AK (arjuntypesslow)

Race #34

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Official speed 77.28 wpm (134.16 seconds elapsed during race)
Without ending ping 77.49 wpm (360 ms delay sending score to TypeRacer’s server)
Timerless 78.06 wpm (985 ms elapsed before first character typed; 132.82 seconds elapsed during race)
Timerless minus one 77.97 wpm, ignoring the first character typed
Race Start April 8, 2024 9:10:58am UTC
Race Finish April 8, 2024 9:13:13am UTC
Outcome No win (2 of 5)
Accuracy 97.8%
Points 208.66
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 TCQALalculus is a tool that helps us understand how a change in one qusaanotity 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 barerell change as a function of the amount of liquid opoured into it? We see change occurring in nearly everything we observe in the world and universe, and powerful modeerrn instruments help us see more and more. Inthis this section we introduce the ideas of averaege and instantaneous rates of change, and show that they are closely related to the slpope of a curve at a apoint P on the curve. We give precise developments of these important concepts oin the next chapetter, but for now we use an informal approach so wilyou will see how they lead natruurally to the main idea of this chapter, the limit. The idea of a limit plays a foundtatiational role throughout calculus.
Timing
Character T -T C Q -Q A L -L -A a l c u l u s i s a t o o
Milliseconds 985 389 126 106 493 179 141 481 159 955 219 418 558 266 178 125 135 106 93 84 122 67 144 73 157
Character l t h a t h e l p s u s u n d e r s t a n
Milliseconds 174 317 154 76 54 150 99 155 90 132 31 127 109 117 80 80 230 96 63 103 103 117 141 91 134
Character d h o w a c h a n g e i n o n e q u s
Milliseconds 86 102 161 33 83 120 95 101 151 112 58 80 133 56 115 148 69 167 156 110 50 117 110 131 179
Character a -a -s a n o -o t i t y i s r e l a t e d t o
Milliseconds 46 375 126 101 110 216 413 77 127 98 134 288 143 76 118 128 117 85 149 113 97 128 90 132 57
Character a c h a n g e i n a n o t h e r . H o w
Milliseconds 128 68 151 99 94 11 176 99 51 100 135 70 148 89 75 49 96 87 77 109 53 147 216 281 90
Character d o e s t h e s p e e d o f a f a l l
Milliseconds 99 151 78 101 148 105 100 63 117 89 118 73 145 160 133 65 107 98 69 478 99 140 140 86 138
Character i n g o b j e c t c h a n g e a s a f u
Milliseconds 190 86 122 107 111 151 161 93 123 202 64 121 50 45 126 75 44 171 75 75 139 70 134 201 126
Character n c t i o n o f t i m e > - -> > -> ? H o w
Milliseconds 94 109 180 41 73 75 199 111 52 101 89 76 90 46 271 262 247 133 252 545 195 669 586 354 144
Character d o e s t h e l e v e l o f w a t e r
Milliseconds 119 128 81 78 167 89 109 82 74 99 111 21 171 44 476 173 144 95 95 90 103 122 109 129 109
Character i n a b a r e -e r e l l -l c h a n g e a s
Milliseconds 102 91 181 131 86 138 109 156 297 347 75 90 239 158 463 159 233 106 27 146 84 68 133 64 85
Character a f u n c t i o n o f t h e a m o u n t
Milliseconds 105 72 130 65 136 114 166 211 70 122 33 225 141 97 85 329 78 65 126 86 89 109 85 94 74
Character o f l i q u i d o -o p o u r e d i n t o
Milliseconds 132 104 122 42 146 123 151 160 149 135 119 136 390 198 209 553 96 148 119 93 109 65 115 54 115
Character i t ? W e s e e c h a n g e o c c u r r i
Milliseconds 135 48 1265 538 612 397 134 142 172 134 201 133 93 14 147 84 51 105 199 25 163 159 81 428 202
Character n g i n n e a r l y e v e r y t h i n g w
Milliseconds 55 130 164 382 119 147 202 164 53 85 237 164 180 252 138 63 117 99 131 100 83 126 128 114 88
Character e o b s e r v e i n t h e w o r l d a n
Milliseconds 80 97 161 166 273 188 443 209 113 200 130 116 119 67 99 85 100 84 70 102 99 160 69 137 84
Character d u n i v e r s e , a n d p o w e r f u l
Milliseconds 82 102 181 338 148 259 192 105 125 297 170 259 110 126 35 167 102 177 121 53 114 221 86 171 154
Character m o d e e r -r -e r n i n s t r u m e n t s h e
Milliseconds 184 72 148 118 147 145 383 151 107 117 149 126 82 101 156 153 141 502 113 106 64 122 126 176 111
Character l p u s s e e m o r e a n d m o r e .
