Aaron (chowderkid)

Race #228

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Official speed 86.39 wpm (120.01 seconds elapsed during race)
Without ending ping 86.56 wpm (230 ms delay sending score to TypeRacer’s server)
Timerless 86.88 wpm (449 ms elapsed before first character typed; 119.34 seconds elapsed during race)
Timerless minus one 86.78 wpm, ignoring the first character typed
Race Start January 31, 2025 5:08:37pm UTC
Race Finish January 31, 2025 5:10:37pm UTC
Outcome No win (3 of 4)
Opponents 1. yohanworku (114.68 wpm)
Accuracy 97.7%
Points 233.26
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 Clalculus is a tool that helps us understand how a change in one quantity is related oto a cahhange in another. How does the speed of a falling object change as a function of time? How fodoes the level of water in a barrel change as a function of the amount of liquid poruured into intnto t? We see change occurring in nearly everyrthing we observe in the world and universe, and powerful modern instruments huelp us see more and more. In this secitonttion we introduce the ideas of average and instanetaneous rates of change, and shoe w that they are coclosely related to the slope of a curve as a t a point P on the curve. We give precise developments of these important ocnconcenpts int he ne the next chapter, but for now we use an informal approach so you will see how they lead naturally tio the main idea of this chapter, thie limit. The idea of a limit plays a foundational role throughout calculus.
Timing
Character C l -l a l c u l u s i s a t o o l t h a t
Milliseconds 449 277 308 90 110 114 302 225 204 130 79 169 78 97 81 118 88 80 139 182 121 81 120 105 52
Character h e l p s u s u n d e r s t a n d h o w
Milliseconds 147 118 466 118 66 101 116 159 107 120 118 85 63 137 47 160 159 163 137 56 118 163 83 149 72
Character a c h a n g e i n o n e q u a n t i t y
Milliseconds 104 78 95 80 88 119 81 84 99 116 62 166 119 82 103 52 149 119 101 99 102 148 35 255 182
Character i s r e l a t e d o -o t o a c a h -h -a h a
Milliseconds 186 126 95 290 93 77 126 162 123 97 117 210 359 98 80 177 67 133 78 185 160 264 120 224 121
Character n g e i n a n o t h e r . H o w d o e s
Milliseconds 80 143 57 24 120 55 160 107 81 99 124 92 84 70 141 138 157 139 123 118 120 123 108 141 79
Character t h e s p e e d o f a f a l l i n g o b
Milliseconds 123 76 110 91 105 92 110 135 86 51 122 78 123 105 100 124 142 75 164 183 81 74 123 102 102
Character j e c t c h a n g e a s a f u n c t i o n
Milliseconds 175 81 66 181 122 125 49 108 123 61 60 101 159 108 120 99 76 122 118 64 37 243 18 86 82
Character o f t i m e ? H o w f o -o -f d o e s t h
Milliseconds 198 156 65 122 78 78 68 86 246 166 161 163 133 89 200 79 283 120 118 126 58 184 54 151 48
Character e l e v e l o f w a t e r i n a b a r
Milliseconds 88 72 372 76 100 142 81 141 165 80 120 783 206 54 124 61 16 122 65 158 69 117 137 64 82
Character r e l c h a n g e a s a f u n c t i o n
Milliseconds 182 133 81 147 91 127 57 122 40 81 100 105 84 98 80 102 94 141 64 46 238 41 80 80 184
Character o f t h e a m o u n t o f l i q u i d p
Milliseconds 120 61 119 86 80 98 75 126 76 129 54 189 74 121 139 83 86 129 172 50 161 83 156 128 140
Character o r u -u -r u r e d i n t o i n t -t -n n t o -
Milliseconds 63 639 142 225 120 201 57 166 100 80 121 79 102 102 124 120 79 80 477 120 632 98 79 143 281
Character -o -t -n t ? W e s e e c h a n g e o c c u r
Milliseconds 145 160 162 120 317 223 204 221 104 336 82 176 86 123 83 80 129 57 64 90 127 137 145 137 104
Character r i n g i n n e a r l y e v e r y r -r t h i
Milliseconds 135 131 80 77 124 93 61 141 203 79 97 105 121 117 126 282 98 104 55 45 197 364 124 86 118
Character n g w e o b s e r v e i n t h e w o r l
Milliseconds 120 64 117 55 109 80 120 80 201 138 68 97 103 117 116 69 158 202 81 122 37 143 92 65 146
Character d a n d u n i v e r s e , a n d p o w e r
Milliseconds 80 131 71 130 41 145 102 61 141 119 143 57 186 79 93 132 134 81 72 118 184 118 54 60 183
