james (chilty14)

Race #6598

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Official speed 88.12 wpm (117.66 seconds elapsed during race)
Without ending ping 88.33 wpm (275 ms delay sending score to TypeRacer’s server)
Timerless 89.23 wpm (1,188 ms elapsed before first character typed; 116.20 seconds elapsed during race)
Timerless minus one 89.13 wpm, ignoring the first character typed
Race Start January 22, 2024 12:20:07am UTC
Race Finish January 22, 2024 12:22:05am UTC
Outcome No win (2 of 4)
Opponents 1. fasttyper_gg1 (97.86 wpm)
Accuracy 96.2%
Points 237.91
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 Calbclululus is a tolool that helps us understna dhoand how a chnage iange in one quanittity is related to a chnange in aotnothoerer. How does the speed fo of a falling objefct change as a function of time? How does the level foof water in a barrel hcchange as a functino oon of the amount of liquid poured into it? We seee change occurring in nearly everythignng we bosobserve in the world and universe, and powerful modern instruments help us see more and more. In this section we introudduce the ideas of average and instrantaneous rater s of change, and show that they are closely reallated to the slope of a curve at ta point P on the curve. We give precise developments of these imooportnaant 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 chpaapter, the limit, Th. The idea of la limit plays fa foundation al forrole throughout calculus.
Timing
Character C a l b -b c l u l -l -u -l u l u s i s a t o l
Milliseconds 1188 126 90 165 578 102 93 102 104 281 92 117 314 87 110 111 125 103 83 64 67 65 53 78 276
Character o -o -l o l t h a t h e l p s u s u n d e r
Milliseconds 179 222 96 265 159 72 41 95 50 27 42 87 113 48 145 71 55 116 90 55 139 169 35 115 50
Character s t n a d h o -o -h -d - -a -n a n d h o w a c
Milliseconds 53 97 88 25 115 9 96 63 210 221 103 106 113 100 199 77 112 27 110 48 62 59 83 44 86
Character h n a g e i -i - -e -g -a -n a n g e i n o n e
Milliseconds 56 151 47 108 61 50 106 230 107 99 111 98 91 122 128 50 37 53 175 33 51 558 58 65 68
Character q u a n i t -t -i t i t y i s r e l a t e d t
Milliseconds 139 94 278 175 134 106 286 73 112 84 64 76 52 210 69 47 133 17 162 57 174 47 158 15 137
Character o a c h n -n a n g e i n a o t -t -o n o t h
Milliseconds 36 34 338 348 102 93 122 356 72 86 61 49 45 108 68 35 81 93 81 249 139 177 68 30 71
Character o e r -r -e -o e r . H o w d o e s t h e s p
Milliseconds 9 63 43 349 96 90 114 37 103 78 299 143 90 74 196 62 55 50 44 207 55 78 55 198 152
Character e e d f o - -o -f o f a f a l l i n g o b
Milliseconds 80 122 129 55 112 41 254 208 88 106 203 64 56 82 535 69 77 31 92 193 358 116 65 273 390
Character j e f -f c t c h a n g e a s a f u n c t i
Milliseconds 109 103 49 440 80 168 55 168 83 52 80 60 54 61 221 219 189 71 412 103 89 150 124 231 62
Character o n o f t i m e ? H o w d o e s t h e
Milliseconds 45 47 51 147 101 68 143 46 45 66 528 224 253 65 153 136 91 81 67 55 72 39 77 47 67
Character l e v e l f o -o -f o f w a t e r i n a b
Milliseconds 110 129 179 11 111 14 247 70 306 78 193 23 117 67 97 78 129 49 83 128 54 68 68 96 109
Character a r r e l h c -c -h c h a n g e a s a f u n
Milliseconds 250 134 159 183 92 60 213 40 423 89 82 83 58 90 78 38 43 182 119 134 69 102 39 81 161
Character c t i n o o -o - -o -n o n o f t h e a m o u
Milliseconds 42 176 61 72 53 127 200 190 101 98 104 316 21 96 119 100 46 280 55 49 78 99 136 115 94
Character n t o f l i q u i d p o u r e d i n t o
Milliseconds 167 113 82 77 109 27 87 267 292 80 67 170 83 115 77 38 112 63 124 66 112 57 82 60 26
Character i t ? W e s e e e -e c h a n g e o c c u r
Milliseconds 158 76 531 227 423 114 142 104 62 131 226 296 96 58 120 53 62 81 52 53 83 171 122 93 64
Character r i n g i n n e a r l y e v e r y t h i g n
Milliseconds 330 136 56 53 78 318 46 76 122 76 74 72 47 140 13 89 163 121 46 213 252 84 83 234 155
Character -n -g n g w e b o s -s -o -b o b s e r v e i n
Milliseconds 236 84 168 19 126 38 112 38 204 66 132 295 92 95 208 81 168 104 133 187 49 73 170 69 101
