grah (dumpsterman)

Race #1806

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Official speed 91.77 wpm (112.98 seconds elapsed during race)
Without ending ping 91.93 wpm (196 ms delay sending score to TypeRacer’s server)
Timerless 92.30 wpm (453 ms elapsed before first character typed; 112.33 seconds elapsed during race)
Timerless minus one 92.19 wpm, ignoring the first character typed
Race Start October 26, 2023 7:32:27pm UTC
Race Finish October 26, 2023 7:34:20pm UTC
Outcome Win (1 of 5)
Opponents 2. dystaco2 (83.03 wpm)
Accuracy 96.0%
Points 247.77
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 Calclululus is a toll ol that help sus us understand how a change in one quantity is realalated to a change in another. How does the speed of a falling object changea s as a function of time? How does the level owff water in a barrleel hangechange as sa funcitontiontttion of the amount of liquid poured into it ? wWe see change occuring rring in nearly eeveverything we observe in the world and universe, and powerful morddre ern instruimenments help us see more and more. In this section we introduce the idea oss of average iaaand instantenaneous rates of change, and show that they are closely related to the slop e oe of a curve at a poinbt tt P on the curve. We give recisprecisd e developments of these inpormportant concpeepts in the next chapter, but for now we use an informal approach so you will see how they lead noaturally to the maainin idea of this chaptehr, rr, the limimt The . The ideaae of a limi t play s ao s a foundational role through out calcullus.us.
Timing
Character C a l c l u l -l -u -l u l u s i s a t o l l
Milliseconds 453 130 122 68 395 99 169 201 114 424 197 41 134 138 46 92 112 82 95 87 169 63 104 125 112
Character - -l -l o l t h a t h e l p s u -u -s - s u s
Milliseconds 186 106 112 361 150 83 66 99 65 32 51 35 99 70 49 114 0 104 365 116 99 119 70 76 171
Character u n d e r s t a n d h o w a c h a n g e
Milliseconds 201 52 117 61 117 53 100 94 70 38 97 130 36 68 36 95 134 48 153 79 54 82 68 65 37
Character i n o n e q u a n t i t y i s r e a l a -a
Milliseconds 69 48 51 79 31 71 50 266 85 99 103 209 109 75 115 38 66 322 143 154 17 117 30 131 257
Character -l -a l a t e d t o a c h a n g e i n a n
Milliseconds 97 83 183 83 51 15 122 66 85 60 36 99 69 112 66 71 48 84 87 30 52 50 64 385 69
Character o t h e r . H o w d o e s t h e s p e e d
Milliseconds 28 71 51 64 66 84 35 195 305 96 63 102 86 52 48 66 54 94 21 104 232 80 83 114 119
Character o f a f a l l i n g o b j e c t c h a n
Milliseconds 84 46 71 52 98 79 354 17 79 135 71 266 129 70 78 115 141 68 117 143 42 313 84 33 97
Character g e a s - -s - -a a s a f u n c t i o n
Milliseconds 68 78 105 15 152 112 185 107 96 104 129 56 64 26 115 55 100 68 84 119 133 10 20 42 78
Character o f t i m e ? H o w d o e s t h e l e v
Milliseconds 32 65 83 51 65 32 58 307 76 295 197 102 35 127 40 100 50 21 98 62 37 83 102 98 145
