Ata (aajan)

Race #5384

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Official speed 78.53 wpm (132.03 seconds elapsed during race)
Without ending ping 78.71 wpm (302 ms delay sending score to TypeRacer’s server)
Timerless 78.91 wpm (334 ms elapsed before first character typed; 131.39 seconds elapsed during race)
Timerless minus one 78.82 wpm, ignoring the first character typed
Race Start April 3, 2024 9:20:35am UTC
Race Finish April 3, 2024 9:22:47am UTC
Outcome No win (2 of 5)
Accuracy 96.6%
Points 212.03
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 8sis related to a change in another. How does the speed of a falling object change as a function of time? How sdoes a tthe level of water in a barrel change as a fucntionciton tion of the amount of liquid poured into it?: We see change occuring ring in rnearly everythinig g we observe in the world and universe, and powerful mofdedern instruments help us ssee more an dmod more. In this seciton tion we introduce the dideas of average and instantanoueous rates of change, and how show that they are closely related to the slope of a curve at a point P on the curve. We give apprecise develpoopmentrs s of these oimportant concepts in the next chapter, but for now we use an informal apporoach tso you will see how they haelead natuallrally to the jamain oidea of this chapter, ahthe limit. The idea of a limit playe s 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 334 86 141 265 98 135 195 140 98 96 87 97 95 144 166 43 141 194 70 146 72 48 87 25 241
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 165 91 215 119 97 207 71 98 241 158 48 145 71 193 143 64 71 146 97 168 70 64 71 314 547
Character c h a n g e i n o n e q u a n t i t y 8 s
Milliseconds 420 72 122 48 190 88 122 94 144 97 184 72 96 120 281 47 142 168 217 40 385 99 92 137 73
Character -s -8 i s r e l a t e d t o a c h a n g e
Milliseconds 335 160 191 97 98 167 65 73 141 143 74 183 72 145 70 73 119 112 169 70 123 71 96 71 64
Character i n a n o t h e r . H o w d o e s t h e
Milliseconds 73 166 75 325 122 72 167 72 48 87 216 74 375 167 146 70 123 70 88 120 49 192 49 47 87
Character s p e e d o f a f a l l i n g o b j e c t
Milliseconds 121 119 119 97 160 73 96 97 119 97 143 256 46 49 145 71 136 97 96 120 327 240 74 191 159
Character c h a n g e a s a f u n c t i o n o f
Milliseconds 50 168 70 48 145 63 72 72 98 166 50 157 97 120 96 120 48 113 22 97 71 49 74 142 76
Character t i m e ? H o w s -s d o e s a t -t - -a t h
Milliseconds 116 40 120 72 312 144 209 95 145 120 134 291 70 120 74 87 72 144 119 168 378 142 162 215 72
Character e l e v e l o f w a t e r i n a b a r
Milliseconds 69 99 119 73 183 50 93 74 119 114 70 456 161 167 98 95 95 90 118 98 262 123 239 63 287
Character r e l c h a n g e a s a f u c n t i o -o -i
Milliseconds 136 120 72 191 258 71 96 48 120 73 25 207 167 97 120 111 50 95 119 50 93 48 74 255 168
Character -t -n -c n c i t o n - -n -o -t -i t i o n o f t h
Milliseconds 120 144 137 192 119 143 26 116 20 71 264 145 136 145 119 167 49 88 31 113 142 265 112 146 71
Character e a m o u n t o f l i q u i d p o u r e d
Milliseconds 48 72 329 118 96 72 168 113 47 97 119 72 121 48 111 145 95 546 96 239 377 94 47 258 143
Character i n t o i t ? : - -: W e s e e c h a n
Milliseconds 74 167 144 308 118 70 162 140 340 22 23 615 113 169 264 145 110 97 144 143 96 211 69 71 98
Character g e o c c u r i n g - -g -n -i r i n g i n r
Milliseconds 119 49 42 262 287 112 123 118 72 118 138 95 216 144 146 134 95 97 49 119 96 65 120 167 167
Character -r n e a r l y e v e r y t h i n i g - -g -i g
Milliseconds 379 215 23 74 93 74 110 74 217 191 73 110 289 304 23 75 92 3 94 145 256 143 143 125 92
Character w e o b s e r v e i n t h e w o r l d a
Milliseconds 91 70 144 617 191 255 73 71 217 71 112 120 122 95 48 95 24 96 87 97 72 96 119 98 209
Character n d u n i v e r s e , a n d p o w e r f u l
Milliseconds 94 97 47 194 134 77 66 124 92 122 40 168 48 146 70 144 19 188 146 22 48 121 232 95 73
Character m o f d e -e -d -f d e r n i n s t r u m e n t s
Milliseconds 119 209 120 96 49 119 255 144 168 281 119 71 49 119 243 86 146 142 194 63 168 98 92 75 94