Character f u l m o d e r n i n s t r u m e n t s h u
Milliseconds 205 85 174 141 158 40 40 107 156 127 177 124 55 211 172 80 37 161 143 123 66 174 126 137 263
Character -u e l p u s s e e m o r e a n d m o r e
Milliseconds 303 251 91 63 220 176 147 77 312 78 159 103 140 59 80 80 69 132 83 78 124 139 80 23 84
Character . I n t h i s s e c i t o n -n -o -t t -t -i t i
Milliseconds 136 158 146 181 171 131 55 45 113 104 59 83 224 199 20 126 50 656 143 158 283 216 122 128 118
Character o n w e i n t r o d u c e t h e i d e a s
Milliseconds 101 55 187 85 74 80 120 80 81 76 80 149 112 89 98 62 138 66 115 58 122 20 103 176 109
Character o f a v e r a g e a n d i n s t a n e -e t
Milliseconds 43 154 39 125 155 108 117 15 206 100 79 117 106 79 81 104 119 59 38 102 186 80 178 448 94
Character a n e o u s r a t e s o f c h a n g e , a
Milliseconds 672 137 158 145 58 103 121 118 202 100 284 226 60 159 55 81 145 59 107 123 57 62 104 114 120
Character n d s h o e - -e w t h a t t h e y a r e
Milliseconds 82 67 131 106 80 146 96 101 308 118 79 136 68 116 165 102 160 72 106 127 34 138 64 163 80
Character c o -o -c c l o s e l y r e l a t e d t o t
Milliseconds 74 142 201 319 122 541 83 142 64 80 80 162 78 304 123 54 145 168 156 63 94 147 42 141 57
Character h e s l o p e o f a c u r v e a s a
Milliseconds 106 102 53 146 83 163 73 162 65 137 66 90 129 77 258 260 169 197 75 92 161 97 42 139 77
Character - -a - -s t a p o i n t P o n t h e c u
Milliseconds 304 123 162 145 122 119 115 82 181 81 179 105 40 160 187 181 174 160 225 64 119 42 121 118 83
Character r v e . W e g i v e p r e c i s e d e v e
Milliseconds 95 121 79 137 167 121 160 79 161 79 120 81 38 186 103 55 201 108 136 84 121 386 93 151 94
Character l o p m e n t s o f t h e s e i m p o r t a
Milliseconds 80 146 80 185 92 125 59 190 74 143 57 120 106 81 433 185 55 81 118 89 165 60 75 64 199
Character n t o c n -n -c -o c o n c e n -n p t s i n t h
Milliseconds 126 105 70 168 16 166 291 143 144 136 121 84 21 85 104 558 230 78 198 106 154 81 184 13 151
Character e n e -e -n - -e -h - -t t h e n e x t c h a p
Milliseconds 12 123 157 36 168 176 161 170 165 133 459 186 102 84 97 60 140 36 214 73 121 144 63 139 119
Character t e r , b u t f o r n o w w e u s e a
Milliseconds 81 134 68 54 174 114 56 105 123 77 122 103 83 156 358 118 119 130 78 122 175 63 80 82 143
Character n i n f o r m a l a p p r o a c h s o y o
Milliseconds 80 161 121 66 91 106 55 120 107 157 184 228 53 162 101 119 57 107 106 142 140 81 162 106 80
Character u w i l l s e e h o w t h e y l e a d
Milliseconds 54 185 62 134 148 135 127 83 93 161 103 164 120 76 125 221 78 121 84 140 123 39 142 121 119
Character n a t u r a l l y t i -i o t h e m a i n i
Milliseconds 160 85 155 78 104 270 118 136 128 85 95 281 343 182 198 102 82 83 97 140 126 58 82 175 125
Character d e a o f t h i s c h a p t e r , t h i -i
Milliseconds 40 98 181 82 145 95 117 83 87 74 79 127 118 98 63 158 65 162 80 122 121 146 93 75 348
Character e l i m i t . T h e i d e a o f a l i
Milliseconds 141 98 224 192 156 135 143 118 161 186 186 117 39 122 35 82 222 81 137 45 120 85 102 159 199
Character m i t p l a y s a f o u n d a t i o n a l
Milliseconds 59 142 84 116 161 82 36 243 102 95 310 105 122 135 59 183 117 164 157 64 83 79 180 128 135
Character r o l e t h r o u g h o u t c a l c u l u s .
Milliseconds 120 82 182 83 73 79 120 81 43 64 118 64 158 60 105 141 98 180 97 131 94 239 327 122 126
WPM Timing
Seconds WPM
2.4 44.99
4.8 69.99
7.2 81.66
9.6 89.99
12 85.99
14.4 84.16
16.8 87.85
19.2 90.61
21.6 92.77
24 90.49
26.4 90.44
28.8 90.41
31.2 93.07
33.6 94.27
36 91.66
38.4 85.93
40.8 85.28
43.21 86.38
45.61 86.31
48.01 87.49
50.41 88.32
52.81 88.85
55.21 87.6
57.61 88.74
60.01 86.19
62.41 87.11
64.81 88.51
67.21 87.13
69.61 87.58
72.01 87.49
74.41 86.44
76.81 87.02
79.21 86.2
81.61 85.73
84.01 86.56
86.41 86.66
88.81 86.88
91.21 85.52
93.61 83.84
96.01 84.37
98.41 84.62
100.81 85.11
103.21 85.46
105.61 85.67
108.01 85.55
110.41 85.75
112.81 85.84
115.21 86.03
117.61 86.32
120.01 86.39