Sebastian (sebastianwatson1)

Race #40

View Pit Stop page for race #40 by sebastianwatson1 — Ghost race

View profile for Sebastian (sebastianwatson1)

Official speed 74.04 wpm (140.03 seconds elapsed during race)
Without ending ping 74.28 wpm (286 ms delay sending score to TypeRacer’s server)
Timerless 74.46 wpm (333 ms elapsed before first character typed; 139.41 seconds elapsed during race)
Timerless minus one 74.37 wpm, ignoring the first character typed
Race Start May 10, 2025 10:42:50am UTC
Race Finish May 10, 2025 10:45:10am UTC
Outcome No win (4 of 5)
Accuracy 95.8%
Points 199.92
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 change in one qyuanuantity is realtedarerrelated to a change in another. How does the seedeed peed of a faliling object change as a function of time> H? How does the level of water in a barrel change as a functinn on of the amount of liquid opoured into it> / ? we sWe see change occuring iring in nearly everything we obsere inrve int he wn the world and universe and , and powerful modern insturmenruments help us see more and ormore. In this section we intoruroduce the ideas of aveeragrage and instantaneous rtes oates of change, and show that they are closelt reallosely related toht the slope of a curve a at a point P on the curve. We give prcieecise dvelo=evelopments of these improtantortant concepts in the next chapter, but for now we yse anause an infomrarmal approach so you wllilll se see how they elad ead naturally to the main idea of this chaoterpter, tjhe lhe limit. The idea of a limit plays a foundational role thoughroughout calculs.us/.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 333 166 107 110 149 167 183 91 92 118 100 66 99 35 1346 733 333 181 153 76 104 41 65 62 100
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 115 33 117 108 45 147 116 67 205 44 34 87 113 139 128 99 41 113 152 61 101 22 114 81 85
Character c h a n g e i n o n e q y u a n -n -a -u -y u a
Milliseconds 80 102 55 62 65 88 48 150 120 145 465 146 88 46 397 150 16 73 78 682 132 122 295 236 96
Character n t i t y i s r e a l t e d a r -r -e -a -l -t -e -d
Milliseconds 66 136 97 52 138 132 128 67 99 67 85 81 0 108 82 119 440 215 832 0 0 0 0 0 0
Character -r e -e r -r -a r e l a t e d t o a c h a n g e
Milliseconds 0 84 284 186 135 127 83 73 77 122 97 115 100 115 85 19 163 39 96 97 70 71 65 62 98
Character i n a n o t h e r . H o w d o e s t h e
Milliseconds 35 197 170 132 148 105 150 66 81 65 68 104 118 192 106 31 148 86 63 99 82 99 84 88 64
Character s e e d -d -e -e e e d - -d -e -e p e e d o f a
Milliseconds 84 99 148 135 152 212 135 100 119 145 105 113 236 129 121 113 183 98 119 132 82 107 69 107 216
Character f a l i -i l i n g o b j e c t c h a n g e
Milliseconds 119 98 84 99 166 517 188 161 116 50 85 102 130 151 32 86 167 96 100 83 83 51 66 83 84
Character a s a f u n c t i o n o f t i m e > H -H
Milliseconds 99 155 134 94 99 84 481 135 99 150 82 117 105 118 109 57 110 54 95 102 19 278 185 181 219
Character - -> ? H o w d o e s t h e l e v e l o f
Milliseconds 134 99 249 236 244 119 83 72 96 32 84 116 98 57 93 100 50 117 50 84 82 67 133 99 66
