rajnish (rajnishkumar31)

Race #23462

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Official speed 79.48 wpm (130.45 seconds elapsed during race)
Without ending ping 79.86 wpm (623 ms delay sending score to TypeRacer’s server)
Timerless 80.87 wpm (1,626 ms elapsed before first character typed; 128.20 seconds elapsed during race)
Timerless minus one 80.78 wpm, ignoring the first character typed
Race Start August 31, 2023 3:05:25pm UTC
Race Finish August 31, 2023 3:07:36pm UTC
Outcome No win (3 of 5)
Opponents 1. mark40511 (117.32 wpm)
2. joehandsome (97.29 wpm)
Accuracy 95.8%
Points 214.59
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 Calculus is a tool that helps us understnad and how a change in one quaintity is related t oo a change in another. How does the sppeeed of a falling object change a assa f a function of itmtime/? Hwoow does the level of water in s a barrel change as a function of athe amount of luqiiquid 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 aveagrage and instantaneous rates of change, and show that they are closely related to the slpe oepe of a curve at a point oP on the curve. We give precise devleelopmentrs os of these oimpimpraoratntant concepts in teh he next chapter, but for now we use ano inforamal appraoaoch oach so you swillse see how they lead naturally to the main idea of this chapter, the limit. The idea of a mlimit plays a foundationa l role thoroughotu ut calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 1626 141 124 353 77 137 199 100 87 178 411 73 57 108 85 119 140 167 92 47 63 48 89 49 113
Character e l p s u s u n d e r s t n a d - -d -a -n a n
Milliseconds 120 87 148 92 35 118 67 50 217 183 75 136 16 228 150 50 0 144 40 328 115 109 93 140 89
Character d h o w a c h a n g e i n o n e q u a
Milliseconds 59 57 163 57 0 100 83 94 136 62 104 71 89 75 49 76 57 70 129 92 40 71 319 57 186
Character i -i n t i t y i s r e l a t e d t o -o - o
Milliseconds 0 400 223 497 52 174 24 410 125 63 52 208 57 60 160 51 81 192 17 148 78 11 445 291 181
Character a c h a n g e i n a n o t h e r . H o w
Milliseconds 42 135 105 190 109 89 80 67 145 129 249 317 84 114 133 346 122 78 51 64 99 55 323 238 73
Character d o e s t h e s p p e -e -p e e d o f a
Milliseconds 31 192 80 96 67 26 101 20 86 4 148 84 160 67 263 104 7 160 165 35 116 82 110 81 166
Character f a l l i n g o b j e c t c h a n g e a a
Milliseconds 306 88 123 231 127 68 46 74 146 145 77 165 156 91 66 144 67 100 100 44 108 90 52 161 135
Character s -s -a - s a f -f - - -a a f u n c t i o n
Milliseconds 34 255 197 153 133 86 41 176 9 330 106 114 129 174 135 71 232 135 189 104 140 0 66 50 72
Character o f i t m -m -t -i t i m e / -/ ? H w o -o -w o w
Milliseconds 138 112 72 136 48 110 282 104 100 150 74 49 63 245 365 182 46 385 225 0 465 79 203 84 161
Character d o e s t h e l e v e l o f w a t e r i
Milliseconds 194 87 79 81 33 72 39 64 41 213 89 136 75 85 102 174 18 94 337 93 105 107 62 78 117
Character n s - -s a b a r r e l c h a n g e a s
Milliseconds 53 92 115 84 334 107 79 76 151 96 240 131 95 77 100 172 78 39 122 80 179 112 366 53 67
Character a f u n c t i o n o f a -a t h e a m o u n
Milliseconds 134 49 198 166 185 85 144 37 68 37 78 124 66 72 103 361 116 81 44 51 204 265 115 100 153
Character t o f l u q i -i -q -u i q u i d p o u r e d
Milliseconds 595 41 117 54 74 155 94 157 195 247 183 112 271 128 202 129 171 156 447 236 90 130 59 168 39
Character i n t o i t ? W e s e e c h a n g e o c
Milliseconds 68 115 149 51 93 115 49 228 92 184 187 98 107 130 146 204 177 91 46 130 20 117 88 200 243
Character c u r r i n g i n n e a r l y e v e r y t h
Milliseconds 235 132 168 168 105 87 53 69 128 48 99 377 93 49 26 151 103 57 161 143 73 56 82 136 112
Character i n g w e o b s e r v e i n t h e w o r
Milliseconds 105 81 31 56 214 32 91 290 133 209 41 36 213 107 92 23 70 123 78 51 37 41 70 114 70
Character l d a n d u n i v e r s e , a n d p o w e
Milliseconds 108 71 109 204 65 55 66 136 171 66 88 146 87 570 44 94 35 79 46 33 69 228 246 12 33
Character r f u l m o d e r n i n s t r u m e n t s h
Milliseconds 34 489 54 150 80 140 98 44 210 45 69 86 188 115 36 118 152 35 487 69 132 75 106 156 299
Character e l p u s s e e m o r e a n d m o r e .
