ben (kbeni)

Race #2020

View Pit Stop page for race #2020 by kbeni — Ghost race

View profile for ben (kbeni)

Official speed 78.24 wpm (132.52 seconds elapsed during race)
Without ending ping 78.42 wpm (310 ms delay sending score to TypeRacer’s server)
Timerless 78.64 wpm (365 ms elapsed before first character typed; 131.84 seconds elapsed during race)
Timerless minus one 78.55 wpm, ignoring the first character typed
Race Start January 10, 2024 6:38:24pm UTC
Race Finish January 10, 2024 6:40:36pm UTC
Outcome No win (2 of 5)
Accuracy 96.3%
Points 211.25
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 Claalculus is a tool that helps us euunderstand how a chngeahnnge in one qunaantity is related to a change in another. How does the speed of a affalling object change as a function of time? hHow does the level of water in a barrel change waas a function of the amount of liquid poured into it? We see chagne nge ocrcurring in nearly everything we observe in the world and universe, and powerful modern insturruments help use se see more and mor.e. In this section we intriocduce the idesasas of average and instantnaanoueouse re reattaeates of cahnghzange, and show that they are closely frelated to the sl9pope of a curve at a point P on the curve. We give precise developments of these imporrttantant concepsts in teh nhe next chapter, but for now we use an inforam lmal approach so you will see how tehy hey lead anaturally to the main idea of this chapter, the limit. The idea of a limit plays a foundational orrole throughout calculus.
Timing
Character C l a -a -l a l c u l u s i s a t o o l t h
Milliseconds 365 192 32 383 106 105 149 75 117 138 118 171 86 116 64 85 120 63 98 32 150 181 53 118 63
Character a t h e l p s u s e u -u -e u n d e r s t a n
Milliseconds 43 75 42 183 97 127 202 97 52 188 86 75 169 96 307 118 222 205 53 190 42 106 460 125 15
Character d h o w a c h n g e -e -g -n a h n -n -h n g e
Milliseconds 156 42 161 41 32 55 128 74 401 75 202 42 139 289 120 154 75 292 195 333 108 207 76 96 41
Character i n o n e q u n a -a -n a n t i t y i s r e
Milliseconds 140 21 106 139 72 54 65 708 106 198 107 329 117 84 148 106 117 370 200 41 148 106 65 413 76
Character l a t e d t o a c h a n g e i n a n o t
Milliseconds 118 138 108 75 191 43 492 86 77 83 117 126 75 96 76 42 128 74 118 52 63 104 96 64 44
Character h e r . H o w d o e s t h e s p e e d o
Milliseconds 96 54 64 194 21 314 86 339 86 362 54 118 96 21 149 10 98 32 202 129 94 142 168 64 32
Character f a a f -f -a f a l l i n g o b j e c t c h
Milliseconds 352 117 74 117 116 93 378 117 84 65 148 158 147 31 107 33 223 319 159 127 245 120 63 672 62
Character a n g e a s a f u n c t i o n o f t i m
Milliseconds 22 119 74 63 106 163 137 75 104 74 74 127 192 116 153 65 54 22 309 139 126 108 118 75 204
Character e ? h -h H o w d o e s t h e l e v e l o
Milliseconds 84 497 357 311 518 244 213 84 53 138 84 84 106 10 87 32 97 21 180 63 108 76 94 107 127
Character f w a t e r i n a b a r r e l c h a n g
Milliseconds 85 43 160 127 107 86 115 96 107 43 75 84 106 118 138 244 128 73 107 105 700 75 75 86 22
Character e w a -a -w a s a f u n c t i o n o f t h
Milliseconds 95 96 94 74 375 126 32 126 23 149 75 223 128 180 95 108 64 64 33 107 293 54 86 115 21
Character e a m o u n t o f l i q u i d p o u r e d
Milliseconds 95 64 264 106 139 170 213 74 84 140 83 42 169 22 255 74 559 55 52 292 129 118 130 76 211
Character i n t o i t ? W e s e e c h a g n e -
Milliseconds 33 76 65 172 127 107 192 64 256 73 232 191 106 137 44 161 74 168 84 21 174 3 75 108 309
Character -e -n -g n g e o c r -r c u r r i n g i n n e a
Milliseconds 128 147 160 223 63 42 75 751 275 161 381 107 158 86 129 84 54 64 67 139 44 76 257 73 127
Character r l y e v e r y t h i n g w e o b s e r v e
Milliseconds 11 115 108 64 149 148 114 119 43 180 65 75 149 20 55 105 65 95 171 128 290 52 107 249 87
Character i n t h e w o r l d a n d u n i v e r s
Milliseconds 106 53 52 96 87 84 43 53 105 54 41 171 20 87 137 11 129 22 194 180 63 85 169 73 116
Character e , a n d p o w e r f u l m o d e r n i n
Milliseconds 120 139 74 86 43 77 42 711 12 107 96 10 182 85 118 83 233 54 403 159 85 54 211 137 63
Character s t u r -r -u r u m e n t s h e l p u s e s e
