(jesterc)

Race #44376

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Official speed 143.20 wpm (72.40 seconds elapsed during race)
Without ending ping 144.12 wpm (461 ms delay sending score to TypeRacer’s server)
Timerless 144.64 wpm (258 ms elapsed before first character typed; 71.68 seconds elapsed during race)
Timerless minus one 144.47 wpm, ignoring the first character typed
Race Start August 22, 2024 3:43:21pm UTC
Race Finish August 22, 2024 3:44:34pm UTC
Outcome Win (1 of 5)
Accuracy 98.2%
Points 386.64
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 undestanrstand how a change in one quantit yis ty is related to a change in antoher. aanother. How does the speed of a faling oling obujectject change as a function of time? How does the lveellevel of water in a barrel change as a function of the amount of liquid poured into it? We see change occurring in nearly everythinhg wg 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 aproaproah \chch so you will see how they lead naturally to thye mae main idea of this chapter, the limit. The idea of a limit plays a foundational roel throurole 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 258 187 108 87 90 97 83 97 48 67 50 60 30 120 56 34 131 139 69 31 97 36 63 94 40
Character e l p s u s u n d e s t a n -n -a -t -s r s t a n
Milliseconds 73 82 11 88 96 203 82 76 29 84 81 121 59 91 67 75 263 135 135 115 35 116 72 26 56
Character d h o w a c h a n g e i n o n e q u a
Milliseconds 62 52 59 39 21 67 78 71 83 48 73 60 89 46 23 367 91 143 74 68 47 72 30 117 71
Character n t i t y i s -y -i -s - - -t t y i s r e l a
Milliseconds 78 83 72 62 118 37 67 98 48 268 0 0 0 134 165 376 96 46 81 53 38 276 23 95 32
Character t e d t o a c h a n g e i n a n t o h e
Milliseconds 83 32 125 68 75 16 74 75 60 75 48 67 72 38 40 42 61 52 69 42 54 62 6 97 22
Character r . - -. a -a -n -t -o -h -e -r -a a n o t h e r . H o
Milliseconds 26 94 41 282 115 208 218 0 0 0 0 0 0 0 216 69 45 46 74 36 45 54 44 114 156
Character w d o e s t h e s p e e d o f a f a l
Milliseconds 52 109 67 319 135 23 75 203 120 97 105 45 93 5 120 113 89 55 58 37 75 76 254 60 40
Character i n g o -o - -g -n -i l i n g o b u j e c t -t -c -e
Milliseconds 155 37 83 61 83 239 128 134 135 120 188 54 35 68 67 39 92 87 7 46 77 133 189 133 150
Character -j -u j e c t c h a n g e a s a f u n c t i
Milliseconds 127 100 126 37 75 129 96 181 59 120 22 23 22 61 44 68 55 57 83 77 88 68 52 112 30
Character o n o f t i m e ? H o w d o e s t h e
Milliseconds 23 30 97 33 43 60 74 98 30 15 180 48 135 150 27 123 42 92 43 46 30 47 67 57 30
Character l v e e l -l -v -e -e -l l e v e l o f w a t e r
Milliseconds 78 126 9 67 155 264 0 0 0 0 171 54 75 51 30 100 43 23 59 30 83 46 90 51 9
Character i n a b a r r e l c h a n g e a s a f
Milliseconds 36 79 27 142 75 90 60 61 112 45 39 58 97 46 104 30 38 30 63 35 74 45 68 82 78
Character u n c t i o n o f t h e a m o u n t o f
Milliseconds 102 35 81 117 60 25 6 92 67 42 41 87 47 20 79 57 67 82 62 118 63 52 43 90 18
Character l i q u i d p o u r e d i n t o i t ? W e
Milliseconds 102 22 165 83 30 131 72 97 82 68 23 67 91 59 46 61 74 36 68 82 90 151 22 105 142
Character s e e c h a n g e o c c u r r i n g i n
Milliseconds 90 75 31 105 77 170 75 112 23 38 22 78 102 52 120 92 88 113 128 45 60 75 37 98 68
Character n e a r l y e v e r y t h i n h g w -w - -g -h g
Milliseconds 404 30 82 40 59 59 52 8 124 81 36 31 111 24 35 98 7 53 38 157 210 135 132 109 45
Character w e o b s e r v e i n t h e w o r l d
Milliseconds 52 67 60 60 45 78 96 69 28 112 37 60 33 42 75 38 30 31 67 37 22 75 83 33 57
Character a n d u n i v e r s e , a n d p o w e r f u
Milliseconds 45 52 53 30 68 128 6 41 103 134 270 37 83 53 74 75 40 73 165 114 59 26 30 117 22