Character w a t e r i n a b a r r e l c h a n g e
Milliseconds 84 52 98 71 94 70 80 85 364 184 99 52 134 197 235 133 149 83 173 93 101 51 100 52 45
Character a s a f u n c t i n -n n - -n o n o f t
Milliseconds 99 84 82 85 52 118 97 167 138 64 167 83 194 467 173 134 297 113 182 117 117 207 0 138 79
Character h e a m o u n t o f l i q u i d o -o p o u
Milliseconds 65 93 56 98 51 146 172 126 82 70 142 45 83 114 134 65 120 121 79 88 239 458 491 187 168
Character r e d i n t o i t > - -> / - -/ ? w e s
Milliseconds 50 106 102 76 113 129 106 0 138 192 51 227 184 247 113 204 236 295 103 200 215 122 96 100 54
Character -s - -e -w W e s e e c h a n g e o c c u r i n
Milliseconds 326 136 123 91 122 194 120 101 235 152 141 86 98 49 85 32 84 99 237 79 117 182 118 117 135
Character g i -i - -g -n -i r i n g i n n e a r l y e v
Milliseconds 63 90 64 298 131 135 119 113 49 137 113 66 83 89 101 126 105 63 84 64 100 66 151 119 164
Character e r y t h i n g w e o b s e r e i n -n -i - -e
Milliseconds 83 67 67 134 66 55 115 182 179 50 83 67 121 132 96 118 65 271 101 128 116 281 125 143 117
Character -r r v e i n t h e w -w -n -t - -h -e - n t h e
Milliseconds 150 710 124 98 66 117 118 133 0 132 37 129 64 203 1494 0 0 0 0 0 124 158 0 119 49
Character w o r l d a n d u n i v e r s e a n d -
Milliseconds 101 81 68 39 112 71 126 68 56 60 85 116 99 117 0 99 84 88 95 731 155 63 98 51 230
Character -d -n -a - , a n d p o w e r f u l m o d e r n
Milliseconds 136 133 114 101 199 165 101 51 87 63 133 116 50 105 161 184 76 144 133 136 94 115 183 99 101
Character i n s t u r m e n -n -e -m -r -u r u m e n t s h e
Milliseconds 121 78 117 32 101 102 37 145 99 52 364 136 140 123 135 115 115 155 64 83 65 108 76 116 100
Character l p u s s e e m o r e a n d o r -r -o m o
Milliseconds 50 125 141 122 111 39 94 99 121 97 133 115 0 56 60 119 48 84 48 192 228 138 110 189 131
Character r e . I n t h i s s e c t i o n w e i n
Milliseconds 186 0 56 106 169 138 406 0 698 132 207 0 51 126 121 153 47 145 88 130 31 84 267 166 102
Character t o r u -u -r -o r o d u c e t h e i d e a s o
Milliseconds 60 110 29 214 298 124 117 76 101 99 434 82 102 90 112 48 90 66 98 38 91 86 82 98 83
Character f a v e e r a g -g -a -r -e r a g e a n d i n s
Milliseconds 67 115 82 140 59 69 101 98 98 276 124 135 230 85 114 101 83 98 53 100 21 113 99 120 0
Character t a n t a n e o u s r t e s o -t -e -s - -o a t e
Milliseconds 129 103 56 106 399 120 185 100 150 97 88 92 186 81 85 106 109 698 0 0 0 0 88 132 81
Character s o f c h a n g e , a n d s h o w t h a
Milliseconds 198 183 118 101 102 130 115 40 98 63 83 69 117 68 101 49 80 99 84 98 68 87 97 98 33
Character t t h e y a r e c l o s e l t r e a l -l -o
Milliseconds 83 67 90 82 61 99 123 61 68 54 79 181 116 101 50 133 84 81 84 84 67 74 33 748 0
Character -s -e -l -t - -r -e -a -l l o s e l y r e l a t e d t
Milliseconds 0 0 0 0 0 0 0 0 0 126 116 23 175 143 78 129 100 75 126 82 156 95 83 115 117
Character o h t -t -h t h e s l o p e o f a c u r v
Milliseconds 67 348 119 247 102 147 52 100 66 84 73 83 120 132 41 100 86 79 67 83 50 40 142 74 143
Character e a a -a - t a p o i n t P o n t h e
