tstats[umartangent2] (umartangent2)

Race #7807

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Official speed 70.18 wpm (147.73 seconds elapsed during race)
Without ending ping 70.32 wpm (295 ms delay sending score to TypeRacer’s server)
Timerless 70.68 wpm (751 ms elapsed before first character typed; 146.69 seconds elapsed during race)
Timerless minus one 70.60 wpm, ignoring the first character typed
Race Start February 21, 2024 5:49:10pm UTC
Race Finish February 21, 2024 5:51:38pm UTC
Outcome No win (5 of 5)
Opponents 1. kakarot_db (109.11 wpm)
2. planta (102.01 wpm)
Accuracy 95.5%
Points 189.48
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 Calccululus is a tool that helps u ss unsederstand how a chang eie in one quatintity is related ato a change in another. ohow How does the speed of a falling object change as sa ta a function of time? How does the leevel of water in a barrel change as a function of a mth the amount of liquid poured into it? We csee chancege occuring ioccurirrnging in nearly everything ew we observe int hiin the wrorld an d universe, and pwoerpowerful modern instruments help us see mor eand smore and more. In this section ew we introduce the ideas of averafe ge and instantaneous rates of cangchange, and show that they are closely related ot theto the sleopslope of a cuverve at a point P on the curve. EW We vgive precise developments of thosees e important tcnoncepts in the tenext chapter, but for now we use a n informal approach so you will see how the leathey lead naturally to the main idea of this chapter, the limit. The idea of a limit plays faa foundational role thoughthoughthroughout alccalclulus.
Timing
Character C a l c c u l -l -u -c u l u s i s a t o o l
Milliseconds 751 145 158 135 168 38 192 331 154 137 232 140 135 134 74 169 89 133 40 85 155 65 154 334 281
Character t h a t h e l p s u s -s - s u n s e -e -s d
Milliseconds 107 117 0 80 63 181 105 19 185 78 41 133 138 133 466 132 132 53 149 216 95 282 333 132 31
Character e r s t a n d h o w a c h a n g e i -i -e -
Milliseconds 163 99 21 134 76 106 90 106 136 76 59 83 110 226 554 75 124 38 120 180 0 319 302 137 129
Character e i n o n e q u a t i -i -t n t i t y i s
Milliseconds 109 107 97 71 75 156 60 109 67 415 91 150 389 91 276 134 169 127 33 107 135 90 195 71 99
Character r e l a t e d a -a t o a c h a n g e i n
Milliseconds 173 74 92 180 97 111 138 91 114 473 168 102 85 30 125 181 117 24 149 67 127 44 114 70 62
Character a n o t h e r . o -o h o w -h -o -w - H o w d o
Milliseconds 339 56 110 41 94 41 69 93 140 273 345 229 145 107 115 323 0 0 0 478 110 168 107 312 40
Character e s t h e s p e e d o f a f a l l i n g
Milliseconds 82 92 42 119 21 70 87 109 87 109 125 164 62 82 73 102 71 78 507 92 111 137 58 79 40
Character o b j e c t c h a n g e a s s a t -t - -a
Milliseconds 108 240 125 197 80 197 216 102 313 99 55 124 118 131 30 318 138 57 109 0 36 151 384 141 129
Character a - -a -s a f u n c t i o n o f t i m e ?
