Ray (gilzea)

Race #930

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Official speed 92.57 wpm (112.00 seconds elapsed during race)
Without ending ping 92.66 wpm (115 ms delay sending score to TypeRacer’s server)
Timerless 93.59 wpm (1,104 ms elapsed before first character typed; 110.78 seconds elapsed during race)
Timerless minus one 93.48 wpm, ignoring the first character typed
Race Start October 9, 2023 5:23:29am UTC
Race Finish October 9, 2023 5:25:21am UTC
Outcome No win (3 of 3)
Opponents 1. miket349 (113.66 wpm)
2. dvorak_king (109.48 wpm)
Accuracy 95.8%
Points 249.95
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 too ll that helps us understand how a changei in one quantity is ralelated to a chagne in nge in another . How does the spped eed of a falling obejeject change as a function of time? How doe sths the level of water ina a bareerel chang ee as a function of the lamamount of liquid poured into it> ?? We see chang ee occuirirring in nearly everything we observe i nthn the world and universe, and powerful modern instruments help us see more and more. In this esection we introduce the ideas of average and instantaneous rates of chagennge, and show that they are closely raelated to the slpope or f a curve aatt a ponint P on the curve. We give precise deveoplopments of these important ceoooncepts in the next chapter, but for now we use an infromaorma apl appraoach so you weiill se he how they lead naturally to the main iaddea o fhtf this chapter, the limit. The idea of a limit plays a foundational roelle thoroughout calcfuulus.
Timing
Character C a l c u l u s i s a t o o l -l - l t h
Milliseconds 1104 98 122 132 104 87 356 109 58 74 106 43 349 81 172 77 111 129 57 326 129 109 93 57 82
Character a t h e l p s u s u n d e r s t a n d h o
Milliseconds 9 64 57 116 62 162 50 156 99 122 81 57 129 172 79 137 51 133 34 308 99 93 69 79 87
Character w a c h a n g e i - -i i n o n e q u a
Milliseconds 58 77 69 106 91 42 98 104 106 40 74 49 397 106 108 71 102 0 116 72 84 80 312 51 149
Character n t i t y i s r a l -l -a e l a t e d t o a
Milliseconds 75 117 76 81 154 76 106 66 67 95 94 45 278 137 90 41 93 62 73 142 38 139 82 101 41
Character c h a g n e i n - -n -i - -e -n -g n g e i n
Milliseconds 114 73 77 52 96 19 49 39 64 77 21 241 130 144 131 145 122 104 154 69 45 56 50 92 36
Character a n o t h e r - . H o w d o e s t h e s
Milliseconds 93 58 109 65 73 42 50 145 316 141 72 133 99 148 102 260 82 105 79 21 192 97 34 115 74
Character p p e d - -d -e -p e e d o f a f a l l i n g
Milliseconds 177 152 85 164 19 230 146 147 120 28 157 203 101 78 64 87 56 77 121 56 71 109 127 82 61
Character o b e j e -e -j -e j e c t c h a n g e a s a
Milliseconds 87 56 301 156 108 167 206 147 98 129 42 101 148 64 126 39 44 113 49 28 91 96 73 87 77
Character f u n c t i o n o f t i m e ? H o w d o
Milliseconds 75 82 57 151 49 188 0 64 60 71 128 69 79 95 58 167 178 186 40 240 96 137 99 104 98
Character e s t h -h -t -s - s t h e l e v e l o f w
Milliseconds 89 90 13 203 0 283 126 141 131 44 111 93 62 70 80 53 81 117 94 67 78 128 84 59 79
Character a t e r i n a - -a a b a r e e -e -e r e l
Milliseconds 77 66 99 58 26 80 75 91 96 326 144 74 107 136 257 212 71 139 149 312 131 62 43 79 38
Character c h a n g e -e - e a s a f u n c t i o n
Milliseconds 123 93 35 131 9 61 11 464 113 117 81 216 96 77 97 41 101 133 137 42 173 0 98 38 11
Character o f t h e l a m -m -a -l a m o u n t o f l i
Milliseconds 126 94 70 101 77 81 59 13 72 77 228 133 123 86 32 135 84 140 69 52 91 114 54 106 103
Character q u i d p o u r e d i n t o i t > ? -? - ->
Milliseconds 182 76 77 147 79 187 139 89 84 57 160 44 101 144 146 43 66 96 64 329 8 32 605 270 148
Character ? W e s e e c h a n g e -e - e o c c u i
Milliseconds 321 253 507 172 92 83 70 140 36 121 34 67 86 55 0 49 379 138 88 50 119 59 120 69 124
Character r i -i -r -i r r i n g i n n e a r l y e v e r
Milliseconds 78 135 222 143 115 64 128 42 104 97 12 133 59 50 206 91 86 22 79 113 26 153 248 88 44
Character y t h i n g w e o b s e r v e i n t h -h -t
Milliseconds 65 109 62 108 106 88 71 95 45 103 144 73 179 90 36 185 116 80 135 79 46 118 130 196 146
Character -n - n t h e w o r l d a n d u n i v e r s
