Amir (amirahmedimtiaz)

Race #8810

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Official speed 61.89 wpm (167.52 seconds elapsed during race)
Without ending ping 61.96 wpm (199 ms delay sending score to TypeRacer’s server)
Timerless 63.19 wpm (3,249 ms elapsed before first character typed; 164.08 seconds elapsed during race)
Timerless minus one 63.12 wpm, ignoring the first character typed
Race Start November 8, 2024 4:26:11pm UTC
Race Finish November 8, 2024 4:28:59pm UTC
Outcome No win (5 of 5)
Opponents 1. alyankhawaja (94.16 wpm)
2. jackthehuman (87.99 wpm)
3. ig_xodussy (87.80 wpm)
4. sati2030 (83.95 wpm)
Accuracy 96.2%
Points 167.11
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 Calculluus is a tool that helps ofus undersatnd understand how a change in one qunaantity is related to a change in another. How does the speed aoof a falling object change as a function of time? How does the level of water in a barrel change as a function of the maozamount of liquid puiooured into it? We see change occuringrin gin g in nearly everything we eobobesserver i in the world and universe, and powefurful modern instruments ehelp us see more and more. In this section we introduce the idea oss of average and instantenanoueeous rate sof rates of change, and show that they are closely related to the slope of a curve at a point P on th e curve. We give precise developments of these important onconcepts in the nesxxtxt chapter, but for now we use an infnoormatl al approach so you wills e see how they lead naturally to the main idea of this chapter, the limti.it. The idea of a limit play s s a foundational role throughou t calculus.
Timing
Character C a l c u l l u -u -l u s i s a t o o l t h
Milliseconds 3249 331 369 138 186 77 205 10 410 137 241 46 120 231 105 75 140 75 117 54 137 133 91 44 118
Character a t h e l p s o f -f -o u s u n d e r s a t n
Milliseconds 45 95 56 48 101 87 48 85 77 97 166 325 133 202 75 66 98 58 67 154 90 120 106 28 101
Character d -u -n -d -e -r -s -a -t -n -d - u n d e r s t a n d h
Milliseconds 67 94 537 0 0 0 0 0 0 0 0 0 0 487 68 42 170 87 110 136 38 109 90 111 54
Character o w a c h a n g e i n o n e q u n a -a -n
Milliseconds 71 44 114 49 132 118 89 68 111 56 96 52 62 38 104 80 102 82 145 97 83 194 114 361 137
Character a n t i t y i s r e l a t e d t o a c h
Milliseconds 87 97 244 134 111 77 95 85 88 77 131 64 96 119 91 76 156 89 100 117 86 147 101 185 31
Character a n g e i n a n o t h e r . H o w d o e s
Milliseconds 85 117 31 110 68 189 84 49 98 98 206 9 213 59 70 110 84 139 181 98 205 97 112 72 89
Character t h e s p e e d a o -o -a o f a f a l l i
Milliseconds 30 80 66 91 75 107 95 149 152 132 47 106 109 274 133 182 51 78 123 164 160 272 156 133 81
Character n g o b j e c t c h a n g e a s a f u n
Milliseconds 88 79 107 157 85 203 63 175 135 118 290 192 85 148 61 60 118 40 143 110 59 130 173 335 89
Character c t i o n o f t i m e ? H o w d o e s t
Milliseconds 22723 200 111 9 78 95 84 123 110 409 64 78 66 164 125 198 268 100 129 75 116 118 52 148 96
Character h e l e v e l o f w a t e r i n a b a
Milliseconds 83 133 129 104 84 117 102 78 128 118 88 57 176 31 149 138 151 128 67 84 100 42 140 49 102
Character r r e l c h a n g e a s a f u n c t i o n
Milliseconds 133 139 121 51 81 108 60 95 83 92 85 7 52 154 86 68 101 278 122 41 60 169 52 61 33
Character o f t h e m a o -o z -m -a -z a m o u n t o f
Milliseconds 67 118 43 61 95 67 109 57 74 93 118 231 210 463 0 0 353 113 101 70 58 49 107 75 69
Character l i q u i d p u i o -o -i -u o u r e d i n t o
Milliseconds 120 234 87 129 113 93 154 146 100 146 112 6 243 141 216 210 67 83 66 139 151 128 74 41 100
Character i t ? W e s e e c h a n g e o c c u r i
Milliseconds 66 84 84 172 85 143 196 105 91 68 156 68 178 56 116 87 51 82 34 170 131 224 138 133 108
Character n g -g -n -i r i n g i n - -n -i -g - g i n n e
Milliseconds 58 93 2616 190 217 244 82 79 105 61 101 79 84 233 155 153 147 142 110 130 106 68 116 211 126
Character a r l y e v e r y t h i n g w e e o b -b -e -o
Milliseconds 75 54 80 81 94 45 121 92 37 47 142 102 49 121 33 87 109 66 83 141 60 88 289 374 0
Character o b e s -s -e s e r v e r i -i - -r i n t h e
Milliseconds 20370 101 109 143 186 122 100 85 72 176 86 87 44 73 309 128 159 81 141 64 45 102 105 209 102
Character w o r l d a n d u n i v e r s e , a n d p
