Lokii (the_godof_stories)

Race #83

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Official speed 85.46 wpm (121.32 seconds elapsed during race)
Without ending ping 85.75 wpm (404 ms delay sending score to TypeRacer’s server)
Timerless 89.16 wpm (4,631 ms elapsed before first character typed; 116.29 seconds elapsed during race)
Timerless minus one 89.06 wpm, ignoring the first character typed
Race Start December 1, 2023 10:45:46am UTC
Race Finish December 1, 2023 10:47:47am UTC
Outcome Win (1 of 4)
Opponents 2. kamal3772 (66.60 wpm)
Accuracy 98.4%
Points 230.74
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 took thl that helps us understand how a cnahange in one quanitity is reallated to a change in another. How does the speed of a falling object change as a funcatiotion of time? How does the leve of el of water in a barrel change as af function of the amount of liquid poured into it? We see change occurring in enearly eveyrrything we observe in the world and universe, and powerful modern instruments help use 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 lslop e of a curve at a point P on the curve. We give precise developments of these importatntnt 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 fuoundational roolle throughout calculus.
Timing
Character C a l c u l u s i s a t o o k t h -h -t - -k
Milliseconds 4631 256 113 106 178 188 208 100 85 73 126 70 150 91 94 64 172 156 88 59 142 259 163 282 182
Character l t h a t h e l p s u s u n d e r s t a n
Milliseconds 406 162 123 44 130 66 52 59 116 103 214 113 74 101 97 94 253 176 50 158 79 102 166 17 138
Character d h o w a c n a -a -n h a n g e i n o n e
Milliseconds 79 107 160 67 60 72 91 84 145 106 138 327 126 162 143 73 98 42 65 99 37 132 603 103 69
Character q u a n i -i t i t y i s r e a l -l -a l a t e
Milliseconds 57 165 33 186 42 218 568 103 89 117 128 115 104 78 88 127 62 56 121 414 134 229 56 100 43
Character d t o a c h a n g e i n a n o t h e r .
Milliseconds 226 96 272 101 101 107 108 128 86 192 86 156 34 65 232 57 131 99 77 58 108 119 69 100 198
Character H o w d o e s t h e s p e e d o f a
Milliseconds 354 187 199 118 85 132 105 111 38 174 95 136 53 61 119 114 109 189 261 84 182 107 59 131 92
Character f a l l i n g o b j e c t c h a n g e a s
Milliseconds 192 77 75 156 670 145 55 64 79 108 162 81 183 241 82 141 101 170 83 152 36 96 117 90 48
Character a f u n c a t i o -o -i -t -a t i o n o f t i m
Milliseconds 135 113 106 79 220 60 131 82 78 45 522 169 178 162 193 82 74 117 114 123 51 84 161 62 96
Character e ? H o w d o e s t h e l e v e o f -
Milliseconds 120 276 132 203 202 104 60 129 47 153 83 85 110 93 90 81 151 157 155 85 103 118 117 69 393
Character -f -o - -e e l o f w a t e r i n a b a r r
Milliseconds 159 169 300 190 532 170 129 134 36 111 119 69 105 109 121 84 229 89 188 184 91 144 159 89 173
Character e l c h a n g e a s a f -f f u n c t i o n
Milliseconds 105 143 80 120 102 131 111 98 54 87 81 97 56 144 144 533 193 201 111 217 65 199 64 52 54
Character o f t h e a m o u n t o f l i q u i d
Milliseconds 87 157 85 53 127 68 71 54 118 87 87 165 167 65 85 91 120 31 107 67 126 102 147 119 106
Character p o u r e d i n t o i t ? W e s e e c h
Milliseconds 160 83 421 93 70 210 81 300 58 125 105 109 229 156 257 146 249 220 75 123 78 166 73 195 112
Character a n g e o c c u r r i n g i n e -e n e a r l
Milliseconds 146 88 83 41 75 96 84 505 224 93 165 120 44 70 69 138 50 64 236 547 196 60 61 71 91
Character y e v e y r -r -y r y t h i n g w e o b s e r
Milliseconds 198 66 339 173 155 100 159 428 143 155 148 141 93 63 177 77 72 387 49 43 140 98 211 75 95
Character v e i n t h e w o r l d a n d u n i v e
Milliseconds 219 95 321 237 39 114 113 73 78 84 104 100 105 138 85 59 127 68 132 53 95 195 97 0 145
Character r s e , a n d p o w e r f u l m o d e r n
