George (wiliu)

Race #2408

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Official speed 118.62 wpm (87.41 seconds elapsed during race)
Without ending ping 118.87 wpm (187 ms delay sending score to TypeRacer’s server)
Timerless 119.12 wpm (180 ms elapsed before first character typed; 87.04 seconds elapsed during race)
Timerless minus one 118.98 wpm, ignoring the first character typed
Race Start November 11, 2023 8:21:18am UTC
Race Finish November 11, 2023 8:22:45am UTC
Outcome Win (1 of 5)
Opponents 2. james_bond777 (90.99 wpm)
Accuracy 97.6%
Points 320.27
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 changei n on in one quanitty quanittity 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 qawater oin a barrel change as a fucntionfunction of the amount of liquid poured into it? We see change occurring in nearly everything we observe in the wworld and universe., and powerful modern instrucments help us see more and more. In this section we introduce the ideas of average and instantenousaneous rates of change, and show that they are closely related to the slope of a curve at a point P on the cufre.eve. We give precise developments of these important concepts in the next chapter, but for now we use an informal approach o yso you will see how they lead naturally to a the main idea of this chapter, the limit. The lididea of a limit plays a foundationa rl role thorugroughout calucluscalculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 180 225 80 68 49 68 84 71 94 105 67 60 69 77 74 57 103 148 58 71 45 45 46 55 27
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 79 82 110 46 68 61 64 69 120 99 77 121 59 79 81 77 42 78 74 54 47 41 75 69 87
Character c h a n g e i n o n -o -n - -n - - -i i n o
Milliseconds 73 77 44 38 49 43 68 17 41 107 123 36 290 0 268 152 125 120 269 126 195 147 53 64 88
Character n e q u a n i t t y -q -u -a -n -i -t -t -y - q u a n
Milliseconds 40 60 55 304 80 63 42 106 5 126 56 164 279 0 0 0 0 0 0 0 0 723 104 79 40
Character i t -t -i t i t y i s r e l a t e d t o a
Milliseconds 112 35 313 92 89 85 65 88 111 83 35 55 76 43 73 64 57 85 114 58 126 30 77 23 85
Character c h a n g e i n a n o t h e r . H o w d o
Milliseconds 88 89 37 42 53 42 64 28 48 67 36 89 57 59 51 69 47 52 89 96 74 61 99 86 86
Character e s t h e s p e e d o f a f a l l i n g
Milliseconds 46 48 42 105 26 83 81 111 30 88 106 26 136 523 45 61 39 72 55 86 3 117 93 37 56
Character o b j e c t c h a n g e a s a f u n c t
Milliseconds 50 67 68 144 35 120 151 69 81 73 72 28 57 45 76 85 64 50 91 71 24 74 102 27 151
Character i o n o f t i m e ? H o w d o e s t h e
Milliseconds 36 22 40 46 81 153 4 51 32 28 74 152 97 276 138 85 92 101 51 52 30 70 91 32 74
Character l e v e l o f q a -a -q w a t e r o -o i n
Milliseconds 30 878 28 104 54 76 81 92 56 72 123 155 209 99 75 53 64 101 51 42 125 218 160 28 55
Character a b a r r e l c h a n g e a s a f u c n
Milliseconds 58 107 25 48 77 99 480 55 92 91 68 48 48 32 49 100 101 44 53 77 63 25 61 115 3
Character t i o n -f -u -c -n -t -i -o -n f u n c t i o n o f t
Milliseconds 178 52 23 49 276 0 0 0 0 0 0 0 234 59 92 65 137 47 30 15 87 48 82 50 104
Character h e a m o u n t o f l i q u i d p o u r e
Milliseconds 14 64 48 65 102 51 59 102 47 63 37 85 52 29 69 63 90 75 112 47 113 126 83 37 106
Character d i n t o i t ? W e s e e c h a n g e
Milliseconds 136 45 83 31 83 519 80 78 68 217 85 242 164 71 101 29 134 189 152 98 64 35 50 21 71
Character o c c u r r i n g i n n e a r l y e v e r y
Milliseconds 99 90 79 144 57 428 116 35 63 49 58 35 66 112 43 79 66 58 89 50 39 109 84 90 138
Character t h i n g w e o b s e r v e i n t h e w
Milliseconds 64 91 74 64 30 61 236 42 48 78 77 91 43 66 201 60 80 53 35 88 70 35 95 94 350
Character -w w o r l d a n d u n i v e r s e . -. , a n
Milliseconds 561 200 79 57 73 67 85 330 71 38 49 155 153 67 54 119 63 63 98 108 325 129 79 33 63
Character d p o w e r f u l m o d e r n i n s t r u c
