bobva (bobva)

Race #2064

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Official speed 116.20 wpm (89.23 seconds elapsed during race)
Without ending ping 116.71 wpm (181 ms delay sending score to TypeRacer’s server)
Timerless 117.18 wpm (362 ms elapsed before first character typed; 88.68 seconds elapsed during race)
Timerless minus one 117.05 wpm, ignoring the first character typed
Race Start October 14, 2023 8:34:10pm UTC
Race Finish October 14, 2023 8:35:40pm UTC
Outcome Win (1 of 5)
Opponents 2. yambda (105.03 wpm)
4. white_darkness (76.09 wpm)
Accuracy 97.5%
Points 313.74
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 lehelps us understand how a change in one quantitiyy is reallated to a change in another. How does the spseeed of a faallialling object change as a function of time? How does the level of water in a bbaarrel change sas a function of the amount of liquid poured into it? We see change occuringringg in nearly everyghing verything we observe in the world and universe, and powerful modern instruments hgelp elp us see more and more. In this seciton wection we indtroduce the ideas aof average and instantaneous rates of change, and swhow how that they are closely relatwd ed to the skoplope of f a curve at a point PO on on the curve. We give prcisrecise developments of these important concepts in the next chapter, but for now we use an infroormal approach so you will see how they lead naturally to the main idea of thhiis chapter, The the limit. The idea of a limimt plays a foundational role throughout calcuuslus.
Timing
Character C a l c u l u s i s a t o o l t h a t l
Milliseconds 362 142 77 94 102 159 137 79 58 102 110 34 84 81 66 61 133 104 109 81 62 52 93 39 64
Character e $h -e e l p s u s u n d e r s t a n d h o w
Milliseconds 88 410 0 110 50 43 92 49 125 60 60 110 43 18 98 81 126 93 81 85 63 44 74 45 40
Character a c h a n g e i n o n e q u a n t i t i
Milliseconds 51 80 86 83 31 120 81 75 47 91 32 51 75 79 60 64 49 99 51 133 12 184 65 67 135
Character y -y -i y i s r e a l -l -a l a t e d t o a
Milliseconds 0 289 111 110 34 90 61 64 60 32 78 19 278 137 60 43 79 76 113 0 132 0 82 106 57
Character c h a n g e i n a n o t h e r . H o w d o
Milliseconds 90 53 104 58 164 72 87 89 41 86 67 71 46 89 44 104 75 38 87 139 142 25 204 154 78
Character e s t h e s p s e -e -s e e d o f a f a a
Milliseconds 87 13 85 288 72 64 55 223 83 109 70 232 137 99 142 41 56 75 86 42 130 83 92 84 94
Character l l i -a -a -l -l -i a l l i n g o b j e c t c h a
Milliseconds 0 176 94 358 0 0 0 0 72 57 144 146 47 69 56 40 122 40 78 68 153 51 104 24 133
Character n g e a s a f u n c t i o n o f t i m e
Milliseconds 50 59 52 121 61 97 47 128 116 179 76 32 77 135 49 27 25 92 80 81 63 54 55 35 85
Character ? H o w d o e s t h e l e v e l o f w
Milliseconds 139 97 100 231 46 91 58 76 77 36 65 101 36 99 36 86 64 73 88 38 58 106 65 29 55
Character a t e r i n a b b a -a -b a r r e l c h a n
Milliseconds 89 84 88 71 33 44 44 92 81 99 106 143 150 134 119 80 62 131 93 71 77 139 64 94 53
Character g e s -s a s a f u n c t i o n o f t h e
Milliseconds 100 51 116 121 373 127 57 49 116 65 92 86 49 44 176 41 18 49 68 89 70 44 109 71 96
Character a m o u n t o f l i q u i d p o u r e d
Milliseconds 48 58 101 114 73 0 50 73 122 139 26 96 157 90 75 57 61 51 115 196 91 76 89 82 40
Character i n t o i t ? W e s e e c h a n g e o c
Milliseconds 49 43 85 65 84 57 72 170 74 75 245 79 91 161 101 88 56 72 52 94 68 35 81 52 73
Character c u r i n g -g -n -i r i n g g - -g i n n e a r
Milliseconds 122 80 90 91 36 119 161 119 196 117 111 29 83 128 103 194 130 325 108 53 96 284 78 58 65
Character l y e v e r y g -g h i n g -v -e -r -y -h -i -n -g - v
Milliseconds 62 102 45 115 74 118 48 58 96 332 92 110 49 83 41 536 0 0 0 0 0 0 0 0 63
Character e r y t h i n g w e o b s e r v e i n t h
Milliseconds 112 54 62 73 99 92 89 39 57 96 112 50 51 129 159 147 49 170 44 55 124 44 71 95 63
Character e w o r l d a n d u n i v e r s e , a n d
Milliseconds 57 44 106 12 95 78 92 45 119 54 98 33 106 33 117 60 92 79 110 111 57 81 93 39 120
Character p o w e r f u l m o d e r n i n s t r u m e
