Jack (jackschpeck)

Race #2868

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Official speed 80.95 wpm (128.08 seconds elapsed during race)
Without ending ping 81.18 wpm (357 ms delay sending score to TypeRacer’s server)
Timerless 81.63 wpm (706 ms elapsed before first character typed; 127.02 seconds elapsed during race)
Timerless minus one 81.53 wpm, ignoring the first character typed
Race Start August 10, 2023 4:07:58am UTC
Race Finish August 10, 2023 4:10:06am UTC
Outcome No win (3 of 5)
Opponents 1. syncorex (100.18 wpm)
2. sattypants (97.31 wpm)
Accuracy 98.4%
Points 218.56
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 undertstand how a change in one quqantity is related to a change in another. How does the speed of a falling object change as a function of time? HOw ow 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 secition we introduce the ideas of average and instantaneous rartes of change, and howshow that they are closely related to the slop oe of a curve ad t a point P aonon thon the cvurcurve. We give precise developments of these important ocnconcepts in the next chapter, but for now we use an informal approahc ch ch so you will see how they lead naturally to the main idea of this cahapter, the limit. The idea of a limit plays a foundational role throughout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 706 245 134 212 60 218 76 301 157 69 119 181 81 160 82 56 497 199 182 82 39 121 80 100 202
Character e l p s u s u n d e r t -t s t a n d h o w
Milliseconds 142 30 200 104 97 81 160 103 57 196 56 206 121 221 595 80 100 79 82 100 101 181 60 140 83
Character a c h a n g e i n o n e q u q -q a n t i t
Milliseconds 118 124 120 123 79 120 57 65 80 77 82 76 126 54 88 79 511 40 219 576 61 159 165 56 206
Character y i s r e l a t e d t o a c h a n g e
Milliseconds 120 101 181 369 182 58 60 143 81 158 57 207 55 107 119 81 122 158 98 164 161 143 55 61 83
Character i n a n o t h e r . H o w d o e s t h e
Milliseconds 82 102 56 204 357 81 202 40 100 118 102 140 204 81 119 99 143 56 166 100 180 163 101 60 56
Character s p e e d o f a f a l l i n g o b j e c t
Milliseconds 222 80 142 101 193 80 78 124 39 119 105 245 80 78 142 103 99 41 60 139 122 220 102 203 88
Character c h a n g e a s a f u n c t i o n o f
Milliseconds 46 188 80 102 100 79 56 126 203 213 57 101 82 123 98 159 61 96 44 101 41 139 143 59 138
Character t i m e ? H O w - -w -O o w d o e s t h e
Milliseconds 104 98 100 125 237 178 352 101 142 137 345 99 122 222 56 125 142 57 102 122 101 80 61 117 345
Character l e v e l o f w a t e r i n a b a r r e
Milliseconds 161 119 142 102 119 121 103 76 64 399 77 125 82 100 54 104 104 78 122 186 201 79 264 121 60
Character l c h a n g e a s a f u n c t i o n o f
Milliseconds 139 82 101 79 142 42 118 40 104 158 224 41 120 100 72 89 170 61 78 82 79 83 120 81 80
Character t h e a m o u n t o f l i q u i d p o u
Milliseconds 80 200 62 120 63 97 102 82 160 167 79 78 60 525 106 119 352 348 63 77 435 141 258 241 189
Character r e d i n t o i t ? W e s e e c h a n g
Milliseconds 182 120 226 81 79 171 139 82 101 139 21 532 494 278 246 117 103 101 140 83 159 100 117 81 82
Character e o c c u r r i n g i n n e a r l y e v e
Milliseconds 44 100 139 164 119 102 118 113 80 99 78 85 99 182 101 139 79 61 183 121 100 83 99 186 101
Character r y t h i n g w e o b s e r v e i n t h e
Milliseconds 161 81 241 101 59 138 104 121 141 174 101 159 186 274 43 237 220 56 106 121 59 101 61 98 142
Character w o r l d a n d u n i v e r s e , a n d
Milliseconds 64 158 56 125 82 119 58 379 18 203 20 118 202 58 81 58 199 170 56 165 139 63 202 312 80
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 162 60 140 101 195 220 37 143 139 105 55 182 153 201 81 100 102 150 69 169 61 44 242 120 103
Character t s h e l p u s s e e m o r e a n d m
Milliseconds 80 404 124 102 99 140 167 175 87 100 62 159 52 146 118 125 58 119 60 81 121 184 39 81 103
