Jack (randomdize)

Race #11796

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Official speed 79.40 wpm (130.58 seconds elapsed during race)
Without ending ping 79.57 wpm (286 ms delay sending score to TypeRacer’s server)
Timerless 80.03 wpm (742 ms elapsed before first character typed; 129.55 seconds elapsed during race)
Timerless minus one 79.94 wpm, ignoring the first character typed
Race Start February 4, 2024 6:55:07am UTC
Race Finish February 4, 2024 6:57:18am UTC
Outcome No win (2 of 5)
Opponents 1. popopontus (86.44 wpm)
Accuracy 97.2%
Points 214.39
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 hlepelps us understand how a change in one quantity is related to a change in another. How does the speed of a lfalling object change as a function of time? How does the level of water in a barrel change as funa function of the amount of liquied d poured into it? We see change coccurring in nearly everything we observe in the world and univserseers,e, and powerful modern instruments help us wsee more and more. In this section we introduce the ideas of average and instatntaneous rates of change, and show that they are closely relatied to hte the slope of a curve at t]aa point P on the curve. We give precise developments of these important concepts in the next chapter, but for now ewwe wuuse an informal approach so you will see how they lead naturlalally to the main idea of this chagtp[ter-r. t., the limit. The idea of a mitlimit plays a funoundational role throughtout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 742 480 119 374 61 168 146 144 176 89 72 98 129 90 267 77 119 332 240 133 94 41 47 107 160
Character l e p -p -e -l e l p s u s u n d e r s t a n d
Milliseconds 151 94 133 312 152 135 48 149 138 205 111 203 92 106 181 133 74 125 73 117 140 102 59 80 101
Character h o w a c h a n g e i n o n e q u a n t
Milliseconds 195 43 75 109 146 125 189 61 77 76 58 92 119 166 85 64 315 87 65 89 312 90 148 180 151
Character i t y i s r e l a t e d t o a c h a n g
Milliseconds 77 363 42 151 103 78 106 179 56 107 194 210 171 129 91 119 74 92 359 106 212 101 46 90 45
Character e i n a n o t h e r . H o w d o e s t h
Milliseconds 106 110 54 89 63 118 91 92 104 74 60 74 91 232 294 103 377 133 315 62 147 91 142 113 48
Character e s p e e d o f a l -l f a l l i n g o b
Milliseconds 77 89 205 159 81 140 133 110 99 45 113 128 94 195 365 68 88 77 150 104 108 11 80 392 46
Character j e c t c h a n g e a s a f u n c t i o n
Milliseconds 174 61 133 164 81 129 75 123 74 61 167 216 293 57 139 192 104 178 92 166 89 137 85 15 75
Character o f t i m e ? H o w d o e s t h e l e
Milliseconds 111 159 79 74 391 74 73 106 234 395 313 63 418 122 252 44 76 108 155 128 33 87 78 118 87
Character v e l o f w a t e r i n a b a r r e l
Milliseconds 122 136 74 122 134 118 138 387 137 89 134 47 95 146 61 92 346 128 169 167 145 61 543 151 78
Character c h a n g e a s f u n -n -u -f a f u n c t i o
Milliseconds 328 72 78 71 43 89 127 129 106 93 300 92 191 261 157 121 273 140 128 122 147 74 121 76 14
Character n o f t h e a m o u n t o f l i q u i e
Milliseconds 88 125 242 88 92 240 71 90 61 179 104 107 125 179 55 94 358 74 109 193 114 241 60 90 105
Character d - -d -e d p o u r e d i n t o i t ? W e
Milliseconds 149 129 405 117 133 110 105 142 151 153 103 165 182 77 100 76 59 60 355 191 8 732 100 176 182
Character s e e c h a n g e c -c o c c u r r i n g i
Milliseconds 122 204 165 150 126 207 58 74 93 57 75 279 204 291 207 86 148 153 120 102 90 88 92 98 266
Character n n e a r l y e v e r y t h i n g w e o b
Milliseconds 71 94 374 56 137 60 136 132 49 175 182 95 87 76 133 106 59 120 50 71 165 75 94 194 86
Character s e r v e i n t h e w o r l d a n d u n
Milliseconds 271 87 109 163 121 94 86 103 44 277 101 59 157 111 92 61 103 76 80 83 89 63 63 102 198
Character i v s e r s -s -r -e e -e -s e r s , -, e , a n d p
Milliseconds 88 58 214 87 104 137 257 117 150 133 335 101 77 58 118 147 326 82 149 71 249 74 60 91 225
Character o w e r f u l m o d e r n i n s t r u m e n t
