Jason (duckyboi)

Race #491

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Official speed 108.06 wpm (95.95 seconds elapsed during race)
Without ending ping 108.23 wpm (148 ms delay sending score to TypeRacer’s server)
Timerless 108.55 wpm (287 ms elapsed before first character typed; 95.51 seconds elapsed during race)
Timerless minus one 108.43 wpm, ignoring the first character typed
Race Start January 11, 2024 10:26:45pm UTC
Race Finish January 11, 2024 10:28:21pm UTC
Outcome No win (2 of 4)
Opponents 1. dudepc (108.65 wpm)
3. aelius_raellla (91.92 wpm)
Accuracy 97.3%
Points 291.75
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 Caclulculus is a tolol that helps us understand how a change in one quantity is related to a change in another. How does the spped eed of a falling obeject change a ss a function of time? How fdoes the level of water in a barrel change a s as funcitontion of the amount of liquid poured into it? We see change occurring in nerlarlyg everything we obnserve in the world and undiverse, and powerful modern instruments help us see more and more. In this section we introduce the ideas of average and sinstagntaneous rates of change, and show that they are closely trelated to the slope of a curve at a point P on the curve. We give prescise developments of these oimimportant comncepts in the next chapter, but for now we use an infrormal approaceh so you will se ee he how they lead naturally to the main idea of this chaptrer, the limit. The idea of a limit plays a foundational role throughout acalculus.
Timing
Character C a c l u -u -l -c l c u l u s i s a t o l -l o
Milliseconds 287 148 94 133 77 284 106 106 271 106 104 81 111 61 143 106 29 91 86 35 111 41 148 401 188
Character l t h a t h e l p s u s u n d e r s t a n
Milliseconds 151 93 104 79 49 56 60 145 66 157 70 105 98 142 59 89 145 48 50 86 86 90 90 142 26
Character d h o w a c h a n g e i n o n e q u a
Milliseconds 95 86 172 36 47 128 66 59 120 81 76 76 75 37 66 113 62 121 100 75 46 99 184 88 122
Character n t i t y i s r e l a t e d t o a c h a
Milliseconds 92 70 101 114 45 191 126 42 92 232 78 69 125 56 81 80 28 130 48 71 155 130 134 85 77
Character n g e i n a n o t h e r . H o w d o e s
Milliseconds 70 62 53 57 113 62 125 30 108 64 17 103 20 64 77 77 163 197 34 119 104 78 50 51 35
Character t h e s p p e d - -d -e -p e e d o f a f a
Milliseconds 120 46 52 94 100 54 131 39 96 105 264 103 114 106 95 170 67 67 108 55 69 67 68 146 57
Character l l i n g o b e -e j e c t c h a n g e a s
Milliseconds 96 142 84 56 57 85 128 257 95 311 186 64 27 179 65 124 37 89 83 81 42 50 113 25 62
Character -s - s a f u n c t i o n o f t i m e ? H
Milliseconds 289 95 84 127 63 70 185 82 59 55 168 31 57 36 119 134 70 78 106 39 67 73 186 204 181
Character o w f -f d o e s t h e l e v e l o f w a
Milliseconds 210 61 143 423 311 203 305 80 35 63 119 28 67 73 96 42 90 52 66 105 103 45 79 100 62
Character t e r i n a b a r r e l c h a n g e a
Milliseconds 108 160 87 122 111 72 110 91 33 149 107 80 186 66 85 97 226 55 92 54 72 54 68 96 83
Character - s a s - -s f u n c i t o n -n -o -t -i t i o n
Milliseconds 241 67 116 72 77 0 317 124 281 119 69 62 43 188 0 72 70 340 113 173 108 54 198 56 16
Character o f t h e a m o u n t o f l i q u i d
Milliseconds 148 109 12 89 63 48 59 97 70 71 65 46 68 16 116 109 40 82 117 44 159 91 60 87 92
Character p o u r e d i n t o i t ? W e s e e c h
Milliseconds 156 178 32 105 103 72 67 123 50 45 93 63 152 41 222 193 119 213 115 63 36 124 95 93 74
Character a n g e o c c u r r i n g i n n e r l -l -r a
Milliseconds 44 130 55 44 64 266 77 121 91 88 132 85 30 80 67 104 67 102 135 30 494 20 413 89 67
Character r l y g - -g e v e r y t h i n g w e o b n
Milliseconds 31 118 53 161 159 272 89 189 71 59 86 58 107 251 108 55 87 79 76 108 13 95 131 56 24
Character -n s e r v e i n t h e w o r l d a n d u
Milliseconds 305 213 276 43 178 77 83 116 57 120 40 103 26 118 70 66 42 156 126 54 83 69 34 111 106
Character n d -d i v e r s e , a n d p o w e r f u l m
Milliseconds 49 80 269 151 35 92 80 39 180 344 91 310 147 75 92 136 75 30 24 59 142 71 121 106 127
Character o d e r n i n s t r u m e n t s h e l p u s
Milliseconds 38 56 95 91 85 104 195 28 260 78 61 70 131 89 87 70 62 89 180 79 66 47 131 97 33
Character s e e m o r e a n d m o r e . I n t h
Milliseconds 113 153 92 235 86 177 30 25 35 95 69 62 41 107 137 48 39 42 116 66 198 164 139 65 85
Character i s s e c t i o n w e i n t r o d u c e t
Milliseconds 35 66 96 112 31 76 178 46 60 24 166 120 27 114 334 88 136 58 162 174 87 110 28 107 109
Character h e i d e a s o f a v e r a g e a n d s
Milliseconds 19 104 38 122 67 31 59 86 109 115 47 80 158 170 61 113 105 106 43 47 123 66 65 52 121
Character -s i n s t a g -g n t a n e o u s r a t e s o f
Milliseconds 278 170 40 26 32 120 160 319 189 76 123 457 120 92 31 69 89 127 69 143 57 39 83 138 27
Character c h a n g e , a n d s h o w t h a t t h
Milliseconds 91 114 20 79 92 94 48 19 76 110 43 74 56 117 34 32 135 46 176 76 47 64 65 89 54
Character e y a r e c l o s e l y t -t r e l a t e d
Milliseconds 38 82 209 31 71 51 71 215 91 128 51 34 98 49 203 55 331 70 33 125 71 62 83 70 50
Character t o t h e s l o p e o f a c u r v e a
Milliseconds 107 37 75 88 42 71 123 121 49 138 86 92 72 102 42 98 53 56 108 118 31 180 71 145 120
Character t a p o i n t P o n t h e c u r v e .
