Cheol (cllcle)

Race #53

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Official speed 108.80 wpm (95.29 seconds elapsed during race)
Without ending ping 108.93 wpm (114 ms delay sending score to TypeRacer’s server)
Timerless 109.43 wpm (432 ms elapsed before first character typed; 94.75 seconds elapsed during race)
Timerless minus one 109.30 wpm, ignoring the first character typed
Race Start March 5, 2024 7:24:47pm UTC
Race Finish March 5, 2024 7:26:22pm UTC
Outcome Win (1 of 4)
Opponents 2. xerb (101.92 wpm)
Accuracy 98.3%
Points 293.76
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 chang ein one in one quantity is related to a chang ein e in another. How does the speed of a falling object change as a cfunction of time? How does the level of water in a barrel change as a function of the amount of liquid opopoured into it? We see change occurring in nearly everything weob observe in the world and universe, and mpowerful modern intstruments help us see more and more. In this section wsee introcuduce 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 oinformal apporach roach 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 caluculuus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 432 279 78 142 77 187 78 125 63 47 94 93 79 76 93 62 125 138 77 48 80 47 46 32 78
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 125 62 16 109 79 46 126 47 467 139 158 157 31 142 30 78 62 94 45 92 31 31 125 126 124
Character c h a n g e i n o n -n -o - -n -i -e - e i n o
Milliseconds 93 64 63 79 31 110 16 77 62 63 46 78 219 110 108 124 123 125 124 154 108 126 63 77 95
Character n e q u a n t i t y i s r e l a t e d t o
Milliseconds 76 78 93 109 93 125 109 127 78 46 173 94 62 46 109 233 62 126 62 77 126 141 64 77 47
Character a c h a n g e i n - -n -i -e - e i n a n
Milliseconds 78 47 110 125 61 47 107 46 128 0 109 76 94 202 123 109 125 125 172 124 188 62 77 235 126
Character o t h e r . H o w d o e s t h e s p e e d
Milliseconds 45 48 91 64 32 108 78 187 140 157 204 31 171 63 108 62 185 46 107 61 77 78 79 123 124
Character o f a f a l l i n g o b j e c t c h a n
Milliseconds 33 91 64 91 78 94 265 93 127 122 31 63 78 94 46 154 92 93 141 94 46 124 93 46 125
Character g e a s a c -c f u n c t i o n o f t i m
Milliseconds 61 154 138 108 92 108 125 140 188 218 94 78 140 93 142 79 46 59 125 78 62 94 62 64 46
Character e ? H o w d o e s t h e l e v e l o f
Milliseconds 93 141 63 202 171 78 342 140 79 31 92 64 92 63 78 78 45 78 125 109 30 94 63 63 140
Character w a t e r i n a b a r r e l c h a n g e
Milliseconds 92 80 107 46 62 30 78 47 78 64 106 109 110 169 124 141 61 62 62 61 64 93 33 138 94
Character a s a f u n c t i o n o f t h e a m o u
Milliseconds 93 79 125 126 124 420 78 140 78 108 60 63 30 79 78 124 62 78 63 79 78 95 78 76 77
Character n t o f l i q u i d o p -p o -o -o p o u r e d
Milliseconds 156 77 46 62 108 64 31 62 123 91 46 107 79 77 16 466 281 217 109 189 156 108 154 263 156
Character i n t o i t ? W e s e e c h a n g e o
Milliseconds 110 109 77 110 108 77 31 94 203 31 217 237 108 141 75 141 62 141 79 93 499 109 171 92 155
Character c c u r r i n g i n n e a r l y e v e r y t
Milliseconds 154 109 94 77 126 93 61 79 111 77 47 77 94 63 77 92 111 77 62 94 141 31 63 92 138
Character h i n g w e o b -b -o o b s e r v e i n t h
Milliseconds 0 77 94 32 110 109 110 778 79 265 110 95 154 78 158 31 62 157 140 76 63 47 62 16 95
Character e w o r l d a n d u n i v e r s e , a n d
Milliseconds 61 62 78 78 78 94 76 64 78 76 94 61 171 156 30 141 77 64 201 31 451 62 341 77 95
Character m -m p o w e r f u l m o d e r n i n t -t s t
Milliseconds 79 79 282 170 62 48 45 48 186 109 63 111 109 62 261 188 93 110 92 123 63 63 375 108 94
