Michael (michaelch)

Race #12227

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Official speed 103.40 wpm (100.27 seconds elapsed during race)
Without ending ping 104.04 wpm (615 ms delay sending score to TypeRacer’s server)
Timerless 104.06 wpm (19 ms elapsed before first character typed; 99.64 seconds elapsed during race)
Timerless minus one 103.94 wpm, ignoring the first character typed
Race Start December 29, 2023 6:29:16am UTC
Race Finish December 29, 2023 6:30:56am UTC
Outcome No win (2 of 5)
Opponents 1. crispyasf (107.31 wpm)
3. manojrawat6453 (89.81 wpm)
4. dmitry_ (79.37 wpm)
Accuracy 97.7%
Points 279.17
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 chagnenge in one qusnantity is related to a change in another. How does the speed of a falling object change as a fucntionciton ofunction of time? How does the leve lofl of water in a barrel change as a function of the amoun tt of liquid poured into it? We see change occuring in ccurring nein nearly everything we observe in the world and universe, and poerfuwerful modern instruments helps us see more and more. In this section we introduce the ideas of average and instantaneous rates of change, and show that hey they are closely realataelated to the slope of a curve at a pointP P on the curve. We give pricesecise 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 dieaidea of this chapter, the limit. The idea of a limit plays a foundational role 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 19 149 69 78 85 139 80 88 76 83 92 113 88 93 77 83 134 177 77 79 76 40 90 22 78
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 105 124 98 30 57 102 109 25 183 67 30 161 62 126 111 62 75 77 85 96 72 54 37 148 13
Character c h a g n e -e -n -g n g e i n o n e q u s n -n
Milliseconds 454 171 82 77 59 80 407 114 126 357 97 52 23 85 68 83 269 95 33 88 117 91 116 56 402
Character -s a n t i t y i s r e l a t e d t o a c
Milliseconds 121 218 52 133 34 121 72 197 99 96 78 149 21 133 7 105 62 148 76 78 68 51 84 96 50
Character h a n g e i n a n o t h e r . H o w d o e
Milliseconds 98 73 108 12 60 76 44 81 64 63 69 84 51 54 116 48 77 70 105 58 88 59 113 73 92
Character s t h e s p e e d o f a f a l l i n g
Milliseconds 58 48 103 112 46 94 62 131 64 151 181 124 70 95 64 120 87 211 30 77 142 62 54 74 53
Character o b j e c t c h a n g e a s a f u c n t i
Milliseconds 76 68 101 56 89 155 94 113 48 79 107 35 48 77 89 84 56 169 388 121 149 44 22 193 36
Character o -o -i -t -n -c n c i t o n o f -u -n -c -i -t -o -n - -o -f
Milliseconds 43 314 101 117 131 87 233 49 163 0 45 71 45 97 139 658 0 0 0 0 0 0 0 0 0
Character u n c t i o n o f t i m e ? H o w d o e s
Milliseconds 64 23 90 154 23 27 61 101 64 84 63 73 130 0 23 238 90 181 109 153 60 104 43 136 35
Character t h e l e v e l o f -f -o -l - l o f w a t
Milliseconds 101 86 85 71 92 68 43 94 96 61 7 166 85 297 118 98 111 211 94 82 25 95 96 82 98
Character e r i n a b a r r e l c h a n g e a s
Milliseconds 91 93 93 101 89 70 132 113 83 69 81 179 71 103 90 122 42 93 96 75 52 84 97 142 0
Character a f u n c t i o n o f t h e a m o u n t
Milliseconds 551 90 110 220 76 45 186 16 43 35 90 92 76 82 98 14 140 98 90 61 51 55 86 113 17
Character -t - t o f l i q u i d p o u r e d i n t o
Milliseconds 509 121 84 49 74 107 26 116 102 106 103 86 89 113 98 128 376 131 174 172 62 35 359 101 191
Character i t ? W e s e e c h a n g e o c c u r i
Milliseconds 122 130 67 280 39 168 190 117 76 87 140 93 143 33 113 92 24 62 55 98 115 152 72 88 90
Character n g i n -c -c -u -r -i -n -g - -i -n - c c u r r i n g
Milliseconds 57 67 96 52 64 90 508 0 0 0 0 0 0 0 0 0 0 100 162 99 102 245 82 74 85
Character n e -e -n i n n e a r l y e v e r y t h i n g
Milliseconds 112 97 64 302 106 148 41 61 122 117 30 68 68 154 22 157 152 85 107 88 92 130 91 95 6
Character w e o b s e r v e i n t h e w o r l d
Milliseconds 114 61 37 125 115 76 570 59 89 203 97 121 77 119 174 127 79 76 90 58 92 69 121 63 44
Character a n d u n i v e r s e , a n d p o e r f u -u