Milliseconds 187 64 54 116 62 94 63 84 84 92 123 117 138 151 122 154 121 75 174 34 114 66 122 95 68
Character o w e f u -u -f r f u l m o d e r n i n s t r u
Milliseconds 81 53 41 241 102 248 130 203 164 156 110 90 146 88 90 136 67 84 123 67 100 72 121 95 79
Character m e n t s e -e h e l p u s s e e m o r e
Milliseconds 188 75 132 31 104 100 156 309 188 82 95 54 82 126 59 92 115 106 173 90 110 76 34 62 84
Character a n d m o r e . I n t h i s s e c t i o n
Milliseconds 43 128 71 78 103 60 32 85 114 76 141 176 37 159 117 12 92 130 117 66 184 146 88 32 64
Character w e i n t r o d u c e t h e i d e a o s
Milliseconds 71 69 74 83 108 92 142 81 104 125 109 79 187 79 178 108 85 98 118 13 144 67 100 69 105
Character -s -o - s o f a v e r a g e a n d i n s t a
Milliseconds 242 133 138 80 92 75 88 89 100 71 151 123 123 106 67 82 48 108 69 78 85 118 139 89 83
Character n t e n -n -e a n o u e -e -u -o e o u s r a t e s
Milliseconds 101 138 339 149 341 124 136 94 217 95 119 221 173 141 95 133 57 83 97 123 81 104 76 79 5
Character o f -s -o -f - -r -a -t -e - r a t e s o f c h a n
Milliseconds 102 109 44 454 0 0 0 161 0 0 0 0 226 87 123 79 77 111 70 101 91 120 74 121 104
Character g e , a n d s h o w t h a t t h e y a r
Milliseconds 63 84 133 67 78 83 72 89 115 112 49 72 113 262 40 128 73 59 160 114 156 126 114 41 76
Character e c l o s e l y r e l a t e d t o t h e
Milliseconds 183 207 55 105 185 62 100 82 137 134 69 104 113 160 167 74 165 62 141 80 77 84 55 111 118
Character s l o p e o f a c u r v e a t a p o i
Milliseconds 99 103 176 88 108 54 88 78 88 124 121 140 103 104 179 64 97 58 132 113 53 127 36 82 104
Character n t P o n t h - e c u r v e . W e g
Milliseconds 106 40 155 139 156 140 104 85 43 103 159 366 74 97 100 130 56 211 89 132 188 200 313 849 244
Character i v e p r e c i s e d e v e l o p m e n t s
Milliseconds 106 128 57 48 76 90 116 241 128 83 62 117 153 145 90 87 100 186 82 177 164 121 92 70 72
Character o f t h e s e i m p o r t a n t o n -n -o c o
Milliseconds 93 82 69 107 79 191 395 84 186 58 190 63 85 103 180 68 94 124 76 290 126 323 148 151 55
Character n c e p t s i n t h e n e s x x t -t -x -x -s x
Milliseconds 68 55 201 117 99 179 10 436 93 70 85 112 68 103 44 75 280 0 102 191 209 145 153 154 26
Character t c h a p t e r , b u t f o r n o w w e
Milliseconds 132 134 104 77 95 134 202 119 94 184 71 139 70 84 94 163 80 83 78 94 69 71 94 477 80
Character u s e a n i n f n o -o -n o r m a t l a -a -
Milliseconds 66 142 110 47 83 87 301 184 173 84 55 44 215 276 134 222 108 117 87 91 10 116 147 224 145
Character -l -t l a p p r o a c h s o y o u w i l l s
Milliseconds 146 123 215 74 139 79 138 82 96 38 112 101 130 158 105 64 125 90 93 55 95 76 61 122 92
Character e -e - -s s e e h o w t h e y l e a d n
Milliseconds 22 60 364 127 134 64 65 86 171 41 159 57 74 75 122 45 90 82 87 156 72 35 129 75 89
Character a t u r a l l y t o t h e m a i n i d e a
Milliseconds 36 91 91 105 79 86 155 83 103 28 129 150 92 77 113 8 247 199 88 79 62 150 92 147 61
Character o f t h i s c h a p t e r , t h e l i m
Milliseconds 50 94 99 81 151 111 49 86 63 281 95 56 110 99 77 144 165 80 164 104 91 90 77 68 99
Character t i . -. -i -t i t . T h e i d e a o f a l
Milliseconds 181 8 242 394 182 150 261 121 103 92 102 114 75 99 85 57 134 72 35 52 109 52 188 123 118
Character i m i t p l a y s - -s - - s a f o u n
Milliseconds 72 90 126 98 91 66 72 87 115 93 32 109 285 127 189 275 129 62 84 44 129 103 397 97 12
Character d a t i o n a l r o l e t h r o u g h o u -
Milliseconds 87 79 146 113 47 66 230 105 109 144 92 221 82 180 154 124 110 192 99 137 249 384 76 214 352
Character t c a l c u l u s .
Milliseconds 126 100 381 173 151 167 143 73 168 119 153
WPM Timing
Seconds WPM
3.35 3.58
6.7 34.03
10.05 39.4
13.4 59.1
16.75 63.75
20.1 73.42
23.45 73.68
26.8 72.53
30.15 64.47
33.5 58.02
36.86 52.75
40.21 48.35
43.56 44.63
46.91 41.44
50.26 42.26
53.61 45.89
56.96 51.2
60.31 51.93
63.66 53.54
67.01 53.19
70.36 51.51
73.71 53.07
77.06 50.77
80.41 48.65
83.76 46.7
87.11 44.91
90.46 43.24
93.81 41.83
97.16 42.86
100.51 44.29
103.86 46.21
107.21 48.8
110.57 50.14
113.92 50.88
117.27 50.76
120.62 52.53
123.97 54.21
127.32 55.33
130.67 55.65
134.02 56.77
137.37 57.13
140.72 57.56
144.07 58.14
147.42 58.36
150.77 59.45
154.12 60.58
157.47 60.81
160.82 61.33
164.17 62.06
167.52 61.89