autumn_tree (autumn_tree)

Race #2482

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Official speed 100.61 wpm (103.05 seconds elapsed during race)
Without ending ping 100.76 wpm (158 ms delay sending score to TypeRacer’s server)
Timerless 101.11 wpm (353 ms elapsed before first character typed; 102.54 seconds elapsed during race)
Timerless minus one 100.99 wpm, ignoring the first character typed
Race Start July 24, 2024 3:12:12am UTC
Race Finish July 24, 2024 3:13:55am UTC
Outcome No win (2 of 5)
Opponents 1. foca248 (122.05 wpm)
4. carloscarpa (87.38 wpm)
Accuracy 98.4%
Points 271.64
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 quantity is related to a change in another. How does the speedo of a falling object change as a function of time? How does the level of water in a barrel change sas a function of the amount of liquid pouredi into it? We see change occurring in nearly everything we observe in the world and universe, and powerful modreern instruments help us see more and more. In this section we introuduce the ideas of averange ge gge and instantaneous rates of change, and show that they are closely related to the slope of a curve tat a point P on the curve. WE ge give precise developments of these improortant concepts in the next chapter, but for now we use an inforamlmal approach so you will se e howt they lead naturally to the main idea of this chapter, the limit. The idea of a lmiimit plays a foundational role throughout calcuullus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 353 178 81 150 100 140 112 154 144 48 101 108 91 108 51 84 115 148 108 58 143 67 40 112 84
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 80 104 174 50 110 65 106 148 65 160 69 52 116 112 110 111 46 65 126 41 98 60 105 105 82
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 76 114 45 128 40 77 107 49 136 39 185 132 54 95 138 85 167 60 132 80 113 58 104 86 76
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 131 98 76 288 180 66 103 109 142 93 84 68 86 108 76 105 86 95 53 75 75 61 118 55 78
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 55 143 120 77 75 64 104 115 99 123 75 97 78 137 130 160 100 61 95 62 89 113 80 106 166
Character d o -o o f a f a l l i n g o b j e c t c
Milliseconds 152 307 293 61 134 75 99 89 100 196 67 69 130 154 82 64 94 47 127 145 80 136 179 124 114
Character h a n g e a s a f u n c t i o n o f t i
Milliseconds 81 89 84 58 66 125 81 116 116 80 121 86 88 113 64 198 59 69 88 84 126 137 165 39 87
Character m e ? H o w d o e s t h e l e v e l o f
Milliseconds 145 92 197 123 134 186 131 120 150 102 80 192 159 37 131 85 86 88 62 95 64 91 144 72 80
Character w a t e r i n a b a r r e l c h a n g e
Milliseconds 119 35 115 86 89 77 86 73 116 67 113 168 147 115 82 155 107 86 131 66 74 77 116 26 81
Character s -s a s a f u n c t i o n o f t h e a
Milliseconds 117 75 371 77 83 154 96 141 82 75 106 68 194 42 57 97 103 83 91 127 62 63 84 100 80
Character m o u n t o f l i q u i d p o u r e d i -i
Milliseconds 88 101 94 149 41 116 43 129 107 89 133 117 87 220 184 113 66 124 147 65 105 116 172 284 43
Character i n t o i t ? W e s e e c h a n g e o c
Milliseconds 171 81 67 133 88 96 130 539 279 147 246 122 76 60 149 178 73 88 66 111 24 73 75 89 109
Character c u r r i n g i n n e a r l y e v e r y t h
Milliseconds 137 212 295 169 161 122 68 140 104 124 74 75 112 106 57 85 131 93 165 136 62 152 105 154 60
Character i n g w e o b s e r v e i n t h e w o r
Milliseconds 74 110 40 164 0 100 171 94 151 84 82 392 199 62 173 84 107 75 55 104 100 75 90 45 89
Character l d a n d u n i v e r s e , a n d p o w e
Milliseconds 109 129 109 88 93 123 88 56 109 136 28 92 135 119 126 162 164 118 102 103 95 134 142 60 71
Character r f u l m o d r e -e -r e r n i n s t r u m e n
Milliseconds 154 177 48 155 79 64 137 43 195 45 255 100 57 66 110 117 88 108 90 94 159 65 178 66 107
Character t s h e l p u s s e e m o r e a n d m
Milliseconds 56 129 96 84 86 86 163 97 83 44 315 69 156 158 100 66 160 21 70 121 113 57 109 58 56
Character o r e . I n t h i s s e c t i o n w e i
Milliseconds 137 15 80 76 142 100 167 131 54 59 145 54 97 75 60 214 198 63 51 141 49 35 77 151 120
Character n t r o u -u d u c e t h e i d e a s o f a
Milliseconds 117 42 169 59 190 257 65 99 104 101 131 64 79 60 100 76 111 63 106 133 123 87 418 135 110
Character v e r a n g e - -e -g g e - -e -g g -g -n g e a n
Milliseconds 88 92 108 106 83 96 83 58 296 146 124 113 63 108 185 128 134 141 195 137 80 93 149 83 70
Character d i n s t a n t a n e o u s r a t e s o f
Milliseconds 99 78 110 104 59 117 98 68 120 236 115 114 241 163 66 113 92 91 98 67 180 91 100 58 94
Character c h a n g e , a n d s h o w t h a t t h e
Milliseconds 119 113 84 119 111 65 99 103 90 74 89 81 240 46 91 73 111 89 149 81 61 106 71 37 148
Character y a r e c l o s e l y r e l a t e d t o
Milliseconds 51 102 61 55 101 88 159 98 145 53 81 84 138 83 57 64 140 160 61 119 136 113 112 80 119
Character t h e s l o p e o f a c u r v e t -t a t
Milliseconds 23 96 73 114 105 53 125 120 50 104 135 164 105 458 100 96 131 102 486 106 139 219 268 61 49
Character a p o i n t P o n t h e c u r v e .