Milliseconds 45 65 86 88 101 59 114 69 66 100 78 48 72 95 84 52 65 60 55 82 80 98 40 63 168
Character n t s h g e l p -g -e -l -p - e l p u s s e e
Milliseconds 61 55 142 21 124 45 41 101 46 57 339 0 0 0 0 120 54 39 39 141 52 39 121 284 225
Character m o r e a n d m o r e . I n t h i s s
Milliseconds 141 144 53 61 26 57 157 93 46 33 82 58 38 57 111 52 698 157 72 55 80 31 83 60 116
Character e c i t o n w -e -c -i -t -o -n - -w e c t i o n w e
Milliseconds 145 118 151 0 51 29 98 36 440 0 0 0 0 0 0 0 125 45 146 36 45 26 55 54 111
Character i n d -d t r o d u c e t h e i d e a s a -a
Milliseconds 58 75 34 51 240 82 97 86 111 114 53 88 64 119 60 70 44 77 48 63 52 128 40 158 234
Character o f a v e r a g e a n d i n s t a n t a n e
Milliseconds 117 41 77 111 98 102 62 71 94 37 72 114 101 50 41 106 29 26 106 110 52 181 315 98 112
Character o u s r a t e s o f c h a n g e , a n d
Milliseconds 85 50 66 46 126 100 96 59 37 67 92 61 73 108 62 145 104 75 63 79 98 83 82 56 35
Character s w h o w -w -h -o -w - h o w t h a t t h e y
Milliseconds 102 7 53 53 43 64 430 0 0 0 0 52 52 37 28 93 85 43 81 122 138 63 105 67 44
Character a r e c l o s e l y r e l a t w d - -d -w e d
Milliseconds 73 70 64 47 103 56 185 0 173 142 59 103 133 55 122 77 84 138 52 61 254 80 161 116 91
Character t o t h e s k o p -k -o -p l o p e o f f
Milliseconds 54 128 22 93 64 47 91 51 107 55 40 76 401 0 0 28 75 49 115 37 92 99 31 139 47
Character - -f a c u r v e a t a p o i n t P O o
Milliseconds 172 140 108 38 109 109 70 192 56 70 93 119 225 91 100 92 25 154 32 44 55 179 11 107 63
Character n - -n -o - -O o n t h e c u r v e . W e
Milliseconds 68 64 249 138 211 158 131 139 89 8 84 71 64 60 52 68 68 101 153 45 110 51 115 157 42
Character g i v e p r c i s -s -i -c -r r e c i s e d e v e
Milliseconds 98 70 76 55 63 45 69 153 107 63 224 116 139 138 391 127 101 143 113 142 78 52 103 97 94
Character l o p m e n t s o f t h e s e i m p o r t a
Milliseconds 77 39 111 120 62 99 61 134 50 23 111 63 83 45 48 93 97 62 143 62 112 39 62 135 134
Character n t c o n c e p t s i n t h e n e x t c
Milliseconds 12 138 77 123 84 47 45 94 116 15 245 62 46 55 82 68 23 123 69 23 104 127 172 48 131
Character h a p t e r , b u t f o r n o w w e u s
Milliseconds 29 104 79 102 121 65 63 27 150 73 96 53 94 48 186 63 80 51 51 55 114 130 52 87 86
Character e a n i n f r o -o -r o r m a l a p p r o a c
Milliseconds 133 30 100 81 72 93 45 91 156 0 335 132 106 80 122 78 72 62 117 143 138 87 97 71 53
Character h s o y o u w i l l s e e h o w t h e
Milliseconds 84 97 56 75 101 165 63 41 52 74 84 54 150 68 128 185 127 57 104 42 29 79 105 14 158
Character y l e a d n a t u r a l l y t o t h e m
Milliseconds 18 79 115 50 18 79 48 78 68 80 36 94 48 47 121 59 43 106 319 82 72 40 107 31 64
Character a i n i d e a o f t h h i -i -h i s c h a p
Milliseconds 86 72 70 57 86 41 88 32 44 55 69 75 78 14 64 250 189 134 86 46 56 108 56 88 36
Character t e r , T h e $t -h -e - h e l i m i t . T h
Milliseconds 101 100 69 54 57 177 76 101 55 415 0 0 0 34 98 48 40 77 79 81 83 123 36 133 97
Character e i d e a o f a l i m i m -m t p l a y s
Milliseconds 84 31 93 64 60 14 86 36 110 60 40 109 34 98 102 105 138 272 160 49 86 32 60 176 64
Character a f o u n d a t i o n a l r o l e t h r o
Milliseconds 23 120 59 64 61 41 33 52 114 79 35 17 51 100 74 66 60 267 175 52 46 76 49 83 63
Character u g h o u t c a l c u u s -s -u l u s .
Milliseconds 46 79 52 100 64 57 60 303 55 54 98 81 282 89 223 145 53 172 60 137
WPM Timing
Seconds WPM
1.78 107.59
3.57 110.95
5.35 132.25
7.14 126.09
8.92 126.42
10.71 126.65
12.49 120.08
14.28 115.16
16.06 118.8
17.85 121.04
19.63 126.54
21.41 123.84
23.2 123.11
24.98 124.88
26.77 125.52
28.55 125.24
30.34 120.65
32.12 117.31
33.91 116.09
35.69 117.01
37.47 118.8
39.26 120.43
41.04 118.12
42.83 117.96
44.61 115.66
46.4 115.87
48.18 116.06
49.97 116.48
51.75 117.56
53.54 117.23
55.32 117.57
57.1 116.21
58.89 115.34
60.67 114.91
62.46 113.74
64.24 113.01
66.03 112.32
67.81 113.26
69.6 114.14
71.38 114.49
73.16 114.65
74.95 114.64
76.73 115.1
78.52 116
80.3 116.11
82.09 115.93
83.87 116.89
85.66 117.12
87.44 117.61
89.23 116.2