Character e l o w f -f -w f w a t e r i n a b a r r
Milliseconds 52 68 102 61 117 218 251 115 98 108 85 46 62 93 97 13 88 29 102 86 99 65 36 82 120
Character l e -e -l e l h a n g e -e -g -n -a -h c h a n g e a
Milliseconds 81 0 379 101 117 101 99 192 58 83 57 98 131 77 134 74 81 168 81 44 68 72 85 98 19
Character s s -s a f u n c i t o n -n -o -t t i o n -n -o -i -t
Milliseconds 64 64 73 381 117 99 95 92 96 84 118 32 17 66 285 96 106 122 111 26 39 213 103 201 93
Character t -t t -t -i t i o n o f t h e a m o u n t o
Milliseconds 214 261 211 247 101 100 103 15 63 89 60 85 67 251 86 69 27 124 80 56 82 180 131 87 17
Character f l i q u i d p o u r e d i n t o i t -
Milliseconds 133 81 270 50 149 84 49 76 66 77 14 212 90 80 114 37 69 29 80 72 71 99 78 285 450
Character ? w -w W e s e e c h a n g e o c c u r i n
Milliseconds 553 112 404 367 199 183 149 42 59 133 77 108 66 95 41 73 42 63 67 133 95 91 83 67 18
Character g - -g -n r -r -i r i n g i n n e a r l y e e
Milliseconds 95 0 271 97 105 142 383 172 195 106 30 68 32 35 63 89 95 72 57 26 30 81 33 570 87
Character v e -e -v -e v e r y t h i n g w e o b s e r v e
Milliseconds 144 123 298 98 117 109 158 30 156 101 109 72 111 0 120 195 68 70 65 80 56 55 113 120 113
Character i n t h e w o r l d a n d u n i v e r s
Milliseconds 97 72 24 91 30 89 67 163 29 141 77 98 83 43 92 82 94 0 105 127 100 128 146 75 130
Character e , a n d p o w e r f u l m o r d -d -r d r e
Milliseconds 54 98 46 121 66 100 35 78 0 65 21 42 152 70 0 99 91 26 98 59 280 84 100 127 55
Character - -e -r e r n i n s t r u i m e n -n -e -m -i m e n
Milliseconds 264 220 109 118 118 51 101 86 50 43 91 61 108 91 0 108 83 97 196 105 101 85 393 73 85
Character t s h e l p u s s e e m o r e a n d m
Milliseconds 91 31 41 100 120 59 57 43 91 111 72 92 39 146 79 43 40 42 32 55 111 38 96 51 36
Character o r e . I n t h i s s e c t i o n w e i
Milliseconds 31 63 21 327 89 152 150 77 71 85 86 88 92 84 69 210 153 41 9 35 100 30 71 84 66
Character n t r o d u c e t h e i d e a o s -s -o - s
Milliseconds 32 86 127 35 134 85 67 67 62 72 75 66 38 49 81 119 35 85 63 53 281 103 85 109 50
Character o f a v e r a g e i a -a a -a -i a n d i n s t
Milliseconds 64 76 96 154 126 118 72 50 128 25 58 89 104 207 161 213 118 55 129 180 74 75 37 94 86
Character a n t e n -n -e a n e o u s r a t e s o f c h
Milliseconds 78 102 90 265 162 218 370 150 115 216 137 31 100 119 101 90 89 44 85 22 96 87 84 201 76
Character a n g e , a n d s h o w t h a t t h e y
Milliseconds 61 54 84 35 124 45 40 97 52 66 78 68 15 64 25 108 101 51 32 73 94 54 85 43 23
Character a r e c l o s e l y r e l a t e d t o t h
Milliseconds 103 28 19 77 108 68 111 52 37 116 83 33 85 35 138 78 78 48 256 159 39 112 100 5 215
Character e s l o p e o -o - -e - e o f a c u r v
Milliseconds 351 87 101 55 126 78 35 13 141 174 208 100 116 93 134 84 39 82 34 115 50 288 111 72 148
Character e a t a p o i n b t - -t t -t -b t P o n