Milliseconds 152 71 129 171 169 183 85 83 79 128 81 183 131 82 97 92 150 72 96 71 124 168 53 83 114
Character W E g -g - -E e g i v e p r e c i s e d e v
Milliseconds 101 68 187 96 214 143 121 62 102 197 86 153 79 130 55 101 76 175 96 121 225 215 71 122 130
Character e l o p m e n t s o f t h e s e i m p r o -o
Milliseconds 56 88 151 103 200 74 99 75 154 138 83 63 150 60 73 152 336 66 132 94 127 96 122 4 417
Character -r o r t a n t c o n c e p t s i n t h e n
Milliseconds 137 168 77 253 130 98 93 151 143 101 129 116 154 105 102 126 117 40 136 171 106 139 93 127 78
Character e x t c h a p t e r , b u t f o r n o w
Milliseconds 56 142 211 136 79 73 91 110 40 87 80 83 92 340 115 69 118 109 62 127 87 43 161 67 122
Character w e u s e a n i n f o r a m l -l -m -a m a l
Milliseconds 128 125 111 60 97 112 171 93 109 95 107 100 62 141 35 367 14 158 276 115 130 132 102 99 95
Character a p p r o a c h s o y o u w i l l s e -
Milliseconds 257 100 122 98 82 109 96 110 89 90 80 87 100 92 69 141 93 146 138 121 62 11 100 169 254
Character e h o w t -t t h e y l e a d n a t u r a l
Milliseconds 93 160 53 118 102 252 319 63 41 119 94 98 75 118 70 105 61 137 15 169 58 97 93 104 49
Character l y t o t h e m a i n i d e a o f t h
Milliseconds 134 165 89 54 98 101 29 142 96 121 97 61 84 122 89 131 154 132 182 154 119 82 121 68 74
Character i s c h a p t e r , t h e l i m i t . T h
Milliseconds 117 29 96 74 143 145 111 42 132 77 81 141 74 95 56 83 83 110 126 70 100 105 201 105 123
Character e i d e a o f a l m i -i -m i m i t p l a
Milliseconds 84 91 79 317 95 93 115 121 103 134 81 123 69 229 78 262 103 153 97 65 102 110 27 147 144
Character y s a f o u n d a t i o n a l r o l e t h
Milliseconds 85 128 130 124 122 175 61 414 159 26 103 102 54 88 103 111 60 118 30 113 134 88 85 52 51
Character r o u g h o u t c a l c u u l -l -u l u s .
Milliseconds 139 85 117 90 100 139 103 47 147 84 106 24 167 19 572 82 252 113 170 78 102 110
WPM Timing
Seconds WPM
2.06 93.16
4.12 107.71
6.18 116.45
8.24 114.99
10.31 117.61
12.37 118.39
14.43 113.12
16.49 113.54
18.55 113.21
20.61 112.37
22.67 112.74
24.73 112.08
26.79 113.31
28.85 111.46
30.92 108.3
32.98 108.08
35.04 107.88
37.1 107.71
39.16 108.79
41.22 108.3
43.28 107.3
45.34 107.45
47.4 108.35
49.46 107.71
51.53 107.6
53.59 104.58
55.65 103.94
57.71 103.97
59.77 104.8
61.83 105.38
63.89 105.18
65.95 104.07
68.01 104.1
70.07 102.75
72.14 102.81
74.2 102.7
76.26 101.5
78.32 101.58
80.38 101.82
82.44 101.89
84.5 100.97
86.56 100.92
88.62 100.74
90.69 101.23
92.75 101.44
94.81 101.64
96.87 101.09
98.93 100.92
100.99 101.48
103.05 100.61