Character r u m e n t s h e l p u s s e e m o r e
Milliseconds 62 140 217 110 93 78 79 92 80 93 79 15 94 110 92 108 77 79 140 126 62 47 63 78 124
Character a n d m o r e . I n t h i s s e c t i o n
Milliseconds 62 31 92 47 61 62 62 33 138 47 172 156 62 46 92 31 64 79 92 48 170 109 63 30 47
Character w s e -e -s e i n t r o c u -u -c d u c e t h e
Milliseconds 265 140 16 31 358 124 236 109 372 31 188 46 127 358 63 202 125 93 63 125 156 61 92 30 110
Character i d e a s o f a v e r a g e a n d i n s
Milliseconds 47 62 93 187 62 140 93 47 77 77 123 174 77 63 94 62 142 46 94 31 140 32 141 62 47
Character t a n t a n e o u s r a t e s o f c h a n g
Milliseconds 63 78 91 361 295 203 234 218 77 110 94 142 93 186 154 62 95 93 93 64 138 94 46 95 62
Character e , a n d s h o w t h a t t h e y a r e
Milliseconds 125 47 78 77 78 92 123 142 92 62 30 110 78 79 47 62 94 61 47 109 46 77 32 61 79
Character c l o s e l y r e l a t e d t o t h e s
Milliseconds 62 124 49 125 63 31 76 126 62 107 46 77 61 63 155 140 77 93 0 93 76 78 79 92 61
Character l o p e o f a c u r v e a t a p o i n
Milliseconds 93 126 139 94 92 63 62 109 62 94 109 109 62 158 139 79 63 63 124 78 109 218 64 170 63
Character t P o n t h e c u r v e . W e g i v e
Milliseconds 46 171 189 201 168 62 79 77 79 94 46 108 126 32 155 125 76 62 221 217 140 94 76 95 142
Character p r e c i s e d e v e l o p m e n t s o f
Milliseconds 45 63 109 76 172 94 140 94 140 125 139 173 126 93 140 126 124 94 63 60 110 61 79 77 94
Character t h e s e i m p o r t a n t c o n c e p t s
Milliseconds 63 61 78 108 31 94 62 93 92 47 62 32 108 122 78 110 93 46 61 79 170 95 62 94 62
Character i n t h e n e x t c h a p t e r , b u t
Milliseconds 62 47 62 17 92 92 45 47 77 110 64 93 126 77 93 62 77 79 48 91 63 78 78 93 92
Character f o r n o w w e u s e a n o -o i n f o r
Milliseconds 125 63 92 46 64 63 77 62 139 61 188 140 155 63 171 171 154 94 155 265 157 46 154 125 31
Character m a l a p p o r a c h - -h -c -a -r -o r o a c h
Milliseconds 140 94 125 94 157 62 108 140 62 63 141 61 78 185 94 109 125 108 140 219 78 93 125 77 80
Character s o y o u w i l l s e e h o w t h e y
Milliseconds 109 78 78 171 64 46 63 61 78 142 109 60 263 124 155 126 77 48 78 92 78 16 139 16 62
Character l e a d n a t u r a l l y t o t h e m a i
Milliseconds 110 79 16 140 62 109 126 125 107 30 80 62 109 80 62 124 109 46 94 94 61 95 46 93 94
Character n i d e a o f t h i s c h a p t e r , t
Milliseconds 30 47 109 80 125 76 78 64 62 63 77 48 47 63 32 142 46 141 63 109 232 49 170 92 95
Character h e l i m i t . T h e i d e a o f a l
Milliseconds 61 76 109 125 77 94 79 94 126 78 173 110 123 62 77 93 124 63 78 46 94 109 61 78 62
Character i m i t p l a y s a f o u n d a t i o n a l
Milliseconds 61 94 62 109 79 45 64 61 93 128 62 92 47 94 31 48 138 107 94 420 153 77 63 110 107
Character r o l e t h r o u g h o u t c a l u -u c u l
Milliseconds 109 218 78 125 48 78 77 93 63 77 62 32 155 170 63 94 122 188 93 157 403 360 109 79 62
Character u u -u s .
Milliseconds 124 496 281 124 169
WPM Timing
Seconds WPM
1.91 88.15
3.81 107.04
5.72 115.43
7.62 96.02
9.53 100.74
11.44 98.64
13.34 98.04
15.25 99.95
17.15 102.84
19.06 101.37
20.96 103.03
22.87 105.46
24.78 108.01
26.68 108.39
28.59 109.98
30.49 105.07
32.4 105.19
34.31 103.89
36.21 106.37
38.12 102.94
40.02 105.24
41.93 104.46
43.84 103.75
45.74 103.1
47.65 105.27
49.55 105.83
51.46 103.54
53.36 103.44
55.27 104.21
57.18 103.05
59.08 104.19
60.99 106.05
62.89 107.04
64.8 107.22
66.71 107.22
68.61 107.04
70.52 107.72
72.42 109.03
74.33 110.1
76.24 109.4
78.14 108.57
80.05 107.64
81.95 108.06
83.86 108.9
85.76 109.7
87.67 109.91
89.58 110.92
91.48 110.58
93.39 110.25
95.29 108.8