Hawk (hawkofdarkness)

Race #1041

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Official speed 88.00 wpm (117.82 seconds elapsed during race)
Without ending ping 88.18 wpm (240 ms delay sending score to TypeRacer’s server)
Timerless 88.78 wpm (791 ms elapsed before first character typed; 116.79 seconds elapsed during race)
Timerless minus one 88.67 wpm, ignoring the first character typed
Race Start October 9, 2023 2:44:15am UTC
Race Finish October 9, 2023 2:46:12am UTC
Outcome No win (3 of 5)
Opponents 1. aelius_qwerty2 (128.63 wpm)
2. bitbat (107.36 wpm)
Accuracy 97.7%
Points 237.61
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 Cacllculu iss is a tool that helps us understand how a change in one quanitytity is related to a cyhanchange in another. How does the speed of a falling ogbject change as a function of time? How does the level of water in a barrel change as a functio nof function of the amount of liquid poured into it? We see cyanc hanchanchange occurring in nearly everything we obvserve in the world and universe, and powerful modern instruments help us see more and more. In this sectino wesection we introduce the ideas of average and instantaneous orates of change, and show that they are closely related to the slope of a crtuurve at a point P on the curve. We give precise dewvelvelopments of these important concepts in the next chapter, but for now we use an infrormal apporoach so you will see how they lead natuarallty y to the main idea of this chapter, the limit. The idea of a limit p[lalays a foundational role throughout calculus.
Timing
Character C a c l -l -c l c u l u i s -s -i - s i s a t
Milliseconds 791 162 150 114 431 137 222 107 176 184 105 185 190 112 252 140 144 144 66 150 131 85 156 84 101
Character o o l t h a t h e l p s u s u n d e r s t
Milliseconds 91 98 200 86 88 89 87 78 26 88 112 81 143 130 70 81 88 152 63 197 91 224 89 145 87
Character a n d h o w a c h a n g e i n o n e q
Milliseconds 87 90 126 65 64 64 88 88 104 129 87 415 88 105 111 120 65 87 64 68 127 70 80 87 152
Character u a n i t y -y -t -i t i t y i s r e l a t e d
Milliseconds 170 150 105 183 89 159 257 144 143 145 82 85 132 68 208 105 47 104 88 122 111 64 111 184 65
Character t o a c y h a n -c -y -h -a -n c h a n g e i n
Milliseconds 63 64 88 104 111 89 130 0 39 128 474 0 0 0 0 182 90 87 104 86 128 65 87 145 17
Character a n o t h e r . H o w d o e s t h e s p e
Milliseconds 487 91 62 87 60 116 40 64 93 171 120 105 111 88 82 109 145 88 88 104 64 63 112 105 136
Character e d o f a f a l l i n g o g -g b j e c t
Milliseconds 176 183 89 208 107 69 104 88 106 110 106 110 104 132 108 64 43 421 313 143 88 112 176 130 85
Character c h a n g e a s a f u n c t i o n o f t
Milliseconds 257 104 112 104 130 142 88 105 87 88 88 105 87 129 160 68 84 61 69 44 19 134 152 40 112
Character i m e ? H o w d o e s t h e l e v e l o
Milliseconds 40 88 41 287 110 218 138 111 87 105 199 126 162 65 64 48 104 22 129 65 191 121 112 16 271
Character f w a t e r i n a b a r r e l c h a n g
Milliseconds 129 63 88 168 62 146 65 64 104 87 46 130 89 167 66 134 201 143 153 144 112 128 88 128 63
Character e a s a f u n c t i o n o f -n -o -f - -f -u
Milliseconds 104 89 104 47 105 111 114 58 108 184 41 103 49 81 62 23 131 87 78 384 0 0 0 137 0
Character -n -c -t -i -o - f u n c t i o n o f t h e a m o
Milliseconds 0 0 0 0 0 0 280 129 199 86 91 128 87 82 135 168 128 61 115 64 40 65 151 87 25
Character u n t o f l i q u i d p o u r e d i n t o
Milliseconds 215 200 66 48 103 87 128 200 82 174 177 61 107 89 86 201 176 231 126 163 64 65 64 126 89
Character i t ? W e s e e c y a n -c -y -a -n c h a n
Milliseconds 88 138 53 250 131 196 319 84 109 209 183 105 87 128 45 154 409 0 0 0 207 16 46 107 88
Character -h -a -n c h a n -c -h -a -n -c - c h a n g e o c c u r
Milliseconds 336 0 0 144 81 87 88 256 0 0 0 149 0 356 80 111 81 112 143 112 125 108 335 241 137
Character r i n g i n n e a r l y e v e r y t h i n g
Milliseconds 255 151 107 69 104 88 106 65 133 88 81 47 88 128 64 106 143 103 88 153 127 64 88 104 41
Character w e o b v -v s e r v e i n t h e w o r l
Milliseconds 87 64 130 46 152 125 29 687 143 88 66 161 119 111 105 70 82 70 71 75 71 80 66 109 83
Character d a n d u n i v e r s e , a n d p o w e r
Milliseconds 109 43 85 66 111 40 109 162 89 127 225 66 165 66 128 87 65 110 62 67 87 201 88 49 60
Character f u l m o d e r n i n s t r u m e n t s h e
Milliseconds 187 82 166 80 135 41 87 201 72 88 255 129 87 88 105 184 152 272 71 114 68 100 65 65 135
Character l p u s s e e m o r e a n d m o r e .