Milliseconds 155 84 105 48 388 67 54 194 50 94 160 166 119 38 130 79 49 68 97 115 86 70 117 67 72
Character W e g i v e p r e s -s c i s e d e v e l o
Milliseconds 61 209 227 101 197 69 91 43 55 136 49 51 79 246 97 134 36 35 110 108 64 125 51 0 168
Character p m e n t s o f t h e s e o i m -m -i -o i m p
Milliseconds 53 110 74 92 50 136 120 204 100 60 94 37 53 134 44 132 170 0 101 239 112 114 198 67 105
Character o r t a n t c o m -m n c e p t s i n t h e
Milliseconds 66 35 24 174 58 162 140 169 98 61 359 179 106 31 87 113 112 84 125 58 116 0 113 55 109
Character n e x t c h a p t e r , b u t f o r n o w
Milliseconds 117 61 150 122 69 128 52 122 34 89 91 60 92 87 394 46 30 132 64 70 76 56 177 49 83
Character w e u s e a n i n f r -r o r m a l a p p
Milliseconds 120 79 57 121 103 39 29 101 80 71 73 416 66 56 287 278 202 76 83 125 185 103 189 74 118
Character r o a c e -e h s o y o u w i l l s e e -e
Milliseconds 71 203 60 109 255 443 175 152 178 38 104 68 58 59 71 63 83 43 107 65 80 37 95 87 231
Character - -e e h -h - e h o w t h e y l e a d n a
Milliseconds 117 109 13 198 155 224 89 94 184 150 42 55 87 47 79 69 85 168 114 43 63 90 63 153 50
Character t u r a l l y t o t h e m a i n i d e a
Milliseconds 71 130 98 0 106 120 60 191 29 83 88 86 103 73 82 139 27 106 66 118 100 43 12 43 70
Character o f t h i s c h a p t r -r e r , t h e l i
Milliseconds 90 26 77 101 45 56 19 135 105 46 114 42 276 10 273 227 70 87 48 209 33 376 201 255 62
Character m i t . T h e i d e a o f a l i m i t
Milliseconds 53 81 49 142 56 163 187 48 126 116 23 40 54 81 106 17 104 67 66 145 59 40 92 67 121
Character p l a y s a f o u n d a t i o n a l r o l e
Milliseconds 89 34 36 117 81 105 44 93 100 84 30 23 106 71 117 77 47 44 385 126 73 184 64 131 99
Character t h r o u g h o u t a -a c a l c u l u s .
Milliseconds 87 115 56 102 33 51 97 41 71 44 63 103 104 261 61 33 105 90 71 116 149 16 169
WPM Timing
Seconds WPM
1.92 43.77
3.84 68.79
5.76 89.63
7.68 101.62
9.59 105.06
11.51 112.56
13.43 109.88
15.35 110.22
17.27 107.7
19.19 108.19
21.11 102.9
23.03 105.27
24.95 106.31
26.87 104.08
28.78 101.72
30.7 103.96
32.62 104.47
34.54 105.96
36.46 102.36
38.38 102.56
40.3 102.44
42.22 102.05
44.14 103.05
46.05 103.7
47.97 105.06
49.89 105.59
51.81 106.31
53.73 106.09
55.65 105.23
57.57 106.93
59.49 107.92
61.41 108.26
63.32 108.58
65.24 108.7
67.16 108.45
69.08 109.09
71 108.34
72.92 107.63
74.84 107.91
76.76 108.65
78.68 107.53
80.6 106.61
82.51 105.73
84.43 106.02
86.35 107
88.27 106.99
90.19 106.58
92.11 107.74
94.03 107.97
95.95 108.06