Milliseconds 145 37 208 272 192 340 77 111 53 87 85 68 48 72 189 28 179 123 111 64 60 160 59 32 138
Character i n s t r u m e n t s h e l p u s e -e s e e
Milliseconds 101 63 58 100 176 59 220 86 131 291 97 103 181 87 113 191 134 118 102 65 386 143 167 49 185
Character m o r e a n d m o r e . I n t h i s s
Milliseconds 78 114 60 68 32 65 203 60 109 62 82 61 72 46 94 149 197 251 162 130 60 50 83 59 146
Character e c t i o n w e i n t r o d u c e t h e i
Milliseconds 88 225 219 113 26 71 68 123 61 80 257 61 87 161 49 165 106 102 203 210 80 77 94 36 167
Character d e a s o f a v e r a g e a n d i n s t a
Milliseconds 60 185 103 111 69 147 163 48 194 78 166 78 78 124 51 80 270 73 73 57 210 140 11 513 154
Character n t a n e o u s r a t e s o f c h a n g e ,
Milliseconds 93 109 211 251 197 311 129 84 75 130 49 164 50 66 76 110 103 51 170 108 127 73 68 44 143
Character a n d s h o w t h a t t h e y a r e c
Milliseconds 126 163 71 98 282 188 96 63 40 117 98 335 391 113 69 124 57 90 118 72 94 48 73 37 222
Character l o s e l y r e l a t e d t o t h e l -l s
Milliseconds 78 167 46 45 118 183 39 106 37 96 149 77 70 143 87 167 80 106 86 74 86 95 30 416 98
Character l o p - e o f a c u r v e a t a p o
Milliseconds 96 179 143 190 359 89 81 146 79 44 124 100 172 168 134 243 69 73 155 371 42 119 99 165 72
Character i n t P o n t h e c u r v e . W e g i
Milliseconds 165 75 63 52 232 149 202 98 57 82 152 56 58 147 259 206 184 58 114 96 601 186 99 151 69
Character v e p r e c i s e d e v e l o p m e n t s o
Milliseconds 116 69 69 139 69 66 187 100 145 78 70 254 177 205 64 98 195 80 144 88 138 50 126 31 147
Character f t h e s e i m p o r t a t n t -t -n -t n t c
Milliseconds 143 86 142 86 40 85 144 52 138 157 36 480 97 204 100 132 52 139 302 167 143 221 78 71 171
Character o n c e p t s i n t h e n e x t c h a p t
Milliseconds 101 72 69 194 153 98 101 107 135 20 98 83 81 110 28 151 92 187 220 78 185 64 169 122 270
Character e r , b u t f o r n o w w e u s e a n
Milliseconds 115 94 57 125 329 66 131 65 173 85 91 74 95 45 88 76 161 60 76 154 70 54 117 152 88
Character i n f o r m a l a p p r o a c h s o y o u
Milliseconds 150 171 59 269 170 127 113 88 128 85 123 95 143 86 101 78 156 122 117 121 47 293 136 130 70
Character w i l l s e e h o w t h e y l e a d n
Milliseconds 49 93 85 171 175 65 81 67 190 84 143 90 57 80 373 91 120 69 122 90 379 67 445 85 143
Character a t u r a l l y t o t h e m a i n i d e a
Milliseconds 130 94 74 95 58 78 160 168 63 104 69 131 150 42 107 56 103 72 160 101 38 153 53 160 66
Character o f t h i s c h a p t e r , t h e l i m
Milliseconds 45 155 113 51 161 51 45 66 52 183 103 147 102 115 67 128 79 106 154 83 109 62 125 86 186
Character i t . T h e i d e a o f a l i m i t p
Milliseconds 61 143 116 130 223 163 63 53 122 56 169 87 93 192 65 56 84 111 78 77 172 87 83 70 83
Character l a y s a f u -u o u n d a t i o n a l r o o
Milliseconds 166 99 127 135 66 134 141 154 51 352 185 127 184 48 71 169 37 48 118 36 169 83 129 61 83
Character l -l -o l e t h r o u g h o u t c a l c u l u s
Milliseconds 250 284 126 182 73 88 98 75 120 65 83 85 118 153 70 62 40 177 72 59 217 65 154 172 116
Character .
Milliseconds 73
WPM Timing
Seconds WPM
2.43 0
4.85 2.47
7.28 28.03
9.71 37.09
12.13 50.45
14.56 53.58
16.98 55.11
19.41 58.11
21.84 62.09
24.26 65.78
26.69 66.99
29.12 67.18
31.54 67.72
33.97 68.18
36.4 66.93
38.82 68.62
41.25 69.24
43.68 71.99
46.1 72.1
48.53 72.7
50.95 73.01
53.38 71.94
55.81 72.46
58.23 73.98
60.66 75.57
63.09 76.09
65.51 77.11
67.94 78.07
70.37 78.79
72.79 79.13
75.22 79.61
77.64 79.75
80.07 81.23
82.5 80.73
84.92 81.11
87.35 81.47
89.78 81.67
92.2 82.12
94.63 81.29
97.06 81.97
99.48 82.39
101.91 82.78
104.34 83.27
106.76 83.29
109.19 83.97
111.61 84.72
114.04 85.23
116.47 85.21
118.89 85.19
121.32 85.46