Milliseconds 86 160 125 131 65 66 151 246 181 67 103 69 68 39 63 90 64 89 20 108 41 70 40 128 88
Character I n t h i s s e c t i n o w e -w -e -s -e -c -t -i
Milliseconds 152 123 69 103 33 80 66 62 128 113 175 128 19 74 0 98 66 154 349 0 128 0 0 0 0
Character -n -o - s e c t i o n w e i n t r o d u c e t
Milliseconds 0 0 0 224 128 192 136 85 43 66 110 152 152 104 112 105 47 177 66 149 168 112 154 23 129
Character h e i d e a s o f a v e r a g e a n d i
Milliseconds 46 129 24 215 208 160 146 87 111 127 129 88 128 129 177 54 125 115 125 68 63 106 49 61 106
Character n s t a n t a n e o u s o -o r a t e s o f c
Milliseconds 112 37 90 84 109 127 207 153 104 207 86 130 88 153 383 144 106 110 88 184 62 90 81 87 113
Character h a n g e , a n d s h o w t h a t t h e y
Milliseconds 105 83 131 128 392 186 111 60 115 81 48 104 111 20 109 65 87 106 45 87 84 110 23 121 88
Character a r e c l o s e l y r e l a t e d t o t
Milliseconds 112 103 112 66 86 101 132 159 113 104 112 128 106 87 47 143 153 152 145 450 149 88 129 71 103
Character h e s l o p e o f a c r t u -u -t -r u r v e
Milliseconds 112 62 86 109 61 187 136 128 41 65 110 106 69 147 110 168 22 106 336 143 136 225 170 206 144
Character a t a p o i n t P o n t h e c u r v
Milliseconds 64 112 128 41 86 130 87 208 105 214 139 62 192 128 153 80 48 66 102 22 86 109 150 168 241
Character e . W e g i v e p r e c i s e d e w v e l
Milliseconds 225 127 112 191 209 87 152 328 168 184 64 170 86 65 498 183 110 107 109 128 169 24 111 128 65
Character -l -e -v -w v e l o p m e n t s o f t h e s e i
Milliseconds 367 144 139 165 106 142 88 161 183 241 112 106 64 109 88 88 82 71 103 43 43 127 132 63 176
Character m p o r t a n t c o n c e p t s i n t h e
Milliseconds 104 131 205 113 199 153 128 20 144 92 64 65 71 176 112 88 143 89 63 64 88 42 112 78 49
Character n e x t c h a p t e r , b u t f o r n o w
Milliseconds 104 48 199 504 111 90 80 111 89 103 128 89 40 64 111 105 88 40 128 112 83 85 89 63 130
Character w e u s e a n i n f r -r o r m a l a p p
Milliseconds 110 216 177 102 178 86 104 49 104 111 65 151 105 113 198 434 183 104 88 130 103 111 208 130 126
Character o -o r o a c h s o y o u w i l l s e e h
Milliseconds 217 480 121 86 112 168 136 57 110 129 152 65 111 82 110 193 111 160 143 19 65 165 200 118 140
Character o w t h e y l e a d n a t u a -a r a l l t y
Milliseconds 87 87 62 114 88 82 86 112 85 86 1325 130 110 106 87 87 88 224 512 113 127 71 113 162 22
Character - -y -t y t o t h e m a i n i d e a o f
Milliseconds 89 361 142 138 222 129 82 46 128 463 104 89 63 66 86 89 128 288 128 103 168 89 127 64 106
Character t h i s c h a p t e r , t h e l i m i t .
Milliseconds 65 86 66 46 64 88 63 106 64 134 88 138 46 106 61 73 83 46 105 110 89 151 83 109 106
Character T h e i d e a o f a l i m i t p [ l a
Milliseconds 110 192 169 88 64 151 153 200 66 110 152 88 64 88 128 105 101 139 151 152 64 111 19 182 105
Character -a -l -[ l a y s a f o u n d a t i o n a l r o
Milliseconds 271 120 168 200 128 112 105 47 104 129 62 330 88 177 70 103 89 63 43 67 435 128 88 176 104
Character l e t h r o u g h o u t c a l c u l u s .
Milliseconds 183 106 48 81 88 110 89 38 126 67 121 62 67 87 130 189 129 87 530 182 153 127 114
WPM Timing
Seconds WPM
2.36 25.46
4.71 43.29
7.07 64.51
9.43 76.39
11.78 74.35
14.14 75.54
16.49 78.57
18.85 82.12
21.21 82.05
23.56 85.56
25.92 87.04
28.28 89.12
30.63 89.71
32.99 86.21
35.35 87.59
37.7 88.17
40.06 85.38
42.41 82.61
44.77 83.09
47.13 83.52
49.48 85.36
51.84 86.57
54.2 87.24
56.55 88.7
58.91 87.19
61.27 87.55
63.62 88.08
65.98 88.76
68.33 88.33
70.69 89.97
73.05 89.86
75.4 89.6
77.76 89.35
80.12 89.42
82.47 88.9
84.83 87.56
87.19 88.23
89.54 88.72
91.9 89.58
94.25 89.25
96.61 88.69
98.97 89.12
101.32 88.47
103.68 87.04
106.04 87.25
108.39 88.23
110.75 88.42
113.11 87.85
115.46 88.24
117.82 88