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Race #628

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Official speed 88.35 wpm (117.35 seconds elapsed during race)
Without ending ping 88.49 wpm (186 ms delay sending score to TypeRacer’s server)
Timerless 88.97 wpm (631 ms elapsed before first character typed; 116.53 seconds elapsed during race)
Timerless minus one 88.87 wpm, ignoring the first character typed
Race Start January 10, 2025 11:04:04pm UTC
Race Finish January 10, 2025 11:06:01pm UTC
Outcome No win (3 of 3)
Opponents 2. cogking (105.21 wpm)
Accuracy 96.8%
Points 238.56
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 quantitiy sy is raelatseed to a changei n in another. How does the speed fofo aof a falling object change as a cufuncton ion of time? HOow does the level of water in a barrleel change as a fucntunction of the amount of liquid poured into tiit? We see change oucccurring in nearly everthiything we observe in the world an d universe, and powerful modern instrumenes ts help us see more and more. In this section we introduce the ideas of averangeage ge and instantaneous reateaaates of change, and show that they are closely related to ghthe slpope of a curve at a point P on the curve. We give prcecise developments of these importatnnt concepts in the next chapter, but for now we use an informal approadch so you will see how they lead natruaurally to the main idea of this dchapter, the limit. The idea of a limit plyaays a foundationnaal role throughout calculius.us.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 631 213 80 173 121 91 120 258 107 147 124 79 108 68 123 55 116 205 139 92 81 86 43 58 129
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 71 98 111 87 61 86 84 96 159 131 66 148 81 108 113 104 116 79 101 93 70 68 79 130 100
Character c h a n g e i n o n e q u a n t i t i y s
Milliseconds 127 45 137 32 112 53 72 76 83 95 105 77 75 104 227 38 134 78 78 115 81 94 118 91 111
Character -s - -y -i y i s r a -a e l a t s e -e -s e d t o
Milliseconds 238 109 139 201 181 64 104 97 106 81 180 266 123 99 128 79 112 28 329 85 102 180 101 206 68
Character a c h a n g e i n -n - -i i n a n o t h e
Milliseconds 67 126 141 95 95 87 78 92 67 86 22 129 306 101 186 187 116 77 109 118 67 78 96 99 53
Character r . H o w d o e s t h e s p e e d f o -o
Milliseconds 50 155 93 324 59 157 80 131 72 95 66 105 76 85 59 98 91 118 84 115 138 62 200 84 249
Character -f f o a -a - -o -f o f a f a l l i n g o b j
Milliseconds 94 117 50 126 214 217 106 107 119 199 56 82 113 81 159 118 66 144 117 74 109 64 76 103 97
Character e c t c h a n g e a s a c u -u -c f u n c t
Milliseconds 81 147 114 68 217 71 130 30 158 44 117 113 68 343 166 233 227 72 461 99 207 101 140 68 94
Character o n - -n -o i o n o f t i m e ? H O -O o w
Milliseconds 101 65 115 258 106 80 219 52 69 109 83 104 65 97 82 67 92 249 117 263 98 517 192 17 158
Character d o e s t h e l e v e l o f w a t e r i
Milliseconds 106 134 27 83 105 79 70 112 117 116 68 138 62 63 100 122 61 100 206 97 74 82 78 64 86
Character n a b a r r l e -e -l e l c h a n g e a s
Milliseconds 70 121 96 133 99 105 98 110 153 47 420 100 151 46 115 88 85 30 170 71 42 117 82 87 96
Character a f u c n t -t -n -c -u u n c t i o n o f t h e
Milliseconds 124 83 134 95 113 67 134 233 109 59 230 545 127 71 107 94 64 84 100 91 90 97 75 77 101
Character a m o u n t o f l i q u i d p o u r e d
Milliseconds 86 133 93 37 131 152 95 112 239 116 85 98 75 146 97 53 97 84 170 53 108 130 70 158 96
Character i n t o t i -i -t i t ? W e s e e c h a n g
Milliseconds 165 126 77 70 101 144 35 402 88 165 33 224 120 263 205 89 142 73 120 127 80 75 141 51 133
Character e o u c -c -u c c u r r i n g i n n e a r l y
Milliseconds 42 98 91 66 22 318 104 117 112 100 105 264 244 109 80 66 89 65 115 78 87 62 37 112 121
Character e v e r t h i -i -h -t y t h i n g w e o b s e
Milliseconds 72 84 166 59 118 178 118 118 301 72 150 199 115 66 64 107 59 102 87 46 115 115 92 136 60
Character r v e i n t h e w o r l d a n - d u n
Milliseconds 93 164 48 94 90 89 116 186 60 57 103 116 117 132 57 123 218 118 86 129 542 214 64 117 163
Character i v e r s e , a n d p o w e r f u l m o d e
