kamal nath (kamal3772)

Race #1654

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Official speed 66.60 wpm (155.68 seconds elapsed during race)
Without ending ping 66.69 wpm (222 ms delay sending score to TypeRacer’s server)
Timerless 67.34 wpm (1,487 ms elapsed before first character typed; 153.97 seconds elapsed during race)
Timerless minus one 67.26 wpm, ignoring the first character typed
Race Start December 1, 2023 10:45:46am UTC
Race Finish December 1, 2023 10:48:22am UTC
Outcome No win (2 of 4)
Opponents 1. the_godof_stories (85.46 wpm)
Accuracy 97.1%
Points 179.82
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 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 cahanbgge as a function of the amount of liquid poured into it? We see change occurriinggn ng in nearly everything we observer in the world and inunviivereser, , and poerwerful modrern instruments help us see more and more. In this section we indtrooduce the ideas of average and isinstantatneous rates of change, and wshow that they are closely reallated to tthe slope of a curve at a point P on the curve. We give precisse e developments of these important comncepts in the nesxxscszxt chapter, but for now we use an informal appraoach so you will ssee how they lead annauttuarally to the main idea of this cahhapter, the limit. The idea of a limit plays a foundational role throughtoout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 1487 126 216 320 98 168 128 168 144 152 104 104 144 129 151 71 153 168 168 112 80 96 72 55 169
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 88 128 248 151 152 137 104 128 126 170 48 167 72 152 121 119 143 90 104 160 97 119 96 160 128
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 144 128 40 160 112 136 96 127 97 96 119 441 152 56 632 136 144 254 130 136 168 120 134 129 121
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 96 248 136 160 144 128 119 177 168 352 72 88 120 159 169 104 78 114 112 112 94 137 89 95 89
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 104 103 137 112 120 72 240 136 376 112 103 208 177 224 160 182 145 153 80 80 72 144 80 168 136
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 200 368 152 56 232 72 175 57 95 105 134 442 128 96 96 119 161 240 184 200 136 110 418 119 23
Character n g e a s a f u n c t i o n o f t i m e
Milliseconds 210 128 272 168 104 104 112 120 112 127 120 177 224 208 88 88 111 113 72 120 128 112 88 88 72
Character ? H o w d o e s t h e l e v e l o f w
Milliseconds 255 153 440 144 448 144 344 88 120 104 64 288 127 121 80 120 82 174 111 280 183 210 79 129 352
Character a t e r i n a b a r r e l c a -a h a n b g
Milliseconds 142 113 121 96 136 96 126 114 72 392 264 87 241 168 136 119 137 432 120 376 230 50 151 121 0
Character -g -b g e a s a f u n c t i o n o f t h e
Milliseconds 368 144 120 119 73 183 169 287 113 241 262 177 184 135 193 72 72 127 113 72 104 135 120 89 64
Character a m o u n t o f l i q u i d p o u r e d
Milliseconds 80 151 105 120 111 192 145 134 114 127 96 649 192 359 65 168 168 136 225 406 201 264 112 263 113
Character i n t o i t ? W e s e e c h a n g e o c
Milliseconds 144 112 103 49 136 119 129 279 153 216 144 152 96 71 177 80 168 616 88 104 480 135 96 601 192
Character c u r r i i n g -g -n -i g n - -n -g n g i n n e
Milliseconds 160 135 113 616 168 200 200 96 208 120 144 168 48 176 248 120 432 216 88 119 185 136 88 192 151
Character a r l y e v e r y t h i n g w e o b s e r v
Milliseconds 153 104 184 160 119 122 167 104 87 81 144 144 143 64 95 146 80 102 113 185 136 328 80 128 248
Character e r - -r i n t h e w o r l d a n d i n
Milliseconds 104 152 31 353 112 104 152 112 136 72 103 105 88 288 136 215 97 128 152 128 103 113 32 152 120
Character -n -i u n v i -i -v i v e r e -e s e r , - -, -r , a
Milliseconds 312 136 272 184 159 136 329 104 208 96 231 112 169 400 56 79 73 112 112 280 144 144 392 143 97
Character n d p o e r -r -e w e r f u l m o d r -r e r n
Milliseconds 97 135 79 609 160 136 104 360 112 96 80 96 328 159 168 145 272 112 224 185 391 32 79 217 248
Character i n s t r u m e n t s h e l p u s s e e m
