rajnish (rajnishkumar31)

Race #26408

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Official speed 82.22 wpm (126.10 seconds elapsed during race)
Without ending ping 82.60 wpm (585 ms delay sending score to TypeRacer’s server)
Timerless 84.11 wpm (2,248 ms elapsed before first character typed; 123.27 seconds elapsed during race)
Timerless minus one 84.01 wpm, ignoring the first character typed
Race Start February 9, 2024 5:54:28am UTC
Race Finish February 9, 2024 5:56:34am UTC
Outcome No win (3 of 5)
Opponents 1. micaroni (84.67 wpm)
4. mohamedabdelfattah005 (77.24 wpm)
Accuracy 96.5%
Points 221.98
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 siis a tool that helps us understand how a chnaange in one quantity is relate dd toa c a change in another. How does the speed of a falling object change a ss a sffunction of time? How does the level of water in a arbarrel change as a function of the amount of luqiiquid poured into it? We see change aoccurring in nearly everything we observe in teh wohe world and universe, and powerful modern instruments help us see more and more. In this sectino on we introduce the ideas of average and instantaneous rates of change, and show that they are closerlyly related to teh she slpe ooe pe of a curve at a tpoint P on the curve. We give precise decevelopments o ff these important ccoconcepts in the next chapter, but for neow we use an oinformal approach so you will see how they lead naturally to the main idea of histhis chapter, the limit. The idea of a limit plays a foundations aal role through otoiut ut calcuulus.
Timing
Character C a l c u l u s s i -i -s i s a t o o l t h
Milliseconds 2248 176 172 281 79 149 121 92 104 195 92 286 84 182 68 15 135 59 197 110 134 231 51 204 44
Character a t h e l p s u s u n d e r s t a n d h o
Milliseconds 75 77 16 145 92 120 146 52 72 115 64 46 228 404 137 149 15 178 88 103 42 102 65 140 75
Character w a c h n a -a -n a n g e i n o n e q u a
Milliseconds 0 103 119 70 106 102 165 14 378 84 115 104 99 117 50 94 88 42 128 91 52 45 295 18 235
Character n t i t y i s r e l a t e d -d - d t o a
Milliseconds 435 179 41 284 100 73 100 83 39 147 50 106 145 47 91 200 34 381 92 37 111 99 97 88 0
Character c -c - - -a a c h a n g e i n a n o t h e
Milliseconds 172 70 232 110 125 120 137 58 105 191 106 21 135 63 96 94 46 82 55 157 77 95 37 122 30
Character r . H o w d o e s t h e s p e e d o f
Milliseconds 59 100 51 295 242 98 50 217 19 189 73 30 121 53 35 54 249 74 153 149 144 24 136 108 0
Character a f a l l i n g o b j e c t c h a n g e a
Milliseconds 100 429 226 90 33 153 86 46 42 40 178 180 105 120 166 102 57 175 84 58 111 44 90 51 104
Character s -s - s a s f -f -s f u n c t i o n o f t
Milliseconds 113 37 380 97 64 92 56 111 130 148 312 319 288 157 259 85 131 39 76 36 75 106 36 96 126
Character i m e ? H o w d o e s t h e l e v e l o
Milliseconds 46 58 45 260 76 203 235 88 53 194 63 94 56 45 96 52 44 57 115 66 162 108 56 79 149
Character f w a t e r i n a a r -r -a b a r r e l c
Milliseconds 36 71 251 79 98 109 61 56 72 61 108 33 188 217 118 357 90 76 273 253 156 409 88 69 259
Character h a n g e a s a f u n c t i o n o f t h
Milliseconds 64 47 141 133 148 110 338 68 84 90 96 78 136 195 121 74 46 61 55 41 108 44 82 100 34
Character e a m o u n t o f l u q i -i -q -u i q u i d
Milliseconds 33 50 224 39 155 80 162 102 162 311 83 36 208 91 127 135 253 107 108 301 211 132 166 178 83
Character p o u r e d i n t o i t ? W e s e e c h
Milliseconds 691 254 55 117 82 195 45 162 69 170 83 299 173 83 290 47 248 217 69 153 46 171 74 193 61
Character a n g e a -a o c c u r r i n g i n n e a r l
Milliseconds 51 98 35 95 81 168 324 162 90 174 98 126 316 114 64 71 34 120 54 92 260 82 66 0 160
Character y e v e r y t h i n g w e o b s e r v e i
Milliseconds 94 59 169 158 81 79 49 171 55 149 70 42 73 183 50 72 368 145 236 14 21 645 139 58 76
Character n t e h w o -o -w - -h -e h e w o r l d a n d
Milliseconds 68 69 104 73 0 62 83 69 290 115 105 113 114 221 72 27 193 7 118 105 148 38 328 45 43
Character u n i v e r s e , a n d p o w e r f u l m
Milliseconds 43 208 177 74 76 176 579 168 52 166 20 88 46 36 70 196 245 60 37 23 270 61 161 78 158