Character t h e w o r l d a n d u n i v e r s e , a
Milliseconds 79 64 56 91 60 40 69 116 49 54 154 88 110 50 115 166 92 204 542 105 119 72 96 97 148
Character n d p o w e r f u l m o d e r n i n s t r u
Milliseconds 88 69 62 154 134 88 13 60 127 81 58 47 164 82 74 176 70 95 28 133 436 122 93 146 75
Character m e n t s h e l p u s s e e m o r e a n
Milliseconds 251 89 69 70 81 24 131 106 20 159 86 104 91 59 112 45 137 79 72 84 27 42 37 146 66
Character d m o r e . I n t h i s s e c t i o n w
Milliseconds 109 58 51 79 52 10 129 49 219 163 40 114 88 1130 72 46 280 35 339 231 36 71 10 35 202
Character e i n t r o u d -d -u d u c e t h e i d e a s
Milliseconds 73 110 86 57 339 133 89 151 275 197 77 160 100 63 63 109 113 47 51 89 149 100 184 94 87
Character o f a v e r a g e a n d i n s t r -r a n t
Milliseconds 108 70 111 34 388 113 138 62 103 103 45 43 114 57 78 55 94 61 25 87 242 325 83 116 89
Character a n e o u s r a t e r - -r s o f c h a n g
Milliseconds 465 83 409 139 88 110 234 305 74 116 88 74 262 299 93 121 32 132 99 63 294 119 97 59 108
Character e , a n d s h o w t h a t t h e y a r e
Milliseconds 42 92 77 56 83 98 76 142 47 74 68 131 244 67 92 25 52 152 96 88 45 43 238 99 82
Character c l o s e l y r e a l -l -a l a t e d t o t
Milliseconds 13 168 103 141 81 22 142 163 68 106 62 139 116 272 106 221 97 59 91 102 99 119 28 53 67
Character h e s l o p e o f a c u r v e a t t -t
Milliseconds 65 63 64 139 56 167 74 260 110 100 89 43 175 117 89 138 43 203 56 66 109 78 32 105 316
Character a p o i n t P o n t h e c u r v e . W
Milliseconds 86 21 154 69 104 171 171 84 239 191 185 74 52 78 80 81 87 133 154 55 189 16 90 72 274
Character e g i v e p r e c i s e d e v e l o p m e n
Milliseconds 40 135 241 114 149 106 279 341 72 33 185 177 83 33 87 330 152 98 78 8 161 40 138 116 92
Character t s o f t h e s e i m o o -o -o p o r t n a -a
Milliseconds 42 141 106 104 72 79 225 80 84 78 110 88 96 76 119 191 257 100 185 108 110 136 127 101 285
Character -n a n t c o n c e p t s i n t h e n e x t
Milliseconds 88 109 109 83 63 172 206 87 68 96 113 112 224 108 286 50 411 85 58 79 122 213 61 174 157
Character c h a p t e r , b u t f o r n o w w e
Milliseconds 77 239 76 143 89 104 194 52 109 54 665 110 74 56 122 70 108 40 113 57 42 60 213 24 107
Character u s e a n i n f o r m a l a p p r o a c h
Milliseconds 107 65 30 220 73 68 71 137 47 223 80 144 54 129 413 101 261 65 114 115 84 117 102 107 45
Character s o y o u w i l l s e e h o w t h e y
Milliseconds 205 40 86 157 60 74 18 63 54 45 111 403 62 56 125 80 107 53 42 96 264 64 82 80 42
Character l e a d n a t u r a l l y t o t h e m a i
Milliseconds 111 109 110 81 82 178 53 97 73 78 89 83 127 109 50 87 74 67 27 59 59 77 138 75 80
Character n i d e a o f t h i s c h p a -a -p a p t e
Milliseconds 49 70 83 115 132 52 105 100 158 14 463 60 63 42 88 125 83 137 128 259 72 127 98 86 99
Character r , t h e l i m i t , T h -h -T - -, . T h e
Milliseconds 84 61 28 175 35 131 90 139 89 79 89 111 118 85 121 76 183 99 116 85 218 70 275 76 113
Character i d e a o f l -l a l i m i t p l a y s
Milliseconds 104 108 54 118 90 143 196 76 72 78 370 99 102 109 118 115 62 93 68 122 40 137 85 102 122
Character f -f a f o u n d a t i o n - a l f o r -r -o -f
Milliseconds 319 364 68 42 98 47 89 105 119 98 80 103 15 45 97 410 92 80 66 70 82 94 202 95 113
Character r o l e t h r o u g h o u t c a l c u l u s .
Milliseconds 107 97 131 29 53 246 41 110 43 42 146 41 74 82 58 145 123 109 107 147 351 79 89 97 133
WPM Timing
Seconds WPM
2.35 20.4
4.71 40.8
7.06 61.19
9.41 63.74
11.77 61.19
14.12 63.74
16.47 66.29
18.83 67.57
21.18 71.96
23.53 69.86
25.88 69.54
28.24 71.82
30.59 74.14
32.94 75.4
35.3 75.13
37.65 74.9
40 76.79
42.36 78.19
44.71 78.1
47.06 79.81
49.42 79.16
51.77 79.51
54.12 80.04
56.48 81.38
58.83 83.43
61.18 83.36
63.54 83.67
65.89 83.6
68.24 84.05
70.59 83.63
72.95 83.57
75.3 84.94
77.65 85.15
80.01 85.64
82.36 85.96
84.71 85.84
87.07 86.42
89.42 85.75
91.77 85.52
94.13 85.8
96.48 86.44
98.83 86.57
101.19 87.4
103.54 88.66
105.89 88.39
108.25 88.24
110.6 88.1
112.95 88.18
115.3 87.84
117.66 88.12