chainship (chainship)

Race #8

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Official speed 95.14 wpm (108.98 seconds elapsed during race)
Without ending ping 95.36 wpm (253 ms delay sending score to TypeRacer’s server)
Timerless 95.74 wpm (428 ms elapsed before first character typed; 108.30 seconds elapsed during race)
Timerless minus one 95.63 wpm, ignoring the first character typed
Race Start January 3, 2024 4:49:59pm UTC
Race Finish January 3, 2024 4:51:48pm UTC
Outcome Win (1 of 4)
Opponents 2. ashwin1994 (84.10 wpm)
Accuracy 98.7%
Points 256.87
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 i n 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 barerel change as a function of the amount of liquid poured into it? We see change occuring ring in nearly everything we observe in the world and universe, and powerful modern instruments help us see more and more. I n this section we introduce the ideas of average and instantaneous rates of change, and show that they arw e ce 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 chaotpter, fbut for mnow we use an informal approach so wiyou will see how they lwaead naturally to the main idea of this chapter, the limit. The idea of a limit plays a foundational role throughout calccuulus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 428 407 141 128 148 331 188 85 61 126 83 70 97 296 83 104 135 147 62 73 121 65 184 65 123
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 96 123 61 113 82 106 100 68 167 52 135 142 142 199 139 160 48 109 62 142 85 69 142 97 94
Character c h a n g e i - n o n e q u a n t i t y
Milliseconds 94 124 91 79 129 182 33 249 98 132 296 408 144 94 62 121 86 122 119 119 135 129 418 142 88
Character i s r e l a t e d t o a c h a n g e i n
Milliseconds 189 49 93 101 167 103 70 182 152 142 89 89 20 119 105 112 111 71 90 88 114 165 70 137 97
Character a n o t h e r . H o w d o e s t h e s p
Milliseconds 0 92 86 59 93 86 92 149 176 28 262 133 126 73 108 68 96 121 69 113 64 108 63 128 51
Character e e d o f a f a l l i n g o b j e c t c
Milliseconds 125 122 139 49 118 88 78 389 138 464 215 34 122 166 66 58 101 99 91 149 96 167 180 58 135
Character h a n g e a s a f u n c t i o n o f t i
Milliseconds 66 126 65 133 178 78 112 156 76 139 172 123 107 117 116 185 64 83 139 97 98 47 107 86 64
Character m e ? H o w d o e s t h e l e v e l o f
Milliseconds 72 90 235 94 284 140 113 61 119 51 119 133 77 84 75 119 20 114 122 65 129 73 116 133 110
Character w a t e r i n a b a r e -e r e l c h a n
Milliseconds 81 391 153 76 113 159 62 130 64 63 91 119 235 398 198 213 454 492 177 61 90 166 98 128 84
Character g e a s a f u n c t i o n o f t h e a
Milliseconds 136 150 74 109 132 73 97 97 132 51 100 52 172 84 83 105 104 104 70 107 66 83 123 24 175
Character m o u n t o f l i q u i d p o u r e d i n
Milliseconds 0 143 76 190 71 79 122 92 52 110 177 105 159 64 85 84 151 99 231 103 139 133 42 119 92
Character t o i t ? W e s e e c h a n g e o c c u
Milliseconds 64 136 64 150 86 303 109 177 209 96 86 154 135 104 99 57 135 51 161 169 53 148 72 141 112
Character r i n g - -g -n -i r i n g i n n e a r l y e
Milliseconds 107 102 34 105 96 257 126 135 151 141 192 94 118 88 145 69 81 132 42 191 298 231 74 183 233
Character v e r y t h i n g w e o b s e r v e i n t
Milliseconds 73 83 141 48 121 47 78 99 51 95 107 140 109 121 96 50 143 181 134 123 90 174 98 0 138
Character h e w o r l d a n d u n i v e r s e , a n
Milliseconds 89 94 103 58 101 89 98 80 81 91 72 102 47 151 74 115 47 155 111 161 164 104 51 323 41
Character d p o w e r f u l m o d e r n i n s t r u m
Milliseconds 140 82 137 92 57 171 156 157 71 116 99 114 125 77 190 142 73 87 146 33 101 171 160 64 101
Character e n t s h e l p u s s e e m o r e a n d