Milliseconds 112 118 305 134 126 144 59 439 108 196 82 234 22 92 78 121 100 58 38 286 13 95 97 279 31
Character H o w d o e s t h e l e e -e v e l o f w
Milliseconds 216 116 187 84 164 86 60 96 84 100 27 76 84 134 66 328 346 125 157 37 161 131 61 73 278
Character a t e r i n a b a r r e l c h a n g e a
Milliseconds 109 66 141 59 64 103 50 91 23 110 139 83 88 179 137 31 138 206 68 84 96 68 130 21 245
Character s a f u n c t i o n o f a m -m t h -t -h
Milliseconds 119 74 116 72 345 121 139 109 216 33 94 116 156 111 35 91 168 96 211 343 213 35 149 310 0
Character - -a - t h e a m o u n t o f l i q u i d p
Milliseconds 0 113 0 195 62 97 56 223 72 122 126 198 70 106 161 35 79 170 126 234 137 88 266 122 283
Character o u r e d i n t o i t ? W e c -c s e e c
Milliseconds 65 57 103 176 164 66 133 71 119 21 177 240 93 314 46 264 58 105 206 446 103 184 117 107 163
Character h a n c e -e -c g e o c c u r i n g i -i -o -c -c -u
Milliseconds 77 23 150 168 166 398 123 57 137 46 330 130 140 87 135 77 65 63 123 100 381 97 0 0 0
Character -r -i -n -g - o c c u r i r -r -i r n g -g -n i n g i n
Milliseconds 0 0 0 0 0 231 243 163 457 184 101 236 205 112 148 180 69 321 126 197 84 70 102 101 55
Character n e a r l y e v e r y t h i n g e w -e -w -
Milliseconds 90 199 113 84 72 18 178 76 169 185 142 51 67 121 86 72 105 35 109 138 0 121 506 0 0
Character w e o b s e r v e i n t h -h i -i -i -n -t - i n
Milliseconds 240 60 64 271 90 217 99 115 289 158 74 124 34 118 29 99 478 248 312 112 0 0 0 211 77
Character t h e w r -r o r l d a n - d u n i v e r
Milliseconds 81 47 115 25 151 84 490 388 194 84 123 78 83 71 50 135 433 98 113 340 240 72 192 196 75
Character s e , a n d p w o e r -p -w -o -e -r p o w e r f u
Milliseconds 100 93 141 77 67 114 66 49 177 87 37 0 92 425 0 0 0 0 221 44 107 33 81 281 78
Character l m o d e r n i n s t r u m e n t s h e l p
Milliseconds 163 117 130 113 130 146 65 73 137 131 65 99 97 144 100 271 87 67 36 105 141 387 114 98 168
Character u s s e e m o r e a n d -e -a -n -d - -m -o -r
Milliseconds 44 158 68 53 183 185 137 83 132 114 51 74 0 123 29 78 63 353 0 0 0 0 128 0 0
Character - s -s m o r e a n d m o r e . I n t h i s
Milliseconds 0 474 311 229 37 135 52 58 67 84 39 86 205 63 100 56 80 138 142 241 73 315 50 86 43
Character s e c t i o n e w -e -w - w e i n t r o d u
Milliseconds 89 165 96 177 214 26 78 43 118 115 0 121 556 0 0 298 43 78 278 49 295 130 390 317 122
Character c e t h e i d e a s o f a v e r a f e -
Milliseconds 84 167 103 77 57 39 103 126 77 103 70 138 123 71 81 49 194 286 158 100 61 212 81 53 307
Character -e -f g e a n d i n s t a n t a n e o u s r a
Milliseconds 134 151 128 124 15 114 82 34 100 149 70 51 129 72 118 76 397 410 515 224 135 120 97 293 102
Character t e s o f c a n g -c -a -n -g c h a n g e , a n
Milliseconds 106 185 0 136 377 99 26 348 119 126 33 421 0 0 0 221 75 50 90 81 126 43 106 87 44
Character d s h o w t h a t t h e y a r e c l o s
Milliseconds 55 86 252 29 106 63 108 44 41 102 38 77 173 15 136 20 83 168 65 69 114 224 36 189 221
Character e l y r e l a t e d o t t h e -t -h -e -o -t - t
Milliseconds 39 141 201 60 223 66 97 75 83 91 186 40 157 0 110 34 97 49 323 0 0 119 0 0 227