Milliseconds 91 46 212 148 100 126 145 277 161 94 196 21 96 24 92 110 59 80 103 154 45 91 31 149 199
Character I n t h i s - -s -i -h -t t h i s s e c t i o n
Milliseconds 251 347 337 99 37 84 114 271 173 142 164 153 434 441 98 45 103 134 453 315 160 208 68 98 75
Character w e i n t r o d u c e t h e i d e a s o
Milliseconds 153 115 27 129 109 73 170 164 77 138 154 85 93 102 83 72 102 92 139 100 73 82 183 241 138
Character f a v e r a e -e g e a n d i n s t a n t a n
Milliseconds 106 76 236 176 211 76 159 242 474 73 111 123 103 75 79 109 141 98 210 207 128 633 356 365 170
Character e o u s r a t e s o f c h a n g e , a n d
Milliseconds 264 187 106 155 205 628 89 145 128 152 101 92 107 65 160 34 22 193 71 65 159 182 88 104 77
Character s h o w t h a t t h e y a r e c l o s e
Milliseconds 131 46 139 54 74 102 79 136 34 105 127 75 127 52 100 83 56 137 64 83 116 77 149 76 166
Character l y r e l a t e d t o t h e s l p -p o p e
Milliseconds 108 134 104 155 91 109 120 147 113 113 132 79 89 131 100 88 103 94 202 123 202 508 266 152 151
Character o f a c u r v e a t a a -a p o i n t
Milliseconds 107 136 68 104 67 120 113 129 90 205 164 169 75 218 103 84 128 132 551 340 102 223 100 90 101
Character P o n t h e c u r v e . W e g i v e p
Milliseconds 211 211 177 99 177 101 73 84 97 128 122 98 221 159 375 332 226 327 106 98 88 104 82 98 89
Character r e c i s e d e v e l o p m e n t s o f t h
Milliseconds 45 101 184 114 143 139 122 180 89 95 113 185 148 132 318 103 134 103 131 120 93 104 56 120 54
Character e s e i m p o r t a n t c o n c e p t s o -o
Milliseconds 80 167 146 86 110 104 115 38 161 159 114 123 64 109 115 77 283 471 149 164 100 161 61 160 482
Character i n t h e n e x t c h a p e t -t -e t e r ,
Milliseconds 190 104 190 69 93 86 101 153 25 199 209 100 128 89 130 100 252 152 305 140 61 128 78 107 293
Character b u t f o r n o w w e u s e a n i n f
Milliseconds 434 115 84 76 131 34 109 91 159 25 93 82 107 78 41 167 49 192 52 125 51 162 133 65 114
Character o r m a l a p p r o a c h s o w i l -l -i -w y
Milliseconds 115 82 232 122 131 218 130 134 152 162 88 88 110 88 180 168 112 169 89 80 180 279 140 164 160
Character o u w i l l s e e h o w t h e y l e a d
Milliseconds 78 63 147 170 9 199 148 85 78 165 131 189 177 41 85 100 79 111 79 94 72 158 20 81 86
Character n a t r u -u -r u r a l l y t o t h e m a i
Milliseconds 79 141 85 113 182 93 390 148 223 67 107 192 145 134 127 144 46 116 133 47 136 85 181 133 51
Character n i d e a o f t h i s c h a p t e r , t
Milliseconds 106 158 111 32 115 68 65 97 83 73 98 83 25 52 137 72 108 58 89 86 119 100 129 133 308
Character h e l i m i t . T h e i d e a o f a l
Milliseconds 128 54 81 115 83 150 154 124 123 214 152 243 93 92 119 115 92 96 90 140 76 73 189 114 153
Character i m i t p l a y s a f o u n d t a t i -i -t -a
Milliseconds 97 153 166 106 158 231 101 82 142 91 125 86 116 93 96 57 70 174 236 83 155 18 294 146 154
Character -t a t i o n a l r o l e t h r o u g h o u t
Milliseconds 135 139 86 96 78 49 179 519 210 273 135 234 134 370 309 99 108 167 51 245 692 190 58 166 117
Character c a l c u l u s .
Milliseconds 195 106 148 182 177 235 204 112 136
WPM Timing
Seconds WPM
2.68 4.47
5.37 11.18
8.05 38.76
10.73 57.02
13.42 60.82
16.1 64.1
18.78 70.92
21.47 73.79
24.15 77.52
26.83 78.26
29.52 72.37
32.2 74.54
34.88 74.31
37.57 75.07
40.25 76.92
42.93 75.75
45.61 73.13
48.3 73.79
50.98 73.44
53.66 73.79
56.35 74.96
59.03 75.01
61.71 74.47
64.4 74.91
67.08 75.49
69.76 73.45
72.45 73.71
75.13 74.59
77.81 73.87
80.5 73.05
83.18 74.59
85.86 75.75
88.55 75.49
91.23 75.37
93.91 75.64
96.6 75.66
99.28 76.15
101.96 76.38
104.65 76.37
107.33 75.92
110.01 76.68
112.7 76.24
115.38 77.17
118.06 76.94
120.75 78.11
123.43 78.36
126.11 78.79
128.8 78.08
131.48 77.58
134.16 77.28