rajnish (rajnishkumar31)

Race #23283

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Official speed 79.76 wpm (129.99 seconds elapsed during race)
Without ending ping 80.21 wpm (723 ms delay sending score to TypeRacer’s server)
Timerless 81.04 wpm (1,326 ms elapsed before first character typed; 127.94 seconds elapsed during race)
Timerless minus one 80.94 wpm, ignoring the first character typed
Race Start August 25, 2023 10:20:08am UTC
Race Finish August 25, 2023 10:22:18am UTC
Outcome No win (2 of 5)
Opponents 1. malformant (87.55 wpm)
3. jvgcalites (79.69 wpm)
5. qw_slow_typist (68.21 wpm)
Accuracy 95.2%
Points 215.37
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 Calcuuslus is a tolol that helps us undesrstnad and hwo ow a chang e in aone quanittiyt ty is related to a change in another. How does the sped ed oddf a falling object change as a function aof time? How does the level of water in a barrle el change as a function of the amount of liquid poured ointo it? We see change cooccurring in neralarly everything we observe in the world and universe, and powerful modern, instruments help us see more and more. In thi sss esection we intorroduce the idea ss of average and instantaneous rates of change, and show that they are closely related to the slope of a vcurve a ta t a point P on the curve. We give precise developments of these important concepts in the next hcapchanpter, but for nwo wowe we use an informal approach so you will see how they lead unaturally to the main idea of htithis chapter, thie e limite. T. The lidea of a limit plays a foundational role thoruroguughtou tout claalculus.
Timing
Character C a l c u u s -s -u l u s i s a t o l -l o l
Milliseconds 1326 166 103 309 69 612 161 248 102 587 478 96 67 126 10 126 98 104 152 68 187 473 176 177 86
Character t h a t h e l p s u s u n d e s -s r s t n a
Milliseconds 82 54 69 68 33 133 94 97 152 81 65 132 68 42 201 197 85 136 234 429 107 173 146 108 0
Character d - -d -a -n a n d h w o - -o -w o w a c h a
Milliseconds 129 88 290 110 111 113 60 134 69 51 183 71 5 105 358 101 111 157 37 56 60 112 134 76 55
Character n g - e i n a -a o n e q u a n i t -t -i t i
Milliseconds 112 68 146 383 52 56 104 44 69 21 404 139 49 38 66 429 38 466 101 231 52 372 82 156 34
Character y t - -t -y t y i s r e l a t e d t o a
Milliseconds 269 136 119 259 109 111 136 88 63 162 63 28 211 69 121 81 68 77 158 38 140 57 48 83 121
Character c h a n g e i n a n o t h e r . H o w d o
Milliseconds 75 110 41 135 29 63 114 81 44 96 147 91 86 75 102 101 55 75 64 207 202 105 49 177 52
Character e s t h e s p e d - -d e d o d -d d -d f a
Milliseconds 113 98 0 109 33 55 43 204 45 194 149 102 368 92 80 146 27 134 145 439 124 260 240 55 46
Character f a l l i n g o b j e c t c h a n g e a s
Milliseconds 142 473 75 85 158 128 62 17 79 127 273 105 129 172 102 96 135 80 40 127 33 80 119 84 204
Character a f u n c t i o n a -a o f t i m e ? H o
Milliseconds 158 462 85 123 232 362 128 128 50 48 63 62 106 334 144 60 30 148 41 35 93 231 76 337 232
Character w d o e s t h e l e v e l o f w a t e r
Milliseconds 63 59 137 76 91 31 71 102 47 52 54 270 71 132 78 130 118 153 63 65 368 61 114 115 60
Character i n a b a r r l e - -e -l e l c h a n g e
Milliseconds 83 413 76 122 29 132 220 140 111 153 133 45 107 361 107 111 108 106 55 188 97 43 127 38 108
Character a s a f u n c t i o n o f t h e a m o
Milliseconds 129 306 58 77 182 482 325 92 180 84 125 48 69 24 55 233 38 66 266 23 58 62 146 253 128
Character u n t o f l i q u i d p o u r e d o -o i n
Milliseconds 96 177 78 42 440 79 47 128 93 280 41 103 166 93 345 276 71 102 72 439 55 186 365 165 189
Character t o i t ? W e s e e c h a n g e c o -o -c
Milliseconds 339 67 75 211 78 198 95 183 185 64 147 83 182 86 193 70 119 38 90 80 141 181 81 319 94
Character o c c u r r i n g i n n e r a l -l -a -r a r l y
Milliseconds 165 91 220 167 122 189 117 63 47 76 105 58 75 210 96 155 103 137 242 209 242 89 97 106 116
Character e v e r y t h i n g w e o b s e r v e i n
Milliseconds 79 318 175 82 66 384 195 79 128 73 35 77 123 35 138 366 138 239 59 34 220 107 102 99 36
Character t h e w o r l d a n d u n i v e r s e ,
Milliseconds 121 137 51 38 38 187 39 111 39 123 48 158 55 49 51 176 163 69 76 161 45 239 35 252 42
Character a n d p o w e r f u l m o d e r n , - -, i