Character o t h e s l e o p -s -l -e -o -p s l o p e o f
Milliseconds 30 104 70 79 28 111 177 72 131 120 103 410 0 0 0 0 367 72 149 135 133 198 148 43 86
Character a c u v e -e -v r v e a t a p o i n t P
Milliseconds 68 88 310 269 190 205 340 127 100 209 158 26 261 110 109 25 119 167 19 141 112 31 177 196 198
Character o n t h e c u r v e . E W - -W -E W e v -v
Milliseconds 189 61 99 47 86 61 64 289 160 99 261 168 54 104 544 0 190 356 156 135 314 85 175 180 366
Character g i v e p r e c i s e d e v e l o p m e n t s
Milliseconds 83 128 105 152 66 400 81 76 262 214 96 56 75 394 136 183 119 73 158 140 159 83 122 52 112
Character o f t h o s e -e -s -o e s - e i m p o r t a
Milliseconds 101 148 47 59 181 25 111 13 100 364 139 117 87 85 183 463 112 111 88 99 185 0 121 75 115
Character n t t -t c n -n o n c e p t s i n t h e t e
Milliseconds 103 0 180 0 496 219 131 364 177 102 123 158 185 154 158 125 128 85 99 0 125 16 165 350 72
Character -e -t n e x t c h a p t e r , b u t f o r n
Milliseconds 478 138 190 57 179 184 119 308 81 71 94 77 143 81 349 95 157 157 97 24 219 15 111 92 138
Character o w w e u s e a - n i n f o r m a l a
Milliseconds 85 121 108 190 22 144 148 84 57 106 65 95 445 182 116 85 65 76 126 65 254 174 31 146 283
Character p p r o a c h s o y o u w i l l s e e h
Milliseconds 124 114 202 85 154 257 72 136 285 64 86 123 59 62 110 100 108 228 182 257 218 205 143 50 153
Character o w t h e l e a -l -e -a -t -h -e - t h e y l e a
Milliseconds 90 74 58 224 53 79 125 135 16 111 454 0 0 134 0 0 0 190 69 25 120 113 167 56 64
Character d n a t u r a l l y t o t h e m a i n i
Milliseconds 324 134 400 168 114 74 80 66 96 144 148 20 181 80 83 32 103 62 84 121 92 111 54 202 113
Character d e a o f t h i s c h a p t e r , t h e
Milliseconds 194 157 12 124 115 103 32 146 20 88 108 139 340 59 175 19 101 146 71 76 69 171 56 86 93
Character l i m i t . T h e i d e a o f a l i m i
Milliseconds 117 113 142 142 102 157 115 170 142 71 81 178 231 122 58 128 133 83 56 64 81 247 102 107 130
Character t p l a y s f a -a -f a f o u n d a t i o n a
Milliseconds 114 115 393 211 115 130 169 82 420 130 257 122 124 78 198 101 39 193 70 107 116 56 57 42 236
Character l r o l e t h o u g h -h -t -h -o -u -g t h o u g h
Milliseconds 52 135 313 54 171 77 29 191 62 94 74 44 159 398 555 0 0 0 0 253 66 150 40 101 113
Character -t -h -o -u -g -h t h r o u g h o u t a l c -a -l -c c a
Milliseconds 337 0 0 0 0 0 230 94 182 84 28 132 64 425 23 93 118 325 75 181 413 0 0 269 159
Character l c l -l u l u s .
Milliseconds 58 372 100 379 202 153 138 134 138
WPM Timing
Seconds WPM
2.95 36.55
5.91 62.95
8.86 62.27
11.82 60.92
14.77 61.73
17.73 67.01
20.68 62.66
23.64 68.03
26.59 69.95
29.55 66.2
32.5 70.15
35.46 72.09
38.41 74.04
41.37 71.94
44.32 73.37
47.28 73.1
50.23 69.76
53.18 67.69
56.14 69.04
59.09 67.82
62.05 67.5
65 67.38
67.96 68.34
70.91 68.54
73.87 68.39
76.82 68.57
79.78 69.49
82.73 69.62
85.69 69.18
88.64 69.45
91.6 71.01
94.55 69.93
97.5 69.54
100.46 70.48
103.41 69.39
106.37 69.49
109.32 69.26
112.28 69.15
115.23 68.94
118.19 69.65
121.14 69.93
124.1 70.2
127.05 69.99
130.01 70.7
132.96 71.57
135.92 72.13
138.87 71.81
141.83 71.41
144.78 70.87
147.73 70.18