Omar (omarango)

Race #449

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Official speed 90.58 wpm (114.46 seconds elapsed during race)
Without ending ping 90.71 wpm (162 ms delay sending score to TypeRacer’s server)
Timerless 91.00 wpm (361 ms elapsed before first character typed; 113.94 seconds elapsed during race)
Timerless minus one 90.89 wpm, ignoring the first character typed
Race Start August 2, 2024 11:37:31pm UTC
Race Finish August 2, 2024 11:39:26pm UTC
Outcome Win (1 of 3)
Opponents 3. dogphile (75.21 wpm)
Accuracy 96.4%
Points 244.56
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 understand how a change in one quanitity is realtelatded to a chnge ange in another. How does the speedo of a fallling ining object change as a function of tiemme? How does the level of water in a barrel chngange as a function of h=tthe amount of liquid poured in to it? We dsee change poccuriring in nearly everything we observe in the world and univrerse, and powerful modern instrument hes help us see more and more. In this secitontion we introdu ce the ideas of average and instantaneous rates of chagennge, and show that they are closely ralteelated to the sloep pe of a curve tat a point P on the urcurve. We give aprecise developments of these important onconcepts 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. Thd e idea of a limit plays oa foundational role thoruroughtouit t calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 361 401 104 141 126 424 80 122 58 134 113 344 177 65 183 65 122 152 109 109 85 56 36 22 103
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 89 96 0 477 76 117 102 76 115 151 32 147 59 140 298 113 111 83 39 106 56 41 55 177 80
Character c h a n g e i n o n e q u a n i -i t i t y
Milliseconds 147 25 131 61 68 50 41 75 58 76 78 74 55 55 185 66 150 55 192 399 105 82 93 75 88
Character i s r e a l t e -e -t -l -a l a t d -d e d t o a
Milliseconds 128 109 47 332 112 4 92 122 29 194 199 99 95 244 24 92 215 278 65 117 62 193 28 110 309
Character c h n g e - -e -g -n a n g e i n a n o t h e
Milliseconds 70 118 67 170 58 51 59 218 107 85 109 117 116 79 34 23 119 76 92 74 83 47 83 79 63
Character r . H o w d o e s t h e s p e e d o -o o
Milliseconds 35 96 65 221 108 87 109 101 64 98 71 30 112 29 54 47 88 75 111 139 345 97 405 116 154
Character f a f a l l l i n g - -g -n -i i n -n -i -l i n g
Milliseconds 71 89 58 466 75 79 51 113 112 16 84 21 80 244 90 95 99 211 90 167 109 358 180 77 84
Character o b j e c t c h a n g e a s a f u n c t
Milliseconds 59 78 90 166 176 167 227 95 338 40 139 46 69 45 116 89 89 61 121 80 208 129 145 126 97
Character i o n o f t i e m -m -e m e ? H o w d o e s
Milliseconds 47 10 88 79 71 71 67 121 42 60 5 351 112 232 48 532 148 307 106 178 345 100 87 108 52
Character t h e l e v e l o f w a t e r i n a
Milliseconds 27 156 41 37 67 100 67 109 37 55 120 78 28 118 84 109 99 109 54 51 62 66 72 384 304
Character b a r r e l c h n g -g -n a n g e a s a f u
Milliseconds 126 117 96 71 252 94 95 192 104 165 48 258 105 110 115 43 24 104 83 72 66 352 99 95 139
Character n c t i o n o f h = -= t -t -h t h e a m o u n
Milliseconds 411 76 138 38 16 93 105 74 87 75 80 445 8 98 221 90 122 87 63 49 121 80 100 89 152
Character t o f l i q u i d p o u r e d i n - t o
Milliseconds 108 110 13 154 320 166 73 42 148 58 90 90 169 77 92 86 69 151 62 29 79 109 436 89 117
Character i t ? W e d -d s e e c h a n g e p -p o c
Milliseconds 76 104 95 264 146 167 139 111 113 278 55 95 97 389 142 175 95 108 53 50 61 300 334 194 21
Character c u r i -i r i n g i n n e a r l y e v e r y
Milliseconds 133 109 306 74 269 228 96 54 78 80 88 83 51 370 80 55 23 85 111 67 221 138 108 51 52
Character t h i n g w e o b s e r v e i n t h e w
Milliseconds 695 62 46 104 54 151 263 64 74 197 82 186 39 32 196 63 95 47 75 112 51 79 59 79 109
Character o r l d a n d u n i v r -r e r s e , a n d
Milliseconds 90 573 66 103 85 162 92 25 70 93 183 3 464 184 393 48 80 96 54 66 198 105 74 49 71
Character p o w e r f u l m o d e r n i n s t r u m e n