Milliseconds 48 44 44 54 275 223 28 34 25 502 61 114 88 146 117 34 321 36 115 353 9 395 91 105 126
Character n s t r u m e n t s h e l p u s s e e m o
Milliseconds 75 52 176 232 94 179 46 118 54 109 181 456 143 57 291 82 102 60 53 180 126 183 38 157 56
Character r e a n d m o r e . I n t h i s s -s -s -
Milliseconds 59 39 20 193 41 46 49 123 84 80 39 422 69 183 129 65 116 41 43 110 7 194 302 100 108
Character s e -e s e c t i o n w e i n t o r -r -o r o d
Milliseconds 71 92 162 413 86 38 204 124 91 39 60 73 195 31 121 154 73 164 112 60 388 82 114 86 351
Character u c e t h e i d e a s -s - s o f a v e r
Milliseconds 103 65 177 44 230 45 39 36 347 55 169 76 185 167 314 87 74 64 119 80 61 478 204 127 83
Character a g e a n d i n s t a n t a n e o u s r a t
Milliseconds 166 119 115 111 196 83 13 92 155 74 65 341 143 62 308 97 241 401 186 97 64 70 329 80 205
Character e s o f c h a n g e , a n d s h o w t h
Milliseconds 145 0 109 152 75 37 237 68 364 102 127 87 123 66 37 67 59 39 136 95 51 78 41 142 32
Character a t t h e y a r e c l o s e l y r e l a t
Milliseconds 102 80 46 115 27 43 153 35 293 105 69 16 350 67 139 11 53 168 108 58 205 58 157 118 61
Character e d t o t h e s l o p e o f a v -v c u
Milliseconds 76 180 37 145 55 52 98 14 73 42 137 100 175 132 135 12 142 61 59 65 94 119 323 63 141
Character r v e a t a - -a -t - t a p o i n t P
Milliseconds 187 198 103 68 192 118 10 148 0 349 287 116 140 85 58 28 133 437 257 207 91 73 65 350 257
Character o n t h e c u r v e . W e g i v e p r e
Milliseconds 200 51 68 84 65 18 41 200 89 96 169 93 183 62 393 163 101 159 57 99 109 45 149 161 66
Character c i s e d e v e l o p m e n t s o f t h e s
Milliseconds 183 101 89 86 47 161 148 132 84 54 217 95 163 128 107 108 72 96 102 30 86 97 61 12 178
Character e i m p o r t a n t c o n c e p t s i n t
Milliseconds 60 55 158 79 126 31 108 410 83 50 131 102 198 70 20 148 188 77 98 95 39 132 41 97 95
Character h e n e x t h c a p -p -a -c -h c h a n -n p t e r
Milliseconds 72 0 63 173 60 145 134 44 229 0 124 120 279 101 107 108 88 132 38 134 576 199 101 77 85
Character , b u t f o r n w o w -w - -o -w o w e - -e
Milliseconds 70 66 171 38 156 15 225 62 81 61 111 77 0 109 166 193 105 119 112 282 48 79 100 317 99
Character w e u s e a n i n f o r m a l a p p r o
Milliseconds 125 126 55 149 192 98 29 147 237 100 65 243 63 85 130 105 72 148 139 81 163 67 109 190 60
Character a c h s o y o u w i l l s e e h o w t
Milliseconds 138 158 61 77 135 50 88 117 93 45 54 139 61 177 117 48 84 81 387 96 174 68 66 48 353
Character h e y l e a d u -u n a t u r a l l y t o t
Milliseconds 42 69 89 75 129 69 78 117 99 95 315 172 62 106 61 462 89 25 126 119 52 123 54 68 103
Character h e m a i n i d e a o f h t i -i -t -h t h i
Milliseconds 48 63 35 173 69 49 95 83 111 101 151 54 72 81 58 70 118 8 98 348 98 115 150 69 66
Character s c h a p t e r , t h i e - -e -i e l i m i
Milliseconds 67 69 229 106 41 438 165 94 66 69 58 78 58 84 8 40 344 97 110 62 71 235 63 152 116
Character t e . T -T - -. -e . T h e l -l i d e a o f
Milliseconds 87 55 100 51 108 261 102 108 119 220 49 130 143 159 97 398 338 158 67 162 54 72 111 54 53
Character a l i m i t p l a y s a f o u n d a t i o
Milliseconds 59 99 122 43 196 129 122 66 169 213 39 86 116 38 106 79 191 84 46 141 46 132 57 63 29
Character n a l r o l e t h o r u -u -r -o r o g u -u -g u g
Milliseconds 54 128 291 78 212 29 161 108 48 245 40 131 39 59 316 105 106 89 151 38 33 397 94 178 106
Character h t o u t -t - -u -o -t o u t c l a -a -l a l c u l
Milliseconds 107 124 106 39 99 26 265 93 120 116 123 215 28 42 48 199 103 156 304 89 65 145 230 80 161
Character u s .
Milliseconds 124 154 96
WPM Timing
Seconds WPM
2.6 23.08
5.2 36.93
7.8 55.39
10.4 50.77
13 55.39
15.6 53.85
18.2 57.37
20.8 65.77
23.4 65.65
26 66.47
28.6 67.56
31.2 69.62
33.8 72.79
36.4 71.87
39 73.24
41.6 74.14
44.2 73.04
46.8 73.85
49.4 74.09
52 72.93
54.6 73.85
57.2 76.58
59.8 76.26
62.4 76.16
64.99 77.54
67.59 76.69
70.19 76.76
72.79 76.32
75.39 76.72
77.99 76.78
80.59 78.62
83.19 79.77
85.79 79.59
88.39 78.74
90.99 79.26
93.59 80.01
96.19 80.84
98.79 80.9
101.39 80.72
103.99 79.85
106.59 80.61
109.19 81.22
111.79 81.58
114.39 81.72
116.99 81.65
119.59 80.57
122.19 81.41
124.79 81.35
127.39 80.54
129.99 79.76