Milliseconds 109 80 99 70 50 75 117 155 118 78 87 135 85 89 74 73 93 103 94 73 110 83 172 40 380
Character -f -r -e w e r f u l m o d e r n i n s t r u m e
Milliseconds 114 113 127 114 58 188 209 81 180 102 181 82 176 150 66 43 92 85 76 157 99 133 43 148 81
Character n t s h e l p s -s u s s e e m o r e a n
Milliseconds 108 82 88 42 102 90 86 151 22 487 160 109 85 68 130 105 172 29 53 73 44 60 47 85 76
Character d m o r e . I n t h i s s e c t i o n w
Milliseconds 64 59 65 47 105 71 120 102 113 95 52 79 84 56 56 97 99 71 133 169 16 60 52 40 81
Character e i n t r o d u c e t h e i d e a s o f
Milliseconds 75 90 92 75 154 200 199 99 119 113 70 109 124 53 93 78 69 51 148 87 70 89 101 66 98
Character a v e r a g e a n d i n s t a n t a n e o u s
Milliseconds 105 119 122 169 63 133 62 87 81 100 39 121 101 71 64 116 93 178 851 41 74 96 192 80 110
Character r a t e s o f c h a n g e , a n d s h o
Milliseconds 136 154 112 472 49 49 118 71 94 61 126 104 86 96 43 68 52 85 65 79 51 104 96 69 63
Character w t h a t h e y - -y -e -h t h e y a r e c
Milliseconds 84 49 113 13 109 87 148 376 73 112 81 327 126 123 99 139 71 108 43 88 38 56 65 71 111
Character l o s e l y r e a l a t a e -e -a -t -a -l -a l a t e
Milliseconds 80 116 31 88 80 121 93 124 74 58 13 141 23 64 2 475 139 113 126 127 336 164 47 59 72
Character d t o t h e s l o p e o f a c u r v e
Milliseconds 139 78 67 72 75 61 99 90 119 97 88 139 46 101 58 123 153 86 103 96 54 148 91 191 64
Character a t a p o i n t P -P P o n t h e c u
Milliseconds 63 120 80 19 445 47 100 88 153 77 32 274 485 149 164 127 241 36 86 75 71 85 72 96 74
Character r v e . W e g i v e p r i c e s -s -e -c -i e c
Milliseconds 82 161 65 108 85 184 140 103 115 131 67 87 92 165 81 121 70 87 88 295 120 108 127 273 258
Character i s e d e v e l o p m e n t s o f t h e s e
Milliseconds 89 82 60 106 203 150 65 92 46 141 31 121 63 133 63 91 163 110 87 73 99 57 99 28 129
Character i m p o r t a n t c o n c e p t s i n t h
Milliseconds 47 75 72 90 50 44 189 81 122 122 107 142 5 80 85 65 143 126 518 70 70 81 80 39 132
Character e n e x t c h a p t e r , b u t f o r n
Milliseconds 37 96 77 39 183 92 87 100 66 49 141 61 78 95 101 89 195 84 90 95 184 79 60 94 105
Character o w w e u s e a n i n f o r m a l a p p
Milliseconds 84 112 59 117 38 93 84 63 76 76 262 122 71 65 85 83 102 92 108 81 124 80 168 89 128
Character r o a c h s o y o u w i l l s e e h o w
Milliseconds 46 118 83 85 82 126 101 83 110 158 101 59 67 88 55 27 139 92 89 68 157 65 71 55 45
Character t h e y l e a d n a t u r a l l y t o t
Milliseconds 80 80 150 56 88 81 107 36 52 117 51 93 50 77 67 90 59 65 136 58 80 111 112 59 55
Character h e m a i n d i e a -a -e -i -d i d e a o f t
Milliseconds 98 80 67 80 89 55 76 68 93 21 154 95 270 118 108 98 174 7 173 74 44 113 81 58 103
Character h i s c h a p t e r , t h e l i m i t . T
Milliseconds 29 70 63 75 115 83 72 101 85 93 82 99 60 183 83 76 72 62 99 73 92 81 132 77 97
Character h e i d e a o f a l i m i t p l a y s
Milliseconds 110 56 99 72 59 159 50 73 101 289 47 162 61 140 115 65 97 113 108 50 97 55 118 104 61
Character a f o u n d a t i o n a l r o l e t h r o u
Milliseconds 77 92 57 76 51 82 13 49 117 26 73 20 245 124 104 241 63 198 62 80 76 101 84 46 89
Character g h o u t c a l c u l u s .
Milliseconds 75 102 88 129 377 92 135 71 26 93 60 146 49 52 126
WPM Timing
Seconds WPM
2.01 131.64
4.01 134.64
6.02 105.71
8.02 98.73
10.03 104.12
12.03 113.69
14.04 115.4
16.04 118.18
18.05 106.38
20.05 102.92
22.06 105.53
24.06 102.22
26.07 104.49
28.08 104.29
30.08 103.72
32.09 102.1
34.09 102.43
36.1 98.4
38.1 97.95
40.11 98.13
42.11 99.16
44.12 99.82
46.12 97.56
48.13 98.73
50.14 98.61
52.14 100.8
54.15 101.06
56.15 102.15
58.16 100.9
60.16 101.53
62.17 100.18
64.17 100.6
66.18 98.82
68.18 99.44
70.19 98.82
72.19 98.9
74.2 97.84
76.21 97.95
78.21 98.66
80.22 99.03
82.22 99.68
84.23 100.3
86.23 100.89
88.24 102
90.24 101.72
92.25 102.37
94.25 102.87
96.26 103.59
98.27 103.92
100.27 103.4