Milliseconds 105 194 83 83 100 285 98 123 109 433 119 149 165 140 458 85 106 193 166 119 121 115 52 79 97
Character c u r v e . W e g i v e p r c i e -e -i -c e
Milliseconds 52 104 96 52 161 101 50 121 131 80 201 0 68 100 464 122 129 65 166 118 99 298 134 117 222
Character c i s e d v e l o = -= -e -l -o -v e v e l o p m e n
Milliseconds 112 118 96 90 33 129 166 0 134 133 279 119 402 0 0 132 246 104 116 33 489 0 413 61 84
Character t s o f t h e s e i m p r o t a n t -t -n -a -t
Milliseconds 40 113 79 106 160 0 219 97 116 83 87 113 120 104 126 99 20 131 83 103 51 244 140 144 124
Character -o -r o r t a n t c o n c e p t s i n t h e
Milliseconds 115 109 170 64 138 112 41 61 85 114 82 182 67 150 83 87 69 110 100 88 129 68 65 89 119
Character n e x t c h a p t e r , b u t f o r n o w
Milliseconds 57 33 153 121 92 101 71 79 99 55 117 85 60 132 151 99 51 116 55 61 84 51 137 89 57
Character w e y s e a n -n a $u -s -e - -a -a s e a n i
Milliseconds 116 154 109 108 181 78 68 67 98 72 226 200 986 0 0 0 0 0 69 96 49 100 51 135 97
Character n f o m r a -a -r -m r m a l a p p r o a c h s o
Milliseconds 99 51 86 96 20 156 444 132 104 43 133 87 79 117 117 50 121 166 110 100 100 100 168 121 48
Character y o u w l l -l -l i l l l s e -e -s - -l s e e
Milliseconds 138 95 30 165 150 84 198 85 333 103 248 135 118 113 85 29 182 167 123 128 116 206 61 105 129
Character h o w t h e y e l a d - -e -a -d e a d n a
Milliseconds 48 150 117 25 124 85 81 87 63 141 117 27 32 117 165 200 1563 0 0 59 60 87 66 163 69
Character t u r a l l y t o t h e m a i n i d e a
Milliseconds 82 113 84 99 117 117 68 164 121 46 171 50 111 40 118 115 61 83 105 113 115 34 115 66 119
Character o f t h i s c h a o t e r -r -e -t -o p t e r ,
Milliseconds 98 105 77 68 99 116 58 109 105 151 110 149 70 120 110 173 143 134 101 165 16 122 78 287 0
Character t j h e l -l - -e -h -j h e l i m i t . T h e
Milliseconds 72 79 0 69 62 131 247 120 121 98 177 294 73 100 133 149 118 148 84 100 141 110 87 120 26
Character i d e a o f a l i m i t p l a y s a f
Milliseconds 91 58 99 51 105 110 83 69 58 97 145 322 0 99 110 190 0 94 53 185 76 80 73 47 85
Character o u n d a t i o n a l r o l e t h o u g h -h -g
Milliseconds 321 169 112 62 135 114 77 144 95 133 34 111 56 56 129 39 119 73 103 150 153 111 49 257 143
Character -u -o r o u g h o u t c a l c u l s . -. -s u s / -/
Milliseconds 134 125 131 91 168 122 0 195 146 67 107 143 152 0 511 134 166 267 105 360 100 217 100 121 701
Character .
Milliseconds 426
WPM Timing
Seconds WPM
2.8 59.99
5.6 66.41
8.4 85.69
11.2 69.63
14 65.13
16.8 68.56
19.6 74.68
22.41 69.63
25.21 70.94
28.01 74.13
30.81 73.23
33.61 76.05
36.41 77.45
39.21 78.04
42.01 77.41
44.81 74.45
47.61 74.35
50.41 74.03
53.21 74.42
56.01 71.77
58.81 71.82
61.61 70.31
64.41 71.72
67.22 71.77
70.02 72.33
72.82 72.84
75.62 73.16
78.42 73.45
81.22 72.4
84.02 74.41
86.82 73.53
89.62 73.91
92.42 74.27
95.22 74.86
98.02 74.31
100.82 73.55
103.62 73.65
106.42 74.19
109.23 75.59
112.03 74.98
114.83 74.93
117.63 73.96
120.43 73.74
123.23 74.2
126.03 74.46
128.83 74.05
131.63 74.94
134.43 75.61
137.23 75.29
140.03 74.04