Character h e l p u s s -s s e e m o r e a n d m
Milliseconds 73 375 73 96 160 96 191 121 72 207 265 519 169 121 39 168 73 70 72 98 135 71 145 24 121
Character o -o -m -d - d m o r e . I n t h i s s e c i
Milliseconds 94 258 141 145 146 71 71 138 94 49 48 146 70 281 142 25 207 49 73 93 75 143 72 186 141
Character t o n - -n -o -t -i t i o n w e i n t r o d u c
Milliseconds 25 72 71 49 208 146 141 146 141 210 49 97 45 281 241 49 119 326 122 167 186 69 191 48 265
Character e t h e d -d i d e a s o f a v e r a g e
Milliseconds 161 120 193 71 71 48 163 334 159 74 141 75 167 23 113 146 47 143 216 135 122 143 144 72 71
Character a n d i n s t a n t a n o u -u -o e o u s r a t
Milliseconds 113 119 76 0 139 124 71 184 238 122 424 400 286 146 72 399 144 72 232 71 122 94 329 96 448
Character e s o f c h a n g e , a n d h o w - -w -o
Milliseconds 72 120 96 233 144 72 167 71 49 112 72 74 44 75 143 97 111 49 118 72 97 145 206 169 144
Character -h s h o w t h a t t h e y a r e c l o s e
Milliseconds 119 72 96 65 71 122 216 46 74 64 46 145 71 97 74 94 112 120 96 22 310 68 147 92 121
Character l y r e l a t e d t o t h e s l o p e o
Milliseconds 144 160 72 167 49 97 118 136 97 167 97 136 71 75 118 72 48 96 137 48 144 262 97 87 97
Character f a c u r v e a t a p o i n t P o n
Milliseconds 120 96 216 87 314 97 117 185 71 97 290 181 74 312 87 120 144 121 98 116 160 432 112 169 96
Character t h e c u r v e . W e g i v e a p -p -a p
Milliseconds 97 94 89 24 96 217 71 119 209 48 143 48 400 194 97 422 71 97 26 142 280 48 288 134 194
Character r e c i s e d e v e l p o -o -p o p m e n t r s
Milliseconds 97 70 234 47 265 94 145 210 142 312 64 120 191 193 281 118 192 160 217 97 143 95 25 95 65
Character - -s -r s o f t h e s e o -o i m p o r t a n t
Milliseconds 312 146 134 72 96 98 93 97 119 64 27 166 72 95 120 330 167 143 74 112 119 192 73 72 97
Character c o n c e p t s i n t h e n e x t c h a
Milliseconds 109 339 45 96 212 140 75 142 73 62 264 120 75 70 112 48 72 168 24 217 137 0 335 96 110
Character p t e r , b u t f o r n o w w e u s e
Milliseconds 97 216 72 96 119 66 334 75 133 49 143 74 98 44 210 71 71 122 142 49 144 497 71 48 113
Character a n i n f o r m a l a p p o -o r o a c h t -t
Milliseconds 171 69 128 88 135 97 142 26 520 95 73 95 280 72 119 145 472 96 71 138 191 71 74 191 257
Character s o y o u w i l l s e e h o w t h e y
Milliseconds 119 97 23 254 123 70 50 142 73 136 168 49 167 146 109 97 147 69 71 97 185 47 49 287 98
Character h a e -e -a -h l e a d n a t u a l l -l -l -a r a l l
Milliseconds 280 96 45 216 161 98 566 50 93 122 94 281 96 120 48 145 87 146 310 139 117 123 45 97 143
Character y t o t h e j a -a -j m a i n o -o i d e a
Milliseconds 63 97 216 49 94 123 64 47 74 216 69 281 118 192 74 48 119 137 95 313 184 72 144 71 73
Character o f t h i s c h a p t e r , a h -h -a t h e
Milliseconds 118 232 49 193 24 70 97 89 144 95 168 184 145 71 120 144 72 184 119 265 112 120 96 72 25
Character l i m i t . T h e i d e a o f a l i m i
Milliseconds 119 98 157 97 119 120 75 328 93 96 50 281 92 171 71 72 97 112 71 71 145 120 25 207 146
Character t p l a y e - -e s a f o u n d a t i o n a
Milliseconds 118 97 142 137 72 142 97 217 231 120 97 71 123 135 434 85 49 167 98 93 145 41 94 97 287
Character l r o l e t h r o u g h o u t c a l c u l u
Milliseconds 136 74 312 46 145 112 96 289 49 448 71 71 144 88 287 74 96 94 522 71 72 233 70 122 143
Character s .
Milliseconds 135 74
WPM Timing
Seconds WPM
2.64 86.35
5.28 88.62
7.92 84.83
10.56 82.94
13.2 83.62
15.84 85.59
18.48 89.59
21.12 90.32
23.76 91.4
26.41 88.62
29.05 87.59
31.69 87.48
34.33 83.2
36.97 84.4
39.61 83.01
42.25 80.95
44.89 79.4
47.53 79.78
50.17 78.21
52.81 79.76
55.45 81.15
58.09 80.15
60.73 79.43
63.37 79.34
66.01 78.35
68.65 78.31
71.29 78.6
73.93 78.39
76.58 77.41
79.22 77.56
81.86 78.58
84.5 79.53
87.14 79.6
89.78 79.66
92.42 78.95
95.06 78.27
97.7 77.87
100.34 78.45
102.98 78.89
105.62 79.42
108.26 79.03
110.9 79.31
113.54 78.53
116.18 78.5
118.82 78.17
121.46 78.34
124.1 78.71
126.74 78.49
129.39 78.56
132.03 78.53