Milliseconds 70 154 78 105 126 68 268 125 81 90 102 70 155 131 74 104 65 199 88 116 100 118 47 106 104
Character r n i n s t r u m e n e s - -s -e t s h e l p
Milliseconds 73 37 96 109 91 83 100 124 102 143 82 108 96 63 137 288 97 116 171 61 100 119 102 89 153
Character u s s e e m o r e a n d m o r e . I n
Milliseconds 102 96 120 69 112 9 181 85 89 121 113 59 82 117 82 104 66 68 56 71 29 129 121 191 137
Character t h i s s e c t i o n w e i n t r o d u c
Milliseconds 99 90 84 54 80 90 245 20 212 60 75 33 81 91 95 51 148 70 78 134 118 59 124 82 75
Character e t h e i d e a s o f a v e r a n g e -e -g
Milliseconds 115 69 98 63 87 45 109 140 93 93 67 145 92 98 88 93 118 81 120 128 137 90 78 248 114
Character -n a g e - -e -g -a g e a n d i n s t a n t a n
Milliseconds 104 155 59 99 99 209 132 86 134 110 63 122 116 84 121 76 101 100 96 87 265 153 116 400 179
Character e o u s r e a t e -e -t -a a -a a -a -e a t e s o f
Milliseconds 167 285 86 103 92 91 47 50 149 65 174 197 128 159 33 140 167 292 109 85 57 107 158 92 93
Character c h a n g e , a n d s h o w t h a t t h
Milliseconds 93 124 124 86 106 101 32 167 91 120 65 82 66 110 66 62 84 128 93 105 44 62 97 183 104
Character e y a r e c l o s e l y r e l a t e d t o
Milliseconds 72 57 101 83 70 71 76 182 41 112 48 42 171 162 60 140 58 104 115 70 84 200 94 104 63
Character g h -h -g t h e s l p -p o p e o f a c u r
Milliseconds 97 76 81 329 104 50 151 65 98 97 88 180 407 186 165 125 87 113 41 100 103 141 97 95 74
Character v e a t a p o i n t P o n t h e c u
Milliseconds 159 55 72 199 22 123 155 131 140 44 215 169 132 88 245 140 127 84 106 68 74 73 54 127 132
Character r v e . W e g i v e p r c -c e c i s e d e
Milliseconds 249 224 79 153 61 591 257 235 100 116 55 47 100 98 73 213 280 151 186 134 111 53 123 124 173
Character v e l o p m e n t s o f t h e s e i m p o r
Milliseconds 155 66 123 122 77 128 141 72 138 66 95 122 82 92 70 97 69 83 112 40 146 114 128 96 105
Character t a t n -n -t n t c o n c e p t s i n t h e
Milliseconds 149 62 86 128 352 114 176 82 92 117 54 83 123 204 116 271 436 117 113 83 102 72 83 95 38
Character n e x t c h a p t e r , b u t f o r n o w
Milliseconds 98 128 172 82 199 106 76 68 138 123 29 479 267 84 136 77 73 93 156 101 78 46 121 93 87
Character w e u s e a n i n f o r m a l a p p r o
Milliseconds 75 94 51 118 82 49 50 98 208 90 168 84 81 100 139 277 218 102 505 80 112 70 131 139 115
Character a d -d c h s o y o u w i l l s e e h o w
Milliseconds 147 89 387 97 132 55 143 82 96 87 66 67 87 92 58 62 104 72 90 41 175 68 85 54 98
Character t h e y l e a d n a t r u a -a -u -r u r a l l
Milliseconds 71 96 56 83 83 67 148 79 27 137 84 175 71 85 107 70 239 252 104 86 184 90 20 88 115
Character y t o t h e m a i n i d e a o f t h i
Milliseconds 149 55 140 53 67 115 69 79 70 88 95 81 76 95 134 114 84 51 82 108 75 109 159 89 58
Character s d -d c h a p t e r , t h e l i m i t . T
Milliseconds 117 81 203 431 85 83 60 97 149 192 84 270 64 121 64 99 72 212 72 127 101 119 117 106 155
Character h e i d e a o f a l i m i t p l y a -a -y
Milliseconds 87 64 87 81 88 110 39 72 98 76 104 82 86 135 65 128 107 104 73 87 113 136 47 335 182
Character a y s a f o u n d a t i o n n a -a -n a l r o
Milliseconds 232 121 104 90 243 148 126 78 61 137 66 50 126 69 65 52 375 82 258 123 162 100 85 145 69
Character l e t h r o u g h o u t c a l c u l i u s . -.
Milliseconds 148 100 83 132 101 368 75 50 123 71 292 58 104 119 184 99 45 171 128 96 141 14 482 92 274
Character -s -u -i u s .
Milliseconds 166 138 298 171 82 85
WPM Timing
Seconds WPM
2.35 71.58
4.69 94.59
7.04 107.37
9.39 95.87
11.74 88.96
14.08 86.92
16.43 90.57
18.78 83.72
21.12 86.92
23.47 83.34
25.82 82.27
28.16 82.66
30.51 84.17
32.86 84
35.21 83.51
37.55 85
39.9 83.91
42.25 84.08
44.59 85.03
46.94 85.13
49.29 84.97
51.63 85.52
53.98 86.7
56.33 86.49
58.68 87.94
61.02 89.67
63.37 88.43
65.72 87.83
68.06 86.21
70.41 86.75
72.76 88.07
75.1 88.2
77.45 88
79.8 88.42
82.15 87.94
84.49 87.63
86.84 88.44
89.19 87.59
91.53 87.84
93.88 88.71
96.23 88.41
98.58 88.74
100.92 88.7
103.27 89.71
105.62 89.42
107.96 90.14
110.31 89.75
112.66 89.47
115 89.63
117.35 88.35