Neatrianty (neatrianty)

Race #16825

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Official speed 113.33 wpm (91.48 seconds elapsed during race)
Without ending ping 113.68 wpm (279 ms delay sending score to TypeRacer’s server)
Timerless 114.67 wpm (793 ms elapsed before first character typed; 90.41 seconds elapsed during race)
Timerless minus one 114.54 wpm, ignoring the first character typed
Race Start December 19, 2023 1:13:03pm UTC
Race Finish December 19, 2023 1:14:35pm UTC
Outcome No win (3 of 5)
Opponents 1. whyme__ (121.45 wpm)
2. richiele_01 (115.70 wpm)
4. redfive5 (98.77 wpm)
Accuracy 97.8%
Points 305.99
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 halphelps us understand how a change in one quantity is related to a change in another. How does the speed ofa fof a sfalling object change as a function ioof time? How does the level of water in a barrel change as a function of the amount of lqiiliquid poured into it? We see change orccurring in nearly everything we observe in the world and universe, and powerful modern instruments help us ssee more and more. In this section we introduce the ideas of aveerarage and instantaneous rates of change, and show that they are closely related to the slope of a curve oat a point P on the curvbee. We gie prgfgive precise developments of the se important concepts in the next chapter, but for now we use an informal approach so yo u will see how they lead naturally to the main idea of this chapter, the lmiiimit. The idea of a limit plays a foundtaionattional role throughout calcuus.lus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 793 153 230 162 107 63 117 115 90 56 60 72 77 94 72 54 116 143 72 79 90 9 65 81 44
Character a l p -h -a -l -p h e l p s u s u n d e r s t a n
Milliseconds 97 73 88 251 0 0 0 161 92 34 44 108 45 90 108 115 107 153 62 179 36 126 89 83 0
Character d h o w a c h a n g e i n o n e q u a
Milliseconds 123 81 26 54 36 146 9 86 135 188 54 100 105 19 71 85 50 83 73 45 107 53 166 162 73
Character n t i t y i s r e l a t e d t o a c h a
Milliseconds 134 98 89 89 72 109 115 80 63 54 43 64 99 80 18 135 72 100 15 63 369 142 98 109 53
Character n g e i n a n o t h e r . H o w d o e s
Milliseconds 53 63 44 91 62 71 72 90 53 73 44 53 90 36 53 71 117 117 71 91 71 62 55 17 98
Character t h e s p e e d o f a f -o -f -a - - -f o f
Milliseconds 72 63 143 72 81 81 71 116 134 63 62 55 117 0 160 127 266 0 0 0 0 0 305 90 89
Character a s -s f a l l i n g o b j e c t c h a n g e
Milliseconds 55 136 15 368 71 53 54 117 35 46 90 36 187 108 88 55 126 92 68 80 117 53 81 75 41
Character a s a f u n c t i o n i o -o -i o f t i m
Milliseconds 54 55 384 145 34 143 98 90 126 53 117 53 55 16 99 81 18 295 109 151 81 27 98 27 44
Character e ? H o w d o e s t h e l e v e l o f
Milliseconds 64 125 117 124 164 63 121 51 89 54 81 94 19 36 127 45 44 109 70 45 20 123 72 82 60
Character w a t e r i n a b a r r e l c h a n g e
Milliseconds 91 71 81 90 53 55 61 27 90 63 107 63 71 100 132 65 98 88 74 62 80 45 81 17 125
Character a s a f u n c t i o n o f t h e a m o u
Milliseconds 63 54 118 70 152 64 115 143 90 126 16 64 28 142 81 89 157 131 80 89 89 145 161 62 100
Character n t o f l q i -i -q -l i -i l i q u i d p o u r
Milliseconds 159 331 120 51 126 97 63 152 72 243 54 79 208 275 170 91 250 89 36 98 72 99 188 80 100
Character e d i n t o i t ? W e s e e c h a n g e
Milliseconds 34 135 125 99 44 99 89 99 144 107 116 116 170 188 72 54 45 125 107 117 81 71 46 70 81
Character o r -r c c u r r i n g i n n e a r l y e v
Milliseconds 82 61 161 243 99 133 143 125 162 134 36 130 50 130 44 135 243 119 35 92 0 69 91 107 125
Character e r y t h i n g w e o b s e r v e i n t h
Milliseconds 109 61 107 72 86 66 107 73 107 54 72 124 170 119 105 36 81 126 88 90 36 54 92 122 64
Character e w o r l d a n d u n i v e r s e , a n d
Milliseconds 89 26 233 117 80 90 56 33 144 80 90 79 55 143 103 47 68 146 7 56 96 96 58 63 105
Character p o w e r f u l m o d e r n i n s t r u m e
