepts in the next chapter, but for now we use ian infroormal aproproach osso you will se hosee how they hlead naturally to the main idea of this chapter, the molimit. The idea of a mlimit play s a foundation al role througouthout calculuis.s.
Timing
Character S -S C a l c u l u s i s a t i -i o l -l o -
Milliseconds 535 388 285 134 148 651 85 114 81 264 88 118 72 121 750 119 133 89 378 184 189 400 235 264 431
Character l t h a t h e l p s u s u n d e r s t a n
Milliseconds 186 75 86 64 25 87 65 140 185 194 195 126 90 116 101 89 245 137 51 140 83 242 194 83 91
Character d h o w a c h a n g e i n o n e q u a
Milliseconds 77 63 169 84 125 123 319 224 131 64 81 67 210 82 89 88 55 60 148 52 109 93 207 168 157
Character n t i t y i s r e a l t e -e -t -l -a l a t e d
Milliseconds 144 164 85 82 115 110 242 72 70 131 61 106 43 189 78 259 109 89 110 234 78 116 83 140 61
Character t o -o - o a c h a n g e i n a n o t h e
Milliseconds 105 94 242 273 162 243 72 266 94 268 32 83 116 86 80 60 66 57 85 187 87 118 82 33 111
Character r . H o w d o e s t h e s p e e d o f
Milliseconds 84 39 57 223 196 126 65 134 66 109 107 36 141 33 77 66 162 39 495 109 139 89 92 102 39
Character a f a l l i n g o b j e c t c h a n g e a
Milliseconds 51 66 135 57 92 142 57 78 89 86 199 132 135 77 145 161 60 166 31 85 59 58 84 64 239
Character s a f u n c t i o n i o -o -i o f t i m e ?
Milliseconds 82 66 83 63 107 70 135 51 170 13 26 57 90 119 56 380 110 212 48 36 133 96 30 79 207
Character H o w d o e s t h e l e v e l o f w a
Milliseconds 183 164 193 107 64 104 39 103 86 63 117 64 79 34 174 99 142 52 67 56 147 20 95 77 166
Character t e r i n a - - -a a b a -a - a r r e l
Milliseconds 87 109 83 65 115 85 101 124 159 356 110 85 442 182 144 317 5 106 389 81 69 377 135 83 97
Character c h a n g e a s a f u n c i o t n o -o -f
Milliseconds 75 167 86 23 99 53 55 67 161 134 39 108 61 216 145 112 105 140 33 25 63 60 65 411 85
Character -u -n -c -i -o -t -n - f j h -h i -i -j n m c -c -m -n u n c i
Milliseconds 0 0 0 0 0 0 0 0 256 246 30 332 234 219 116 309 0 144 249 108 424 234 159 110 117
Character t o n o -o -f -u -n -c -i -t -o -n - f u n c i t o n -n -o
Milliseconds 24 11 83 87 67 383 84 0 0 0 0 0 0 0 0 234 60 165 81 143 27 6 85 412 113
Character -t t -t -i t i o n o f t h e a m o u n t o f
Milliseconds 83 228 149 116 67 150 0 107 115 62 81 69 101 35 58 65 157 67 91 104 139 107 6 176 104
Character l i q u i e d p -p - -d d - -d -e d p o u r u
Milliseconds 5 118 60 128 146 35 182 191 34 143 323 111 116 65 99 528 110 114 101 85 145 53 83 135 116
Character -u e d o n i -i -o -n i n t o i t ? W e s e e
Milliseconds 351 100 165 85 172 53 3 389 138 0 261 84 84 67 80 169 79 202 104 234 197 115 105 141 136
Character c h a n g e o c c u r r i n g i n n e a r
Milliseconds 88 108 65 50 95 29 82 64 301 104 138 141 57 652 91 55 83 89 141 108 28 147 74 85 91
Character l y e v e r y h t -t -h t h i n g o -o w e o b
Milliseconds 40 104 57 116 151 75 83 144 0 114 430 114 127 86 85 84 80 36 118 428 74 57 87 170 186
Character e s e -e -s -e s e r v e i n t h e w o l -l r l
Milliseconds 131 84 85 282 86 115 119 8 87 193 54 62 119 58 50 95 62 26 64 105 68 140 424 101 117
Character d a n d u n i v e r s e , a n s d -d -s d p
Milliseconds 105 90 101 122 77 120 294 162 6 522 112 106 115 85 117 108 104 122 50 115 310 109 66 44 198
Character o w e r f u l m o d e r n i n s t r u m e n t
Milliseconds 26 49 58 117 144 82 63 108 195 63 283 138 84 117 83 91 77 83 116 165 87 166 76 68 54
Character - s h e l p u s s e e m o r e a n d
Milliseconds 143 458 66 68 135 80 95 141 189 160 78 89 134 85 164 62 89 84 57 50 70 135 67 74 64
Character m o r e . I n t h i s e -e s e c d t -t -d t i
Milliseconds 97 30 106 53 97 82 148 137 136 191 57 35 132 118 407 76 84 78 169 82 430 241 92 126 115