Character l m o d e r n i n s t r u m e n t s h e l p
Milliseconds 38 97 60 38 44 120 22 25 73 67 68 75 52 120 11 192 40 103 67 32 28 60 82 38 10
Character u s s e e m o r e a n d m o r e . I n
Milliseconds 110 97 57 35 83 50 128 55 51 17 72 22 71 72 30 75 60 37 38 70 20 75 60 63 117
Character t h i s s e c t i o n w e i n t r o d u c
Milliseconds 68 52 48 42 56 26 108 20 106 141 38 22 23 60 67 30 83 187 60 47 111 45 97 84 21
Character e t h e i d e a s o f a v e r a g e a n
Milliseconds 25 73 52 45 47 51 67 31 119 48 88 38 40 71 69 51 77 73 108 110 30 52 61 37 82
Character d i n s t a n t a n e o u s r a t e s o f
Milliseconds 53 60 37 63 50 67 143 262 90 90 443 83 82 52 45 68 60 99 51 22 60 38 30 83 32
Character c h a n g e , a n d s h o w t h a t t h e
Milliseconds 102 23 108 27 52 30 45 38 40 73 29 85 57 83 45 68 53 46 88 10 65 45 72 26 75
Character y a r e c l o s e l y r e l a t e d t o
Milliseconds 52 8 112 11 27 39 88 38 97 76 7 105 39 7 75 29 75 37 53 30 120 42 85 446 79
Character t h e s l o p e o f a c u r v e a t a
Milliseconds 23 105 60 22 293 53 151 51 130 20 47 59 44 90 15 113 97 48 140 9 68 58 83 29 68
Character p o i n t P o n t h e c u r v e . W e
Milliseconds 82 47 51 37 38 25 83 109 135 55 59 49 58 35 59 45 90 150 105 135 38 60 33 439 120
Character g i v e p r e c i s e d e v e l o p m e n t
Milliseconds 68 67 90 68 22 39 37 68 60 96 77 58 26 57 76 126 72 56 62 140 68 97 78 68 82
Character s o f t h e s e i m p o r t a n t c o n c
Milliseconds 83 19 48 83 19 91 14 42 124 68 10 86 54 25 86 53 113 74 11 81 68 103 30 60 55
Character e p t s i n t h e n e x t c h a p t e r ,
Milliseconds 35 75 61 98 31 20 52 84 22 74 32 73 54 23 201 53 74 125 80 88 46 74 97 61 7
Character b u t f o r n o w w e u s e a n i n
Milliseconds 30 106 51 75 48 68 49 76 74 38 22 56 51 112 81 75 76 56 33 60 76 75 72 41 52
Character f o r m a l a p r o a -a -o -r p r o a h - \ -\ c
Milliseconds 30 105 74 25 134 45 77 58 82 164 158 61 216 120 143 143 59 98 7 143 48 394 7 0 0
Character h -h -c -h c h s o y o u w i l l s e e h o
Milliseconds 110 205 110 113 61 88 62 29 60 93 19 60 56 34 53 67 135 84 22 90 43 123 21 114 89
Character w t h e y l e a d n a t u r a l l y t o
Milliseconds 83 82 77 43 108 26 68 121 29 90 52 38 60 48 65 68 58 16 44 75 83 52 61 37 68
Character t h y e m a -m -a - -e -y e m a i n i d e a o
Milliseconds 39 68 5 30 83 47 110 218 0 122 290 135 60 53 52 67 46 47 110 40 35 105 45 60 45
Character f t h i s c h a p t e r , t h e l i m i t
Milliseconds 83 22 106 32 27 68 40 84 33 150 90 69 97 37 8 32 102 38 82 11 283 44 82 75 85
Character . T h e i d e a o f a l i m i t p l a
Milliseconds 88 60 52 135 53 68 67 45 105 61 51 30 75 31 88 63 163 53 60 61 106 51 18 81 58
Character y s a f o u n d a t i o n a l r o e l t h
Milliseconds 92 43 39 73 83 46 59 52 121 37 130 27 56 27 60 75 70 58 80 40 135 8 49 56 53
Character r o u -t -h -r -o -u -r -o -e -l - r o l e t h r o u g h
Milliseconds 67 41 40 206 0 0 0 0 135 0 0 0 0 95 107 126 45 62 20 83 64 56 30 82 63
Character o u t c a l c u l u s .
Milliseconds 87 65 25 67 90 68 37 78 12 113 82 92 88
WPM Timing
Seconds WPM
1.45 124.31
2.9 136.74
4.34 107.73
5.79 122.23
7.24 116.02
8.69 107.73
10.14 117.2
11.58 106.7
13.03 107.73
14.48 111.05
15.93 103.21
17.38 98.06
18.82 103.91
20.27 108.32
21.72 107.73
23.17 113.43
24.62 118.46
26.06 121.08
27.51 123
28.96 123.89
30.41 125.09
31.86 123.55
33.31 127.91
34.75 128.45
36.2 130.6
37.65 133.55
39.1 135.05
40.55 137.33
41.99 137.74
43.44 137.84
44.89 141.15
46.34 141.4
47.79 141.63
49.23 143.32
50.68 142.06
52.13 142.95
53.58 144.46
55.03 145.46
56.47 146.83
57.92 146.27
59.37 143.51
60.82 143.25
62.27 143.96
63.71 142.76
65.16 143.64
66.61 143.76
68.06 144.41
69.51 144.85
70.95 143.59
72.4 143.2