Milliseconds 121 95 138 51 395 106 172 96 220 94 96 64 129 107 129 108 118 172 95 160 65 42 22 222 30
Character -e -s - -e s e e m o r e a n d m o r . -. e .
Milliseconds 265 149 171 125 63 76 96 118 86 139 64 52 65 21 148 73 74 11 138 74 23 254 432 53 200
Character I n t h i s s e c t i o n w e i n t r i
Milliseconds 54 244 157 96 55 42 65 42 98 125 54 223 138 42 43 43 95 127 74 64 792 74 192 179 95
Character -i o c -c d u c e t h e i d e s a s -s -a -s a s
Milliseconds 367 211 87 340 86 137 75 210 105 130 32 484 84 158 94 157 115 33 117 337 148 138 95 83 147
Character o f a v e r a g e a n d i n s t a n t n a -a
Milliseconds 170 40 63 171 125 147 106 65 166 95 55 114 53 54 64 136 73 104 140 182 32 600 179 44 524
Character -n a n o u -u -o e o u s e - -e r e -e -r r e a t -t
Milliseconds 149 263 115 276 53 439 138 126 138 53 52 63 74 443 126 180 95 336 137 94 51 84 119 105 273
Character -a -e t a e -e -a -t a t e s o f c a h n g -g -n -h -a
Milliseconds 137 139 94 10 107 369 136 137 95 32 96 225 167 146 84 43 199 117 10 158 22 315 127 156 127
Character h z -z a n g e , a n d s h o w t h a t t h
Milliseconds 244 32 487 107 141 117 22 160 64 116 32 73 43 180 86 64 43 75 678 10 76 97 43 118 86
Character e y a r e c l o s e l y f -f r e l a t e d
Milliseconds 22 149 96 200 63 95 84 136 54 158 53 33 139 74 96 149 412 73 23 159 63 96 74 179 53
Character t o t h e s l 9 p -p -9 o p e o f a c u r
Milliseconds 85 43 97 107 52 32 85 337 115 159 64 406 148 180 169 95 77 115 65 33 137 86 147 212 98
Character v e a t a p o i n t P o n t h e c u
Milliseconds 265 138 65 148 115 32 139 64 159 43 64 95 127 127 275 277 95 84 43 118 43 73 33 628 106
Character r v e . W e g i v e p r e c i s e d e v e
Milliseconds 52 183 86 42 75 191 149 85 119 86 74 73 75 138 127 488 216 127 204 65 114 254 147 137 21
Character l o p m e n t s o f t h e s e i m p o r r t
Milliseconds 97 210 63 278 63 148 54 85 96 10 141 44 215 53 42 95 107 11 204 105 53 497 96 178 11
Character t a n -n -a -t -t -r t a n t c o n c e p s -s t s i
Milliseconds 138 10 84 304 149 158 148 137 85 140 52 43 116 214 54 52 152 157 95 137 509 63 107 21 434
Character n t e h n -n - -h -e h e n e x t c h a p t e
Milliseconds 53 53 73 96 10 96 142 275 126 157 137 359 73 44 179 105 253 95 74 691 129 63 159 129 128
Character r , b u t f o r n o w w e u s e a n
Milliseconds 74 147 75 150 118 64 65 150 10 162 53 84 54 42 86 149 84 65 148 75 32 44 172 45 159
Character i n f o r a m l -l - -m -a m a l a p p r o a c h
Milliseconds 115 52 158 10 362 170 11 191 11 329 137 151 127 223 51 160 84 137 85 160 128 76 127 170 98
Character s o y o u w i l l s e e h o w t e h y
Milliseconds 85 116 74 106 98 83 53 65 95 85 158 149 74 85 64 170 10 341 64 21 74 278 107 11 139
Character - -y -h -e h e y l e a d a -a n a t u r a l l y
Milliseconds 33 299 329 149 127 215 43 108 10 761 63 86 117 54 150 338 189 72 86 96 117 97 130 125 32
Character t o t h e m a i n i d e a o f t h i s
Milliseconds 53 162 10 106 73 43 74 63 198 183 127 64 63 171 138 158 118 30 130 75 43 151 64 44 43
Character c h a p t e r , t h e l i m i t . T h e
Milliseconds 86 277 85 74 127 137 119 75 128 75 53 55 76 41 116 45 223 86 128 139 43 214 130 42 53
Character i d e a o f a l i m i t p l a y s a f
Milliseconds 215 148 165 87 179 54 137 33 140 95 586 33 233 114 106 65 171 147 75 202 115 117 170 85 158
Character o u n d a t i o n a l o r -r -o r o l e t h r o
Milliseconds 127 54 221 85 108 105 42 53 646 86 170 115 137 107 358 130 117 117 169 54 85 395 96 126 74
Character u g h o u t c a l c u l u s .
Milliseconds 33 108 125 447 75 98 73 210 96 12 542 64 95 210 84 137
WPM Timing
Seconds WPM
2.65 72.44
5.3 74.71
7.95 78.48
10.6 70.18
13.25 64.29
15.9 68.67
18.55 73.74
21.2 74.71
23.85 73.95
26.5 77.88
29.15 74.5
31.8 79.24
34.45 78.02
37.1 79.88
39.75 79.99
42.4 80.93
45.06 78.3
47.71 78.98
50.36 81.02
53.01 82.63
55.66 83.01
58.31 82.32
60.96 82.09
63.61 82.82
66.26 81.14
68.91 80.46
71.56 80.66
74.21 78.75
76.86 76.35
79.51 75.16
82.16 75.37
84.81 76.12
87.46 76.29
90.11 77.11
92.76 77.49
95.41 77.6
98.06 78.07
100.71 77.33
103.36 76.51
106.01 76.63
108.66 77.3
111.31 77.08
113.96 77.29
116.61 76.46
119.26 77.48
121.91 78.45
124.56 78.51
127.21 78.76
129.86 78.45
132.52 78.24