Character o r e . I n t h i s s e c i -i t i o n w e
Milliseconds 58 83 57 143 101 161 140 80 83 98 41 101 82 199 83 242 140 446 200 62 100 56 253 259 120
Character i n t r o d u c e t h e i d e a s o f a
Milliseconds 122 120 117 125 59 56 230 84 280 158 61 119 18 185 40 99 140 116 62 242 81 122 101 59 141
Character v e r a g e a n d i n s t a n t a n e o u s
Milliseconds 181 121 202 81 200 62 78 141 226 140 43 118 144 409 138 83 181 138 729 180 176 200 142 113 418
Character r a r -r t e s o f c h a n g e , a n d h o
Milliseconds 140 82 216 427 97 44 192 136 42 158 67 162 120 713 180 143 62 159 123 61 118 102 57 143 56
Character w -w -o -h s h o w t h a t t h e y a r e c l
Milliseconds 127 366 114 120 121 101 55 64 83 99 156 90 217 122 59 80 103 117 59 86 160 55 42 294 41
Character o s e l y r e l a t e d t o t h e s l o p
Milliseconds 161 56 104 552 141 80 141 56 167 60 202 59 222 61 500 81 81 102 38 140 60 143 58 184 201
Character o -o - e o f a c u r v e a d - -d t a
Milliseconds 100 362 252 92 202 100 201 101 55 146 101 77 84 181 221 61 100 141 298 203 414 100 118 60 341
Character p o i n t P a o n -n -o o n t h -h -t - -n -o -a
Milliseconds 121 117 55 188 179 122 65 217 221 124 256 142 204 98 202 100 78 55 106 261 110 139 121 129 132
Character o n t h e c v u r -r -u -v -c c u r v e . W e
Milliseconds 278 82 139 104 60 159 81 141 22 116 165 334 111 119 139 551 80 141 221 57 144 179 414 209 101
Character g i v e p r e c i s e d e v e l o p m e n t s
Milliseconds 206 60 149 41 97 123 142 157 453 57 204 83 78 181 194 192 80 164 448 194 241 55 178 81 218
Character o f t h e s e i m p o r t a n t o c n -n -c
Milliseconds 100 101 121 55 167 15 197 177 61 99 122 123 119 99 84 184 102 386 174 158 142 38 266 296 100
Character -o c o n c e p t s i n t h e n e x t c h a
Milliseconds 116 294 80 182 60 202 120 219 201 100 100 93 67 57 122 83 39 102 81 201 79 83 335 99 78
Character p t e r , b u t f o r n o w w e u s e
Milliseconds 145 100 98 139 159 104 100 41 184 121 199 42 157 20 125 57 123 120 142 102 139 221 85 59 80
Character a n i n f o r m a l a p p r o a h c - -c c h
Milliseconds 143 593 141 60 137 103 102 139 61 80 184 100 80 100 149 206 81 99 171 22 250 230 120 119 103
Character - -h -c -h c h s o y o u w i l l s e e h
Milliseconds 78 320 101 140 115 99 123 37 138 106 101 213 81 78 102 81 78 123 105 54 79 107 142 60 183
Character o w t h e y l e a d n a t u r a l l y t o
Milliseconds 37 104 135 247 60 139 84 59 160 65 55 366 81 201 40 222 78 141 17 59 185 181 158 144 99
Character t h e m a i n i d e a o f t h i s c a
Milliseconds 103 80 37 176 60 140 103 100 77 123 82 412 155 56 289 120 99 81 122 39 55 106 55 167 101
Character -a h a p t e r , t h e l i m i t . T h e i
Milliseconds 640 183 100 118 312 82 163 140 81 140 41 194 143 118 51 189 79 120 145 74 226 161 39 78 205
Character d e a o f a l i m i t p l a y s a f o
Milliseconds 164 462 141 312 100 101 59 64 140 120 37 169 83 159 40 307 218 59 178 365 103 100 117 205 102
Character u n d a t i o n a l r o l e t h r o u g h o u
Milliseconds 97 193 41 60 181 59 77 84 122 120 100 162 54 168 38 99 144 141 533 230 182 198 101 79 123
Character t c a l c u l u s .
Milliseconds 78 100 123 80 161 178 59 174 121 241 123
WPM Timing
Seconds WPM
2.56 60.9
5.12 72.61
7.68 73.39
10.25 77.3
12.81 76.83
15.37 79.64
17.93 82.98
20.49 86.08
23.05 88.49
25.62 84.79
28.18 85.17
30.74 87.06
33.3 89.37
35.86 87.33
38.42 86.2
40.99 85.79
43.55 87.08
46.11 86.93
48.67 88.02
51.23 88.07
53.79 88.12
56.35 89.22
58.92 88.6
61.48 89.01
64.04 89.19
66.6 87.75
69.16 86.58
71.72 85.66
74.29 86.1
76.85 86.2
79.41 85.38
81.97 84.32
84.53 82.48
87.09 81.02
89.66 80.71
92.22 80.29
94.78 80.65
97.34 79.64
99.9 80.12
102.46 80.58
105.02 80.78
107.59 79.75
110.15 80.51
112.71 80.92
115.27 81.1
117.83 80.76
120.39 80.73
122.96 80.81
125.52 80.98
128.08 80.95