Milliseconds 73 17 78 110 43 39 32 135 43 62 103 28 69 43 115 28 83 69 68 47 44 85 68 117 132
Character -c m e n t s h e l p u s s e e m o r e a
Milliseconds 298 96 74 61 77 84 94 257 62 47 131 86 38 84 51 80 46 104 80 38 66 51 24 201 40
Character n d m o r e . I n t h i s s e c t i o n
Milliseconds 84 43 27 69 47 47 32 101 65 154 125 70 71 32 52 47 62 92 47 176 188 48 14 45 82
Character w e i n t r o d u c e t h e i d e a s o f
Milliseconds 47 67 64 116 39 60 99 81 67 95 62 71 68 108 6 81 44 72 73 106 40 74 54 128 93
Character a v e r a g e a n d i n s t a n t e n o u s
Milliseconds 175 94 83 73 86 79 84 31 86 54 85 35 56 69 40 43 95 60 74 316 192 107 80 86 50
Character -s -u -o -n -e a n e o u s r a t e s o f c h a n
Milliseconds 240 134 161 172 158 78 60 110 73 49 73 47 87 69 109 71 17 90 75 48 59 99 49 71 55
Character g e , a n d s h o w t h a t t h e y a r
Milliseconds 44 82 71 139 91 85 52 45 166 48 65 48 82 70 83 20 65 40 81 51 56 68 22 58 59
Character e c l o s e l y r e l a t e d t o t h e
Milliseconds 44 73 175 214 179 68 53 67 114 80 43 51 72 79 56 77 118 81 126 94 81 68 103 18 81
Character s l o p e o f a c u r v e a t a p o i
Milliseconds 89 77 105 190 90 66 115 42 63 49 93 95 97 81 136 26 120 122 73 95 217 85 95 112 33
Character n t P o n t h e c u f -f r e . -. -e e -e v e
Milliseconds 22 37 68 154 138 81 74 65 56 60 31 39 116 111 211 389 92 185 69 512 123 201 334 74 29
Character . W e g i v e p r e c i s e d e v e l o p
Milliseconds 97 99 152 215 80 107 86 58 33 80 64 68 240 171 77 83 53 83 267 79 118 58 47 131 108
Character m e n t s o f t h e s e i m p o r t a n t
Milliseconds 146 124 48 95 166 40 136 44 77 76 60 33 81 77 60 80 48 94 109 63 153 136 107 80 58
Character c o n c e p t s i n t h e n e x t c h a p
Milliseconds 283 47 47 39 51 112 72 76 69 64 37 74 78 26 48 38 60 63 115 154 52 103 66 46 136
Character t e r , b u t f o r n o w w e u s e a
Milliseconds 75 107 38 76 111 28 116 45 63 109 67 69 82 44 35 77 92 112 55 76 99 53 38 74 91
Character n i n f o r m a l a p p r o a c h o y -y -
Milliseconds 97 87 46 48 48 100 71 124 116 201 113 170 23 90 321 91 10 110 102 82 275 89 120 245 131
Character -o s o y o u w i l l s e e h o w t h e y
Milliseconds 153 115 74 79 49 72 70 50 48 56 148 89 86 18 70 118 111 81 51 77 63 126 58 41 69
Character l e a d n a t u r a l l y t o a - -a t h
Milliseconds 52 94 37 57 72 68 53 73 73 119 38 62 70 77 111 67 118 69 58 58 68 337 113 159 85
Character e m a i n i d e a o f t h i s c h a p t
Milliseconds 53 37 84 48 55 48 67 86 65 94 46 71 57 63 59 104 60 14 86 47 296 91 54 53 94
Character e r , t h e l i m i t . T h e l i d -l -i -d
Milliseconds 70 67 56 108 82 59 66 41 105 2 81 97 73 80 78 164 100 30 56 58 47 74 344 0 0
Character i d e a o f a l i m i t p l a y s a f
Milliseconds 245 50 132 63 50 87 57 48 65 87 4 78 35 93 90 61 81 109 63 76 71 132 77 86 77
Character o u n d a t i o n a r -r - l r o l e t h o r
Milliseconds 56 40 98 45 74 88 42 27 31 60 764 56 244 283 200 61 50 74 109 51 42 102 21 107 3
Character u g -g -u -r -o r o u g h o u t c a l u c l u s -c -a
Milliseconds 59 112 296 127 168 168 95 45 56 67 69 84 83 31 87 259 65 19 93 16 123 60 88 253 0
Character -l -u -c -l -u -s c a l c u l u s .
Milliseconds 0 0 0 0 0 0 268 85 116 132 166 409 101 37 210
WPM Timing
Seconds WPM
1.75 130.43
3.5 147.59
5.24 128.14
6.99 109.83
8.74 90.61
10.49 93.82
12.24 108.85
13.98 109.83
15.73 116.7
17.48 121.5
19.23 118.57
20.98 117.27
22.73 116.17
24.47 113.76
26.22 118.99
27.97 118.41
29.72 117.91
31.47 118.6
33.21 119.95
34.96 117.38
36.71 117.35
38.46 118.88
40.21 118.19
41.95 120.13
43.7 121.91
45.45 123.03
47.2 122.29
48.95 120.87
50.7 122.62
52.44 123.56
54.19 124.01
55.94 124.21
57.69 122.94
59.44 120.33
61.18 120.23
62.93 120.7
64.68 121.15
66.43 122.3
68.18 123.21
69.92 122.36
71.67 121.55
73.42 122.75
75.17 122.29
76.92 122.94
78.66 122.34
80.41 123.26
82.16 122.25
83.91 120.99
85.66 119.78
87.41 118.62