Character o n w e i n t r o d u c e t h e i d e a s
Milliseconds 35 78 87 265 82 146 218 81 82 167 90 153 144 82 80 122 214 7 78 65 143 107 138 75 112
Character o f a v e r a g e a n d i n s t a n t a e
Milliseconds 70 61 80 59 397 219 133 60 107 118 56 59 136 93 82 90 118 77 84 165 131 172 365 160 272
Character n -n -e e n -n -e n e i o u s - -s -u -o -i o u s r a
Milliseconds 142 377 86 177 9 511 85 205 50 125 55 79 138 117 276 137 113 112 110 237 78 83 113 368 237
Character t e s o f c h a n g e , a n d s h o w t
Milliseconds 169 81 53 99 117 47 90 110 65 49 96 55 55 97 82 77 66 82 93 127 40 92 99 432 165
Character h a t t h e y w -w a r e c l o s e l y r e
Milliseconds 56 50 76 52 219 53 113 36 83 102 388 45 142 82 60 267 94 163 87 48 66 133 88 238 82
Character l a t e d t o t h e s l o p e o f a c
Milliseconds 97 45 144 81 142 143 234 66 110 26 64 83 62 136 37 143 55 129 94 87 107 114 21 125 442
Character u r v e a t a p o i n t P o n t h e
Milliseconds 167 28 196 75 66 103 148 7 660 145 168 55 83 51 90 92 196 365 173 78 55 61 90 51 38
Character c u r v e . W e g i v e p r i -i e c i s e
Milliseconds 444 116 83 294 76 128 76 109 252 114 131 95 107 54 62 306 96 120 452 100 193 117 101 85 199
Character e -e d e v e l o p m e n t s o f t h e s e i
Milliseconds 286 485 75 135 116 74 69 194 55 347 131 36 112 157 145 57 112 64 81 88 105 114 54 125 190
Character m p o r t a n t c o n m -m c e p t s i n t h
Milliseconds 80 93 78 80 144 77 95 30 190 135 66 81 195 324 75 471 121 102 162 143 111 83 57 35 89
Character e n e x t c h a p t e r , b u t f o r n
Milliseconds 52 67 92 48 166 165 88 157 90 50 128 158 185 57 67 82 319 193 107 33 161 39 109 35 116
Character o w w e u s e i -i a n i n f r o -o -r o r m
Milliseconds 57 49 148 103 116 91 137 105 31 121 164 298 100 118 55 116 80 53 530 43 346 111 186 79 89
Character a l a p r o -o -r p r o a c h o s -s -o s o y o
Milliseconds 101 124 159 184 123 206 37 432 111 186 102 93 202 193 64 108 113 78 281 84 174 92 83 141 65
Character u w i l l s e h o -h -o -s -e - s e e h o w
Milliseconds 78 30 161 65 144 86 104 84 84 115 244 115 325 0 86 0 0 281 84 168 141 216 60 132 86
Character t h e y h -h l e a d n a t u r a l l y t o
Milliseconds 113 63 56 83 61 168 329 182 21 83 141 115 217 106 117 88 75 90 69 112 78 83 215 33 85
Character t h e m a i n i d e a o f t h i s c h a
Milliseconds 85 194 155 90 91 126 175 80 107 171 106 140 75 99 59 132 117 265 62 58 77 66 215 88 79
Character p t e r , t h e m o -o -m l i m i t . T h e
Milliseconds 41 161 106 83 68 83 111 66 51 64 65 59 379 107 265 81 84 168 132 93 99 122 140 80 63
Character i d e a o f a m -m l i m i t p l a y - s
Milliseconds 90 108 136 81 91 63 103 67 27 90 145 374 183 84 88 160 184 115 142 110 99 94 112 534 71
Character a f o u n d a t i o n - a l r o l e t h
Milliseconds 90 106 91 162 91 52 142 109 107 117 92 6 50 140 435 119 125 127 165 66 139 128 92 264 87
Character r o u g o u t -t -u -o h o u t c a l c u l u i s .
Milliseconds 108 94 53 87 132 89 117 429 113 162 232 60 81 113 62 163 132 118 159 89 141 77 9 163 122
Character -. -s -i s .
Milliseconds 321 112 85 98 508
WPM Timing
Seconds WPM
2.7 35.59
5.4 35.59
8.09 48.93
10.79 57.83
13.49 67.62
16.19 63.02
18.88 69.27
21.58 73.96
24.28 79.08
26.98 79.63
29.67 83.71
32.37 78.59
35.07 78.36
37.77 72.76
40.46 69.1
43.16 70.9
45.86 68.56
48.56 67.72
51.25 69.54
53.95 70.51
56.65 69.48
59.35 70.97
62.04 70.98
64.74 72.47
67.44 73.67
70.14 73.74
72.83 73.98
75.53 75.47
78.23 73.94
80.93 72.51
83.62 74.19
86.32 74.65
89.02 75.76
91.72 75.89
94.41 76.39
97.11 75.62
99.81 76.35
102.51 76.33
105.2 77.22
107.9 77.63
110.6 76.71
113.3 76.79
115.99 76.35
118.69 76.84
121.39 77.6
124.09 77.75
126.78 77.8
129.48 77.85
132.18 77.62
134.88 76.87