Milliseconds 98 35 151 100 81 99 62 243 32 50 41 0 28 95 397 102 183 354 98 61 100 330 212 144 50
Character t h e c u r v e . W e g i v e r e c i s
Milliseconds 319 126 63 94 20 128 42 94 265 96 123 65 155 164 94 68 70 98 50 53 152 62 137 109 55
Character -s -i -c -e -r p r e c i s d - -d e d e v e l o p m
Milliseconds 130 109 107 104 198 233 74 48 201 100 49 101 101 330 118 85 80 135 143 175 68 130 132 14 153
Character e n t s o f t h e s e i n p o r -r -o -p -n m p
Milliseconds 71 175 0 97 125 208 171 36 178 44 102 76 87 27 117 51 156 14 131 165 100 108 109 272 27
Character o r t a n t c o n c p e -e -p e p t s i n t h
Milliseconds 37 113 124 68 59 89 95 368 39 26 130 51 121 395 540 203 39 222 88 46 134 35 99 15 132
Character e n e x t c h a p t e r , b u t f o r n
Milliseconds 31 59 56 45 148 268 113 95 70 85 32 132 120 69 84 46 110 22 67 79 89 37 90 131 0
Character o w w e u s e a n i n f o r m a l a p p
Milliseconds 27 76 54 470 68 50 68 91 41 215 113 86 164 54 44 72 115 643 121 70 103 94 37 76 120
Character r o a c h s o y o u w i l l s e e h o w
Milliseconds 84 118 105 58 92 28 102 62 53 100 22 31 86 69 80 129 119 47 64 42 127 90 19 62 12
Character t h e y l e a d n o -o a t u r a l l y t o
Milliseconds 120 33 88 90 17 69 31 41 97 96 84 231 5 321 200 53 187 55 107 0 98 81 80 98 48
Character t h e m a a i n -n -i -a i n i d e a o f t
Milliseconds 58 30 70 84 24 35 122 303 276 62 186 109 193 238 45 69 69 128 124 31 65 45 71 53 85
Character h i s c h a p t e h r , - -, -r r -r -h r , t h
Milliseconds 75 16 35 83 100 73 116 99 84 106 11 34 167 83 201 98 103 166 335 114 52 127 66 72 53
Character e l i m i m -m t T h e - -e -h -T - . T h e
Milliseconds 114 13 103 92 70 140 0 509 119 201 102 87 97 35 150 113 85 102 94 228 114 95 70 98 54
Character i d e a a e -e -a o f a l i m i - t p l a
Milliseconds 46 101 126 116 106 33 354 113 133 67 65 56 64 180 167 81 32 355 311 400 73 82 71 13 49
Character y s a o - -o -a - -s - s a f o u n d a t i
Milliseconds 117 77 21 114 61 98 8 336 80 126 128 137 133 119 79 80 87 87 55 23 83 105 43 67 64
Character o n a l r o l e t h r o u g h - o u t c a
Milliseconds 9 31 85 77 309 93 55 273 155 72 76 54 87 47 17 92 42 53 413 230 22 77 83 186 67
Character l c u l l u s . -. -s -u -l u s .
Milliseconds 94 112 100 100 159 7 114 103 299 129 97 148 159 117 99
WPM Timing
Seconds WPM
2.26 21.24
4.52 42.49
6.78 58.42
9.04 83.64
11.3 82.85
13.56 89.4
15.82 94.84
18.08 96.26
20.34 95
22.6 98.78
24.86 99.94
27.11 96.04
29.37 95.19
31.63 88.39
33.89 90.28
36.15 91.61
38.41 88.41
40.67 87.63
42.93 87.49
45.19 88.16
47.45 90.28
49.71 91.01
51.97 89.36
54.23 92.5
56.49 93.89
58.75 94.57
61.01 94.22
63.27 92.94
65.53 95.41
67.79 97.01
70.05 96.28
72.31 95.76
74.57 94.95
76.83 94.19
79.08 93.01
81.34 93.53
83.6 92.87
85.86 92.52
88.12 93.28
90.38 93.34
92.64 95.08
94.9 95.72
97.16 95.22
99.42 94.63
101.68 93.94
103.94 93.28
106.2 92.88
108.46 92.72
110.72 92.67
112.98 91.77