Milliseconds 73 87 32 60 245 38 137 142 112 46 91 149 61 60 123 89 88 179 150 107 169 209 194 105 58
Character s h e l p u s w -w s e e m o r e a n d
Milliseconds 134 114 172 118 136 122 167 100 107 93 220 321 114 121 152 80 221 72 29 89 111 144 46 113 8
Character m o r e . I n t h i s s e c t i o n w e
Milliseconds 214 9 122 59 177 150 193 189 382 160 40 47 87 110 387 119 183 118 59 42 45 141 222 75 122
Character i n t r o d u c e t h e i d e a s o f a v
Milliseconds 147 61 164 170 41 316 134 14 184 94 82 106 59 77 135 61 163 63 447 116 202 58 97 126 155
Character e r a g e a n d i n s t a t -t n t a n e o u s
Milliseconds 132 60 136 275 158 111 178 86 75 63 131 76 261 160 91 421 424 145 59 135 318 314 316 44 103
Character r a t e s o f c h a n g e , a n d s h o
Milliseconds 155 326 245 128 75 240 94 145 74 85 172 75 76 105 29 44 142 71 146 78 27 110 192 92 28
Character w t h a t t h e y a r e c l o s e l y r
Milliseconds 45 105 151 120 75 78 90 312 196 88 90 123 163 72 78 107 198 8 154 87 90 104 166 111 174
Character e l a t i -i e d t o h t e - -e -t -h t h e s
Milliseconds 45 135 120 89 90 369 81 149 82 99 62 108 133 7 111 95 361 128 153 122 286 85 59 127 129
Character l o p e o f a c u r v e a t t ] a -a -] -t
Milliseconds 166 150 75 103 126 114 91 66 159 78 162 75 91 286 89 101 182 110 156 142 428 99 191 106 155
Character a p o i n t P o n t h e c u r v e . W
Milliseconds 85 79 242 57 55 150 4 167 227 91 428 104 92 87 46 66 107 170 61 80 360 105 161 168 196
Character e g i v e p r e c i s e d e v e l o p m e n
Milliseconds 134 216 250 120 85 119 79 147 105 59 241 105 218 100 157 269 145 135 132 121 153 42 210 74 74
Character t s o f t h e s e i m p o r t a n t c o n
Milliseconds 45 165 110 55 106 95 83 75 123 91 73 95 159 229 180 44 74 149 122 103 106 109 191 26 78
Character c e p t s i n t h e n e x t c h a p t e r
Milliseconds 334 149 150 8 168 112 144 90 62 101 76 60 94 100 75 181 164 141 345 87 105 257 101 135 48
Character , b u t f o r n o w e w -w -e w e w u -u -w
Milliseconds 168 120 390 56 134 98 142 61 77 104 193 74 30 109 259 132 225 121 71 58 94 192 88 276 117
Character u s e a n i n f o r m a l a p p r o a c h
Milliseconds 208 43 76 124 274 71 109 301 67 106 119 78 182 39 151 143 131 132 120 105 118 142 149 117 138
Character s o y o u w i l l s e e h o w t h e y
Milliseconds 344 41 113 82 104 60 79 86 92 179 90 77 164 136 151 214 284 9 121 95 160 75 74 89 95
Character l e a d n a t u r l a l -l -a -l a l l y t o t
Milliseconds 100 61 138 118 107 194 94 116 106 74 151 29 104 424 150 106 100 119 120 120 65 131 59 112 144
Character h e m a i n i d e a o f t h i s c h a g
Milliseconds 29 107 110 113 136 106 90 95 159 136 193 61 141 324 75 108 117 75 65 43 103 211 103 58 134
Character t -t -g p [ -[ t e r - -- -r r . t -t - -. . -. , t h
Milliseconds 275 314 121 438 12 454 144 125 36 202 364 238 746 64 106 223 266 165 134 277 540 184 146 206 102
Character e l i m i t . T h e i d e a o f a m i
Milliseconds 48 91 343 120 122 58 59 155 121 161 138 72 93 86 91 210 103 127 308 110 137 126 97 83 135
Character t -t -i -m l i m i t p l a y s a f u n -n -u o u
Milliseconds 135 443 131 117 245 87 168 56 43 201 195 100 61 92 88 129 282 72 144 107 154 438 118 195 40
Character n d a t i o n a l r o l e t h r o u g h t -t o
Milliseconds 218 53 135 105 164 45 108 101 91 122 192 78 136 103 94 131 165 74 77 74 48 116 47 393 178
Character u t c a l c u l u s .
Milliseconds 73 45 110 190 119 80 225 71 183 194 210 143
WPM Timing
Seconds WPM
2.61 50.54
5.22 57.44
7.83 67.39
10.45 75.82
13.06 78.11
15.67 82.71
18.28 82.71
20.89 83.28
23.5 84.75
26.12 82.71
28.73 83.96
31.34 83.09
33.95 80.94
36.56 82.71
39.17 80.56
41.79 80.12
44.4 79.46
47.01 80.16
49.62 81.5
52.23 81.56
54.84 80.3
57.45 81.46
60.07 81.31
62.68 81.94
65.29 82.34
67.9 82.53
70.51 82.03
73.12 81.4
75.74 82.55
78.35 82.86
80.96 81.97
83.57 81.99
86.18 81.59
88.79 81.63
91.41 81.79
94.02 82.45
96.63 82.83
99.24 82.83
101.85 82.12
104.46 82.48
107.08 83.04
109.69 82.71
112.3 83.14
114.91 81.87
117.52 80.16
120.13 80.01
122.74 79.38
125.36 79.17
127.97 79.71
130.58 79.4