Milliseconds 174 113 97 184 184 160 182 122 119 57 143 89 200 176 344 208 168 183 105 96 190 114 160 103 161
Character o r e a n d m o r e . I n t h i s s e c
Milliseconds 80 80 78 59 143 88 120 48 264 102 65 144 145 104 542 154 88 143 48 169 112 159 168 153 206
Character t i o n w e i n d -d t r o o -o d u c e t h e
Milliseconds 122 120 88 87 112 112 88 152 201 112 104 319 145 280 80 72 472 118 161 159 194 120 128 79 88
Character i d e a s o f a v e r a g e a n d i s -s
Milliseconds 57 192 151 160 112 369 136 136 128 88 160 175 136 129 127 160 96 129 126 129 56 88 153 168 399
Character -i i n s t a n t a t -t n e o u s r a t e s o f
Milliseconds 119 474 127 73 167 136 192 152 313 144 375 265 136 224 127 161 112 167 128 112 96 265 143 137 120
Character c h a n g e , a n d w -w s h o w t h a t
Milliseconds 95 168 145 112 119 112 129 167 105 79 121 86 97 184 297 79 113 88 63 176 481 80 80 88 104
Character t h e y a r e c l o s e l y r e a l -l -a l a
Milliseconds 112 103 88 137 135 81 103 48 105 152 111 177 86 73 161 198 105 184 89 126 24 402 95 216 71
Character t e d t o t t -t h e s l o p e o f a c
Milliseconds 121 129 176 112 183 57 176 46 304 330 192 224 239 144 97 200 63 273 80 119 121 104 127 175 210
Character u r v e a t a p o i n t P o n t h e
Milliseconds 151 97 191 120 97 192 406 146 96 175 135 184 250 175 145 143 273 384 296 104 119 56 192 129 135
Character c u r v e . W e g i v e p r e c i s s e -
Milliseconds 393 135 63 208 128 137 96 247 104 218 175 112 103 97 81 207 81 376 248 184 168 175 16 136 337
Character -e -s e d e v e l o p m e n t s o f t h e s e
Milliseconds 120 376 168 239 217 200 136 111 161 336 176 342 88 154 88 151 137 328 176 23 353 112 104 168 80
Character i m p o r t a n t c o m -m n c e p t s i n
Milliseconds 102 144 82 128 184 167 201 160 183 121 135 216 112 95 346 206 210 223 111 128 145 143 145 105 144
Character t h e n e s x -x x -x -s s -s c -c s -s z -z x t c h
Milliseconds 71 177 78 129 128 65 191 7 337 88 319 113 217 328 704 472 320 392 766 290 135 417 152 511 185
Character a p t e r , b u t f o r n o w w e u s e
Milliseconds 136 112 392 103 105 119 143 178 110 130 87 136 71 138 56 94 74 79 128 113 47 144 176 31 113
Character a n i n f o r m a l a p p r a -a o a c h s
Milliseconds 112 265 88 128 128 144 216 135 104 120 145 416 160 223 128 144 113 111 519 208 104 201 160 136 168
Character o y o u w i l l s s -s e e h o w t h e y
Milliseconds 73 118 144 97 65 95 88 192 529 119 129 151 289 351 113 166 146 80 119 105 104 119 168 104 152
Character l e a d a n -n -a n a u t -t -u t u a -a r a l l y
Milliseconds 152 408 121 151 144 161 174 50 384 128 200 88 238 145 297 136 47 144 168 377 94 137 88 160 153
Character t o t h e m a i n i d e a o f t h i s
Milliseconds 135 152 65 144 127 96 96 47 154 39 160 80 136 112 152 167 90 151 120 104 112 153 104 158 24
Character c a h -h -a h a p t e r , t h e l i m i t .
Milliseconds 225 424 217 71 281 111 200 144 112 191 105 96 112 129 151 48 129 23 136 104 177 111 136 160 121
Character T h e i d e a o f a l i m i t p l a y s
Milliseconds 207 128 103 49 120 88 160 104 113 136 119 681 144 199 328 144 160 128 153 118 153 176 104 112 127
Character a f o u n d a t i o n a l r o l e t h r o
Milliseconds 98 151 135 498 118 113 216 104 145 144 128 71 96 585 135 161 175 104 152 104 144 128 119 145 81
Character u g h t o -o -t o u t c a l c u l u s .
Milliseconds 103 113 111 321 95 265 135 256 88 72 128 160 104 128 296 305 192 182 112 113
WPM Timing
Seconds WPM
3.11 42.4
6.23 67.45
9.34 78.37
12.45 74.19
15.57 78.62
18.68 79.01
21.79 78.18
24.91 78.05
28.02 77.51
31.14 77.08
34.25 76.38
37.36 74.19
40.48 75.6
43.59 74.06
46.7 74.26
49.82 72.02
52.93 70.06
56.04 70.87
59.16 71.2
62.27 68.99
65.38 67.36
68.5 66.75
71.61 67.2
74.72 67.93
77.84 68.3
80.95 68.34
84.06 68.09
87.18 67.72
90.29 68.31
93.41 69.12
96.52 68.38
99.63 68.65
102.75 68.67
105.86 68.81
108.97 67.94
112.09 68.2
115.2 68.12
118.31 67.04
121.43 65.62
124.54 66.2
127.65 66.46
130.77 66.35
133.88 66.33
136.99 65.52
140.11 66.29
143.22 66.27
146.34 66.5
149.45 66.56
152.56 66.94
155.68 66.6