Milliseconds 149 126 119 119 46 90 54 63 93 81 95 73 159 105 67 207 91 84 106 135 110 63 152 79 39
Character e , a n d p o w e r f u l m o d e r n i n
Milliseconds 116 55 87 114 115 76 58 78 149 97 32 51 169 27 87 70 198 110 59 156 26 106 41 112 59
Character s t r u m e n t s h e l p u s s e e m o r
Milliseconds 120 63 148 68 161 78 102 60 83 58 240 181 95 191 62 110 85 54 147 76 185 56 65 129 25
Character e a n d m o r e . I n t h i s e -e s e c
Milliseconds 37 93 106 49 91 50 84 109 61 25 152 38 182 97 93 83 99 78 32 121 52 301 45 117 164
Character t i o n w e i n t r o d u c e t h e i d e
Milliseconds 156 19 48 81 82 102 355 129 108 52 43 136 64 145 42 149 66 68 175 63 88 57 81 97 168
Character a s o f a v e r a g e a n d i n s t a n t
Milliseconds 160 123 5 136 92 66 112 122 141 46 82 83 72 17 180 27 191 271 118 64 43 128 58 73 134
Character a n e o u s r a t e s o f c h a g e n -n -e -g
Milliseconds 370 106 154 61 44 126 45 121 98 107 60 104 26 115 68 145 74 77 46 81 95 0 383 130 116
Character n g e , a n d s h o w t h a t t h e y a
Milliseconds 108 140 48 110 53 76 76 68 62 264 64 104 72 105 83 51 49 70 48 174 79 107 69 37 50
Character r e c l o s e l y r a -a e l a t e d t o t
Milliseconds 72 54 46 138 80 153 71 31 79 123 11 112 91 422 93 66 68 65 89 105 66 103 135 138 16
Character h e s l p -p o p e o r - -r f a c u r v e
Milliseconds 514 136 51 77 69 74 326 193 90 113 25 139 134 78 310 132 112 58 54 84 51 118 69 147 166
Character a a t -t -a t a p o n -n i n t P o n t h
Milliseconds 10 68 340 149 298 145 109 145 57 90 181 122 150 337 91 77 43 65 194 204 207 73 43 61 70
Character e c u r v e . W e g i v e p r e c i s e
Milliseconds 67 74 109 50 117 223 68 83 76 497 179 85 125 139 59 103 59 101 97 256 183 139 13 146 59
Character d e v e o p -p -o l o p m e n t s o f t h e s e
Milliseconds 228 151 96 62 115 167 342 127 165 177 39 180 84 89 43 202 98 138 65 82 190 187 239 121 97
Character i m p o r t a n t c e o -o o -o -e o n c e p t s
Milliseconds 37 123 116 56 138 56 165 11 170 250 113 151 85 44 277 205 259 130 82 72 78 147 75 102 67
Character i n t h e n e x t c h a p t e r , b u t
Milliseconds 13 101 58 50 23 105 30 99 95 50 157 118 92 116 74 278 114 119 91 70 64 57 168 65 115
Character f o r n o w w e u s e a n i n f r o m
Milliseconds 268 56 439 87 52 69 80 271 89 127 91 81 128 22 71 57 87 18 112 155 79 119 145 26 95
Character a -a -m -o -r o r m a a p -p -a - l a p p r a -a o a
Milliseconds 75 263 125 132 119 152 124 87 80 105 242 15 225 131 119 131 77 84 112 118 68 88 358 140 24
Character c h s o y o u w e i -i -e i l l s e h -h -
Milliseconds 80 98 53 141 78 74 139 106 41 8 101 56 12 385 306 136 100 144 49 68 39 123 193 307 135
Character e h o w t h e y l e a d n a t u r a l l y
Milliseconds 91 21 71 52 104 59 190 71 78 82 30 107 41 69 107 26 87 118 86 151 71 44 64 133 138
Character t o t h e m a i n i a d -d -a d e a o f
Milliseconds 52 65 50 68 79 32 58 68 156 50 87 51 60 106 138 0 396 140 68 116 64 18 119 129 23
Character h t -t -h -f - f t h i s c h a p t e r , t h e
Milliseconds 212 16 215 148 143 121 61 97 86 36 58 58 102 66 109 23 98 56 127 16 96 45 156 56 69
Character l i m i t . T h e i d e a o f a l i m
Milliseconds 48 54 95 121 304 106 102 44 290 87 63 28 109 89 147 81 9 97 96 17 87 50 89 95 164
Character i t p l a y s a f o u n d a t i o n a l r
Milliseconds 113 55 82 69 142 47 122 98 65 131 93 215 63 77 166 30 109 65 46 86 62 61 90 81 228
Character o e l -l -e l e t h o -o r o u g h o u t c a l c
Milliseconds 41 135 20 390 301 126 99 48 103 109 124 308 81 315 94 89 71 73 65 80 64 126 83 70 113
Character f u -u -f u l u s .
Milliseconds 0 63 553 193 104 93 102 81 51
WPM Timing
Seconds WPM
2.24 48.21
4.48 69.64
6.72 82.14
8.96 85.71
11.2 88.93
13.44 82.14
15.68 85.71
17.92 83.03
20.16 84.52
22.4 87.32
24.64 89.61
26.88 89.28
29.12 87.77
31.36 86.48
33.6 87.86
35.84 89.4
38.08 86.97
40.32 86.31
42.56 85.99
44.8 87.86
47.04 86.73
49.28 88.15
51.52 90.14
53.76 91.29
56 92.14
58.24 92.92
60.48 93.85
62.72 94.51
64.96 94.21
67.2 95.89
69.44 95.56
71.68 94.59
73.92 93.34
76.16 93.75
78.4 93.52
80.64 92.71
82.88 92.81
85.12 92.48
87.36 92.86
89.6 93.35
91.84 91.72
94.08 91.96
96.32 90.95
98.56 92.29
100.8 91.78
103.04 92.47
105.28 93.01
107.52 93.75
109.76 92.71
112 92.57