Milliseconds 57 36 73 70 18 36 170 63 71 90 89 81 81 144 31 49 89 62 64 143 91 114 45 152 73
Character n t s h e l p u s s -s s e e m o r e a n
Milliseconds 89 71 53 74 76 129 80 82 106 57 122 109 115 278 264 67 198 35 53 64 62 36 54 80 63
Character d m o r e . I n t h i s s e c t i o n w
Milliseconds 80 63 36 19 97 27 66 86 116 118 71 80 73 17 54 107 36 80 144 108 44 53 45 108 53
Character e i n t r o d u c e t h e i d e a s o f
Milliseconds 72 107 81 83 105 142 54 74 124 98 136 275 56 72 93 90 89 78 168 72 80 90 71 99 90
Character a v e e r a -a -r -e r a g e a n d i n s t a n t
Milliseconds 44 108 125 116 63 116 269 161 72 179 89 117 28 97 72 89 91 152 37 57 111 72 85 113 178
Character a n e o u s r a t e s o f c h a n g e , a
Milliseconds 197 134 120 104 44 81 63 152 54 89 72 20 60 72 170 151 65 90 51 65 73 32 90 54 35
Character n d s h o w t h a t t h e y a r e c l o
Milliseconds 108 54 89 90 71 49 50 89 56 79 44 72 72 89 28 133 36 90 72 143 54 71 116 45 134
Character s e l y r e l a t e d t o t h e s l o p e
Milliseconds 56 34 222 99 64 251 26 189 57 92 0 123 143 66 72 98 81 55 89 116 90 62 152 126 163
Character o f a c u r v e o -o a t a p o i n t
Milliseconds 34 80 90 72 45 135 62 98 80 144 62 73 63 239 55 79 82 81 98 45 54 55 72 87 36
Character P o n t h e c u r v b e -e -b e . W e g i
Milliseconds 171 152 117 48 44 80 111 44 63 164 47 60 198 18 18 358 367 107 89 55 161 125 81 89 55
Character e p r -g -i -e - -p -r g -g f -f g i v e p r e c i s
Milliseconds 116 61 55 107 304 0 0 0 0 0 403 269 89 341 27 116 45 53 53 46 90 44 144 81 72
Character e d e v e l o p m e n t s o f t h e - s e
Milliseconds 19 87 117 135 124 54 45 152 46 160 116 92 78 36 72 63 80 45 80 55 53 89 305 99 402
Character i m p o r t a n t c o n c e p t s i n t h
Milliseconds 117 71 109 34 72 171 187 63 90 90 97 117 45 62 108 116 54 125 90 152 73 70 72 152 98
Character e n e x t c h a p t e r , b u t f o r n
Milliseconds 37 107 45 71 161 126 80 99 63 88 46 108 89 44 46 71 73 70 90 62 82 70 63 58 59
Character o w w e u s e a n i n f o r m a l a p p
Milliseconds 53 73 113 44 64 73 62 91 47 71 145 124 122 48 100 46 141 126 80 90 80 108 98 108 80
Character r o a c h s o y o - u w i l l s e e h
Milliseconds 128 42 107 108 71 72 80 99 70 37 94 139 306 97 68 57 90 108 116 268 99 54 120 50 71
Character o w t h e y l e a d n a t u r a l l y t o
Milliseconds 63 36 116 64 62 90 44 71 54 45 72 89 92 51 109 70 117 62 63 90 134 36 80 81 72
Character t h e m a i n i d e a o f t h i s c h
Milliseconds 71 215 63 100 70 63 107 64 61 91 80 143 143 72 80 81 89 81 73 44 44 64 88 80 92
Character a p t e r , t h e l m i i -i -i -m i m i t . T
Milliseconds 52 134 171 125 81 60 56 80 54 166 49 63 165 0 148 279 124 295 162 80 94 70 88 75 89
Character h e i d e a o f a l i m i t p l a y s
Milliseconds 90 141 51 46 60 145 19 99 72 81 53 144 170 117 169 100 456 160 54 63 71 74 277 124 90
Character a f o u n d t a i o n -n -o -i -a -t a t t -t i o n a
Milliseconds 63 134 98 97 37 116 54 117 54 98 19 45 348 89 135 136 114 205 10 388 293 215 26 64 159
Character l r o l e t h r o u g h o u t c a l c u u s
Milliseconds 91 90 63 89 116 82 106 81 67 103 19 71 672 88 109 70 91 97 90 134 108 161 45 125 107
Character . -. -s -u l u s .
Milliseconds 37 339 160 105 278 86 97 17
WPM Timing
Seconds WPM
1.83 52.47
3.66 78.7
5.49 102.75
7.32 109.85
9.15 114.12
10.98 121.33
12.81 118.99
14.64 114.77
16.47 115.14
18.3 114.12
20.13 117.46
21.96 120.78
23.79 121.58
25.62 119.46
27.45 114.55
29.28 114.36
31.1 113.81
32.93 114.04
34.76 114.6
36.59 115.76
38.42 117.74
40.25 118.95
42.08 118.62
43.91 120.24
45.74 119.89
47.57 118.05
49.4 118.05
51.23 119.46
53.06 120.54
54.89 120.68
56.72 120.38
58.55 121.13
60.38 118.85
62.21 116.12
64.04 116.93
65.87 116.05
67.7 116.28
69.53 117.19
71.36 117.88
73.19 117.72
75.02 118.21
76.85 118.83
78.68 119.27
80.51 118.05
82.34 118.2
84.17 117.62
86 115.96
87.83 115.18
89.66 114.84
91.48 113.33