Milliseconds 146 117 68 171 65 153 115 181 119 126 196 102 132 210 178 124 110 135 55 69 149 62 95 68 92
Character m o r e . I - n t h i s s e c t i o n
Milliseconds 69 155 66 34 186 91 64 188 280 240 152 49 79 100 58 178 96 94 153 169 181 64 67 123 82
Character w e i n t r o d u c e t h e i d e a s o f
Milliseconds 40 176 43 106 94 100 144 51 107 78 84 206 91 88 86 107 45 75 86 149 140 145 37 94 99
Character a v e r a g e a n d i n s t a n t a n e o u
Milliseconds 71 127 98 108 132 192 77 99 104 74 91 130 40 120 86 45 159 210 136 150 492 106 159 90 79
Character s r a t e s o f c h a n g e , a n d s h
Milliseconds 189 97 152 176 53 122 154 30 103 125 67 123 39 168 84 135 175 90 44 96 74 103 36 135 41
Character o w t h a t t h e y a r w - e c -c - -e -w
Milliseconds 74 119 101 95 71 166 205 49 94 88 119 64 62 128 200 219 32 245 151 103 133 273 116 133 119
Character e c l o s e l y r e l a t e d t o t h e
Milliseconds 172 295 203 43 104 49 151 153 223 118 153 199 144 46 185 170 262 30 375 60 87 98 70 146 66
Character s l o p e o f a c u r v e a t a p o i
Milliseconds 135 82 224 66 111 88 110 84 105 84 74 119 75 126 175 110 94 119 197 86 133 42 171 83 210
Character n t P o n t h e c u r v e . W e g i v
Milliseconds 79 110 139 192 164 131 69 89 138 67 119 54 142 87 133 124 90 224 100 142 258 111 129 136 101
Character e p r e c i s e d e v e l o p m e n t s o f
Milliseconds 182 89 177 56 167 157 103 108 165 111 135 168 186 193 52 169 82 165 141 60 105 264 78 120 107
Character t h e s e i m p o r t a n t c o n c e p t s
Milliseconds 47 336 85 107 134 156 81 163 60 188 55 74 135 200 57 150 41 140 84 46 54 186 93 82 181
Character i n t h e n e x t c h a o t -t -o p t e r ,
Milliseconds 86 174 45 50 367 114 106 65 136 56 161 189 67 106 74 119 75 123 208 148 99 97 154 143 88
Character f -f b u t f o r m -m n o w w e u s e a
Milliseconds 66 102 316 139 68 60 87 155 40 107 90 163 331 140 126 100 70 102 148 81 73 84 159 43 137
Character n i n f o r m a l a p p r o a c h s o w i
Milliseconds 61 103 124 47 74 97 102 112 126 127 67 152 80 166 100 65 205 178 62 101 119 37 131 73 111
Character -i -w y o u w i l l s e e h o w t h e y l
Milliseconds 270 148 105 108 126 92 65 88 173 164 85 83 144 117 69 149 93 65 118 67 72 117 75 41 383
Character w a -a -w e a d n a t u r a l l y t o t h e
Milliseconds 104 185 294 136 52 222 178 56 117 105 198 66 112 185 67 134 99 86 111 57 83 145 110 118 72
Character m a i n i d e a o f t h i s c h a p t e r
Milliseconds 169 84 67 57 75 122 37 165 130 175 177 97 95 89 73 88 91 49 117 106 89 51 166 169 127
Character , t h e l i m i t . T h e i d e a o f
Milliseconds 109 65 122 35 171 37 145 181 63 151 46 192 61 263 197 137 71 112 39 150 162 40 123 83 69
Character a l i m i t p l a y s a f o u n d a t i o
Milliseconds 142 42 182 132 82 133 62 87 181 33 104 146 91 110 65 103 117 49 66 148 63 163 191 66 49
Character n a l r o l e t h r o u g h o u t c a l c c
Milliseconds 120 74 96 46 122 47 181 81 89 197 96 120 35 114 101 130 180 103 206 66 161 163 44 165 169
Character u -u -c u l u s .
Milliseconds 371 160 128 48 196 157 80 142
WPM Timing
Seconds WPM
2.18 60.56
4.36 85.34
6.54 91.76
8.72 86.72
10.9 86.99
13.08 91.76
15.26 95.17
17.44 93.6
19.62 94.82
21.8 96.35
23.97 97.6
26.15 96.81
28.33 92.33
30.51 94.38
32.69 96.17
34.87 95.66
37.05 96.19
39.23 93.9
41.41 94.18
43.59 95.25
45.77 95.7
47.95 96.1
50.13 95.99
52.31 96.58
54.49 96.24
56.67 97.2
58.85 97.68
61.03 97.14
63.21 97.97
65.39 96.53
67.57 95.37
69.74 95.15
71.92 95.6
74.1 95.7
76.28 95.49
78.46 95.28
80.64 95.38
82.82 95.63
85 95.01
87.18 94.56
89.36 95.21
91.54 94.78
93.72 94.62
95.9 94.35
98.08 94.82
100.26 95.27
102.44 95.36
104.62 95.78
106.8 96.07
108.98 95.14