Character o d e r n i n s t r u m e n t s h e l p u s
Milliseconds 162 224 199 19 79 91 200 70 29 143 198 110 187 102 102 85 68 191 461 98 95 145 126 82 68
Character s e e m o r e a n d m o r e . I n t h
Milliseconds 77 189 111 154 503 130 116 54 24 51 148 57 46 34 144 86 63 29 172 27 207 110 67 121 45
Character i s s e c t i n o - -o -n o n w e i n t r o
Milliseconds 51 96 25 168 75 246 122 96 109 0 108 375 104 112 206 41 87 108 47 138 180 61 121 182 12
Character d u c e t h e i d e a s o f a v e r a g e
Milliseconds 424 95 144 178 11 90 37 70 33 335 75 181 67 169 146 102 89 35 498 142 636 163 71 189 99
Character a n d i n s t a n t a n e o u s r a t e s
Milliseconds 95 96 30 50 49 195 99 152 274 91 57 456 108 179 385 462 51 72 39 289 59 402 83 84 131
Character o f c h a n g e , a n d s h o w t h a t
Milliseconds 99 90 29 204 65 54 103 53 107 74 24 59 41 67 20 240 85 73 66 95 99 56 92 67 92
Character t h e y a r e c l o s e r l y -y -l -r l y r e
Milliseconds 96 87 30 144 59 118 81 52 90 306 57 164 37 32 32 237 33 270 105 122 277 114 64 238 30
Character l a t e d t o t e h s -s - -h -e h e s l p e
Milliseconds 95 140 39 88 204 35 167 84 88 14 109 11 74 170 228 97 117 108 311 102 161 170 141 182 82
Character o -o - -e -p o e - -e p e o f a c u r v e
Milliseconds 79 70 325 144 150 123 209 73 100 389 111 227 60 123 115 42 63 84 96 107 134 120 314 104 63
Character a t a t -t p o i n t P o n t h e c u r
Milliseconds 308 66 64 97 84 8 501 200 259 80 72 39 78 285 221 187 91 61 171 29 68 11 235 109 83
Character v e . W e g i v e p r e c i s e d e c e -e
Milliseconds 210 125 146 63 338 220 67 202 53 127 71 67 270 126 683 224 75 105 39 88 163 148 171 205 320
Character -c v e l o p m e n t s o f -f - f t h e s e
Milliseconds 97 299 235 199 227 66 169 78 142 85 65 43 101 125 0 492 110 65 107 143 67 22 260 49 47
Character i m p o r t a n t c c o c -c -o -c o n c e p t s
Milliseconds 175 78 94 75 147 352 97 53 130 156 262 68 19 188 267 101 123 213 34 75 201 99 66 117 38
Character i n t h e n e x t c h a p t e r , b u t
Milliseconds 131 61 80 141 18 71 23 164 75 208 120 81 396 102 53 220 7 402 33 82 15 265 70 132 46
Character f o r n e -e o w w e u s e a n o -o i n f
Milliseconds 169 76 82 53 138 83 488 171 65 66 206 402 64 203 55 31 149 210 81 65 153 329 184 72 235
Character o r m a l a p p r o a c h s o y o u w i l
Milliseconds 91 102 68 152 83 70 299 107 137 144 85 144 161 70 57 153 34 100 87 93 53 39 145 44 178
Character l s e e h o w t h e y l e a d n a t u r
Milliseconds 120 96 0 55 185 0 426 83 69 80 364 45 43 147 50 142 58 50 136 61 131 40 131 120 71
Character a l l y t o t h e m a i n i d e a o f
Milliseconds 60 68 107 134 64 138 57 45 78 34 70 29 139 82 64 77 61 98 135 156 63 82 82 46 75
Character h i s -s -i -h t h i s c h a p t e r , t h e l
Milliseconds 111 50 68 385 97 116 48 138 32 86 51 206 83 23 172 90 99 64 110 33 155 70 38 34 215
Character i m i t . T h e i d e a o f a l i m i t
Milliseconds 81 115 120 102 126 55 96 93 40 70 365 151 151 52 96 62 72 49 79 94 138 83 162 109 95
Character p l a y s a f o u n d a t i o n s a -a - -s
Milliseconds 106 152 187 80 43 153 44 108 81 92 110 34 148 50 79 71 67 31 60 96 140 116 222 102 122
Character a l r o l e t h r o u g h o t -t -o - o i u t
Milliseconds 65 144 56 159 91 206 41 64 128 47 178 75 43 106 91 71 126 88 247 112 451 226 35 0 48
Character - -t -u -i u t c a l c u u -u l u s .
Milliseconds 62 416 98 235 318 226 43 58 297 48 340 533 81 611 390 173 58 107 129
WPM Timing
Seconds WPM
2.52 9.52
5.04 40.44
7.57 60.27
10.09 70.18
12.61 75.18
15.13 69.79
17.65 76.13
20.18 80.29
22.7 81.95
25.22 79.94
27.74 83.92
30.26 83.66
32.79 83.08
35.31 85.65
37.83 83.11
40.35 82.08
42.87 82.29
45.4 83.8
47.92 83.89
50.44 82.79
52.96 83.15
55.48 83.92
58.01 83.58
60.53 85.45
63.05 84.5
65.57 84.73
68.09 84.59
70.62 83.61
73.14 85.65
75.66 85.01
78.18 84.57
80.7 82.37
83.23 82.62
85.75 82.71
88.27 82.25
90.79 81.42
93.31 81.4
95.84 80.89
98.36 81.62
100.88 81.48
103.4 81.12
105.92 81.91
108.45 82.55
110.97 83.59
113.49 83.95
116.01 84.61
118.53 84.73
121.06 84.36
123.58 83.32
126.1 82.22