Milliseconds 111 77 162 76 90 51 99 127 122 207 58 141 49 84 52 33 188 23 55 67 162 26 114 23 137
Character I n t h i s s e c t i o n w e i n t r o
Milliseconds 39 221 111 52 118 71 51 106 21 210 66 217 93 73 17 65 95 111 41 95 196 54 144 189 58
Character d u c e t h e i d e a s o f a v e a g -g -a
Milliseconds 365 104 77 194 82 56 52 46 77 121 136 134 63 167 169 97 98 43 366 112 139 281 59 377 96
Character r a g e a n d i n s t a n t a n e o u s r a
Milliseconds 151 19 172 313 141 73 107 43 73 129 85 8 118 116 114 150 447 175 568 115 55 89 90 147 83
Character t e s o f c h a n g e , a n d s h o w t
Milliseconds 137 53 80 106 74 80 52 550 73 93 90 48 84 160 233 231 76 71 55 219 93 53 63 50 109
Character h a t t h e y a r e c l o s e l y r e l a
Milliseconds 62 51 101 50 126 27 56 116 52 93 83 35 54 282 89 159 35 24 164 92 44 212 68 127 141
Character t e d t o t h e s l p e - -e -p o e -e p e
Milliseconds 36 71 198 20 160 30 83 178 78 0 58 148 77 177 111 41 389 100 431 169 106 547 223 105 131
Character o f a c u r v e a t a p o i n t o -o P
Milliseconds 135 73 44 66 111 116 113 95 316 280 92 119 98 39 129 59 332 245 61 79 88 32 155 382 184
Character o n t h e c u r v e . W e g i v e p r
Milliseconds 232 147 84 62 109 55 30 42 215 80 66 206 101 140 51 394 191 61 180 66 91 91 23 227 133
Character e c i s e d e v l e -e -l e l o p m e n t r s o
Milliseconds 66 178 124 93 49 74 197 152 153 99 36 370 107 101 129 254 73 151 117 90 105 0 83 51 123
Character -o - -s -r s o f t h e s e o i m p -p -m -i -o i m
Milliseconds 249 206 107 109 73 123 67 95 54 152 40 28 226 44 49 334 0 103 102 344 205 124 111 343 46
Character p r a -a -r o r a t n -n -t -a t a n t c o n c e p t
Milliseconds 130 176 175 311 95 190 80 71 140 0 373 101 122 231 78 44 137 88 165 61 48 170 151 94 44
Character s i n t e h - -h -e h e n e x t c h a p t
Milliseconds 164 23 177 60 85 56 84 25 76 405 116 108 288 81 37 235 72 163 144 156 312 97 75 126 110
Character e r , b u t f o r n o w w e u s e a n
Milliseconds 197 47 69 31 160 23 159 44 234 95 54 88 113 99 11 127 170 33 115 230 51 40 155 338 91
Character o - -o i n f o r a -a m a l a p p r a o -o -a a
Milliseconds 92 11 419 121 173 121 83 104 430 195 264 470 162 59 119 76 223 230 181 224 111 124 430 98 146
Character o c h - -h -c -o -a o a c h s o y o u s -s w i
Milliseconds 37 156 59 66 276 114 104 225 106 209 115 231 154 130 202 91 69 131 87 68 53 73 322 56 161
Character l l s e - -e -s s e e h o w t h e y l e a
Milliseconds 193 98 128 87 5 400 109 126 125 75 319 167 118 149 65 52 85 395 51 34 146 36 125 91 48
Character d n a t u r a l l y t o t h e m a i n i
Milliseconds 157 73 164 78 64 122 109 79 46 114 127 75 119 72 52 60 22 72 50 134 62 71 86 82 119
Character d e a o f t h i s c h a p t e r , t h e
Milliseconds 108 155 87 90 105 74 57 221 64 176 152 59 209 71 89 196 105 125 54 58 40 180 0 87 25
Character l i m i t . T h e i d e a o f a m -m l i
Milliseconds 200 37 177 114 100 130 62 420 184 52 55 310 70 147 81 90 90 56 61 53 112 97 372 178 74
Character m i t p l a y s a f o u n d a t i o n a -
Milliseconds 269 126 68 122 191 206 15 88 107 62 94 599 194 85 37 150 84 106 107 59 19 69 186 184 365
Character l r o l e t h o -o r o u g h o t u - -u -t u t
Milliseconds 147 60 210 22 165 59 44 203 63 113 417 72 137 45 14 578 226 34 31 106 374 111 463 202 38
Character c a l c u l u s .
Milliseconds 62 183 79 271 507 84 145 136 388 752
WPM Timing
Seconds WPM
2.61 27.6
5.22 68.99
7.83 68.99
10.44 78.19
13.04 78.19
15.65 75.89
18.26 80.82
20.87 80.49
23.48 79.73
26.09 78.65
28.7 74.43
31.31 76.28
33.92 76.07
36.53 78.19
39.13 77.89
41.74 75.32
44.35 76.57
46.96 77.68
49.57 79.16
52.18 81.64
54.79 81.92
57.4 82.37
60.01 84.19
62.61 85.28
65.22 85.55
67.83 85.09
70.44 84.84
73.05 86.41
75.66 87.55
78.27 85.4
80.88 85.61
83.49 85.52
86.1 85.58
88.7 84.55
91.31 83.58
93.92 82.54
96.53 82.17
99.14 82.79
101.75 82.32
104.36 81.41
106.97 79.87
109.58 79.29
112.19 79.8
114.79 81.01
117.4 81.57
120.01 81.49
122.62 81.81
125.23 81.45
127.84 80.54
130.45 79.48