Milliseconds 316 93 16 30 24 158 70 65 106 119 46 59 147 21 74 66 81 245 101 74 173 73 154 59 91
Character t h e -e -h - s h e l p u s s e e m o r e
Milliseconds 76 65 109 129 229 80 100 100 122 164 302 88 87 104 113 77 94 230 86 106 243 95 80 45 43
Character a n d m o r e . I n t h i s s e c i t o
Milliseconds 32 285 44 110 74 341 51 62 52 112 16 221 98 60 168 43 56 52 56 143 108 184 192 6 27
Character n -n -o -t -i t i o n w e i n t r o d u - c e
Milliseconds 75 257 126 151 117 138 109 62 36 84 108 72 74 318 105 27 160 74 121 138 100 361 43 166 89
Character t h e i d e a s o f a v e r a g e a n d
Milliseconds 127 48 76 25 100 62 441 161 75 65 115 86 45 254 107 178 41 165 53 63 65 109 79 63 45
Character i n s t a n t a n e o u s r a t e s o f c h
Milliseconds 108 85 105 103 94 107 302 94 75 133 180 54 123 76 137 140 75 65 63 63 50 108 47 185 73
Character a g e n -n -e -g n g e , a n d s h o w t h a t
Milliseconds 117 80 53 18 276 112 72 337 61 43 116 76 49 91 55 63 104 58 58 72 55 330 36 100 41
Character t h e y a r e c l o s e l y r a l t e -e -t
Milliseconds 65 121 23 100 49 76 77 61 56 35 182 66 151 48 37 79 105 49 169 144 40 129 22 157 90
Character -l -a e l a t e d t o t h e s l o e p - -p -e
Milliseconds 94 100 92 142 52 119 40 134 82 145 212 123 216 60 67 25 137 141 147 117 16 97 293 78 91
Character p e o f a c u r v e t -t a t a p o i n
Milliseconds 202 87 62 83 47 82 121 121 106 135 50 153 87 75 258 358 46 51 62 145 42 312 44 111 68
Character t P o n t h e u r -r -u c u r v e . W e
Milliseconds 41 136 324 80 192 69 89 96 43 89 29 580 108 227 112 79 128 30 145 92 38 71 308 97 123
Character g i v e a -a p r e c i s e d e v e l o p m e n
Milliseconds 134 90 90 27 58 134 251 267 73 45 159 71 125 58 34 236 181 67 79 50 164 102 344 66 120
Character t s o f t h e s e i m p o r t a n t o n -n
Milliseconds 84 76 251 141 72 65 120 34 48 95 113 45 520 142 71 133 153 483 108 84 108 67 348 56 259
Character -o c o n c e p t s i n t h e n e x t c h a
Milliseconds 116 111 71 54 75 168 62 122 75 43 78 75 55 179 71 147 88 79 87 181 72 118 379 58 116
Character p t e r , b u t f o r n o w w e u s e
Milliseconds 18 134 136 59 62 80 149 69 142 179 131 70 124 12 127 58 60 56 209 46 81 120 70 32 87
Character a n i n f o r m a l a p p r o a c h s o y
Milliseconds 89 63 84 94 77 190 102 129 48 157 86 92 130 78 108 94 141 150 84 36 100 227 98 100 5
Character o u w i l l s e e h o w t h e y l e a d
Milliseconds 542 55 66 130 86 217 351 92 85 78 95 106 445 77 23 101 345 48 110 51 76 338 138 73 76
Character n a t u r a l l y t o t h e m a i n i d
Milliseconds 79 101 236 84 98 89 86 29 114 125 51 140 43 84 146 56 57 54 92 122 40 79 92 59 47
Character e a o f t h i s c h a p t e r , t h e l
Milliseconds 166 62 113 87 112 88 113 69 23 34 54 157 80 203 57 136 117 67 28 61 132 52 60 29 96
Character i m i t . T h d - -d e i d e a o f a l
Milliseconds 101 71 96 110 95 88 176 119 56 112 247 98 80 66 94 99 165 109 78 46 368 423 100 75 249
Character i m i t p l a y s o -o a f o u n d a t i o n
Milliseconds 80 62 108 56 70 76 62 99 116 86 104 29 397 49 117 104 62 65 146 74 154 347 52 39 44
Character a l r o l e t h o r u -u -r -o r o u g h t -t o u
Milliseconds 97 101 63 86 83 154 38 83 172 46 92 82 34 241 84 97 80 103 54 95 72 155 329 187 49
Character i t - -t -i t c a l c u l u s .
Milliseconds 7 34 68 295 97 94 100 111 141 65 68 229 113 152 107 107 102
WPM Timing
Seconds WPM
2.29 57.66
4.58 81.25
6.87 92.61
9.16 96.98
11.45 84.92
13.74 82.12
16.02 92.11
18.31 88.46
20.6 81.54
22.89 83.35
25.18 83.39
27.47 84.31
29.76 86.29
32.05 85.37
34.34 84.22
36.63 85.84
38.92 85.72
41.21 85.04
43.5 84.15
45.78 84.13
48.07 85.62
50.36 84.59
52.65 86.61
54.94 86.05
57.23 86.6
59.52 86.89
61.81 86.59
64.1 86.68
66.39 87.49
68.68 87.36
70.97 89.28
73.26 89.11
75.55 88.48
77.83 88.5
80.12 88.06
82.41 87.95
84.7 88.26
86.99 88.01
89.28 88.04
91.57 88.46
93.86 89.37
96.15 89.49
98.44 89.36
100.73 89.95
103.02 90.98
105.31 91.28
107.59 91.34
109.88 91.41
112.17 91.04
114.46 90.58