Bacteria (fragile_duck)

Race #12

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Official speed 84.54 wpm (122.64 seconds elapsed during race)
Without ending ping 84.66 wpm (177 ms delay sending score to TypeRacer’s server)
Timerless 85.25 wpm (838 ms elapsed before first character typed; 121.63 seconds elapsed during race)
Timerless minus one 85.15 wpm, ignoring the first character typed
Race Start February 19, 2024 1:28:54pm UTC
Race Finish February 19, 2024 1:30:57pm UTC
Outcome No win (2 of 3)
Opponents 1. mookiekulit (95.37 wpm)
Accuracy 97.5%
Points 228.25
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 CAlcualculus i s ats a tollool that helps us undrerstand how a changei n on in one quantity is lrelated to a changei n an in another. HOw ow 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 acoumount of liquid oupoured into it? We see change occurring innearlin nearly everything we observe in the world and universe, and powerful modern intrstruments help us see more and more. In this seciontion we introduce the ideas od f 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 thseeese important concepts in the next chapter, but for now we use nan informal approach so you will see how they lead nartuturally to the main idea of this chapter, the limit. The idea of a limite pl playes a foundational role througouthout calculus.
Timing
Character C A l c u -u -c -l -A a l c u l u s i s a t -t -a
Milliseconds 838 78 93 218 124 672 155 157 127 171 75 157 110 188 187 155 78 266 111 77 123 62 111 424 171
Character - -s - s a t o l l o -o -l -l o l t h a t h e
Milliseconds 155 156 139 126 96 111 139 96 76 251 154 286 233 158 294 251 171 77 94 95 35 73 66 61 109
Character l p s u s u n d r -r e r s t a n d h o w a
Milliseconds 46 173 108 95 79 93 110 299 186 124 187 452 62 94 204 76 125 16 142 62 77 78 47 45 109
Character c h a n g e i n o n -n -o - -n - -i i n o n
Milliseconds 77 110 93 94 95 77 76 63 47 46 111 125 64 845 170 159 171 157 156 297 156 63 144 501 45
Character e q u a n t i t y i s l -l r e l a t e d t
Milliseconds 80 64 144 79 93 79 144 33 124 96 112 157 175 78 175 457 140 46 77 141 78 108 146 91 107
Character o a c h a n g e i n a n -n -a - -n - -i i n
Milliseconds 65 63 72 117 93 108 109 78 78 94 123 0 31 142 78 92 424 295 172 173 158 177 236 158 76
Character a n o t h e r . H O w - -w -O o w d o e s
Milliseconds 107 126 92 62 64 77 82 73 93 143 233 31 171 126 437 172 125 202 110 93 124 94 78 108 47
Character t h e s p e e d o f a f a l l i n g o b
Milliseconds 126 49 105 62 311 110 109 156 172 78 47 108 94 81 188 515 47 451 156 47 124 63 34 91 109
Character j e c t c h a n g e a s a f u n c t i o n
Milliseconds 93 92 186 125 64 173 77 47 155 47 92 93 110 93 94 94 80 232 107 220 127 122 80 64 61
Character o f t i m e ? H o w d o e s t h e l e
Milliseconds 94 95 92 62 125 93 95 142 766 188 1154 204 125 140 156 235 107 94 77 126 50 106 62 108 361
Character v e l o f w a t e r i n a b a r r e l
Milliseconds 124 107 79 110 79 201 141 110 94 94 125 92 79 48 78 62 76 126 265 111 139 157 61 141 47
Character c h a n g e a s a f u n c t i o n o f t
Milliseconds 141 77 94 93 61 79 62 124 94 77 110 67 150 142 188 79 93 97 75 47 99 123 82 63 266
Character h e a c o u -u -o -c m o u n t o f l i q u i d
Milliseconds 78 95 62 64 110 33 90 338 175 138 562 111 76 172 66 76 47 123 63 94 140 265 109 63 157
Character o u -u -o p o u r e d i n t o i t ? W e s
Milliseconds 108 279 96 392 139 253 46 156 170 265 173 76 110 63 126 139 358 124 78 296 144 204 170 96 124
Character e e c h a n g e o c c u r r i n g i n n e a
Milliseconds 97 154 93 141 78 93 92 65 93 32 157 124 411 171 93 172 141 78 172 94 140 63 233 111 93
Character r l -i -n -n -e -a -r -l i n n e a r l y e v e r y t
Milliseconds 95 77 656 0 0 0 0 0 0 794 77 78 156 94 93 79 62 109 171 173 109 124 64 93 108
Character h i n g w e o b s e r v e i n t h e w o
Milliseconds 111 62 111 0 121 126 63 108 107 78 187 79 48 216 95 76 77 78 47 78 94 47 92 109 140
Character r l d a n d u n i v e r s e , a n d p o w
Milliseconds 78 125 126 93 96 106 93 79 110 173 49 90 190 152 156 62 208 124 78 190 62 63 156 76 78
Character e r f u l m o d e r n i n t r -r -t s t r u m e
Milliseconds 62 63 171 77 79 109 188 64 92 156 62 111 92 79 94 187 46 325 155 78 79 68 93 245 110
Character n t s h e l p u s s e e m o r e a n d
Milliseconds 61 79 111 97 187 108 95 201 203 93 114 41 156 107 187 111 92 63 47 64 62 78 62 109 61
Character m o r e . I n t h i s s e c i o n -n -o -i t i
Milliseconds 141 63 45 47 141 110 187 142 62 203 77 62 46 78 126 63 188 218 78 63 345 173 124 139 93
Character o n w e i n t r o d u c e t h e i d e a s
Milliseconds 62 63 77 157 62 205 110 78 78 64 108 126 139 94 156 123 95 62 96 76 110 92 157 79 202
Character o d - -d f a v e r a g e a n d i n s t a
Milliseconds 172 233 156 127 418 141 144 61 172 107 142 93 171 79 138 77 108 109 93 62 65 92 79 109 93
Character n t a n e o u s r a t e s o f c h a n g e ,
Milliseconds 62 608 93 48 266 266 173 111 122 157 78 110 62 93 93 108 79 79 138 94 88 83 77 125 48
Character a n d s h o w t h a t t h e y a r e c
Milliseconds 156 77 141 109 109 171 109 76 64 93 110 94 31 77 78 78 46 108 62 79 93 50 76 63 185
Character l o s e l y r e l a t e d t o t h e s l o
Milliseconds 33 123 63 77 93 94 143 123 64 360 110 78 93 156 77 107 62 78 94 110 61 64 126 143 168
Character p e o f a c u r v e a t a p o i n t
Milliseconds 111 125 93 126 93 48 93 93 142 141 77 172 93 94 139 109 79 108 77 528 63 79 111 76 49
Character P o n t h e c u r v e . W e g i v e p
Milliseconds 236 59 186 64 93 110 61 94 61 142 63 93 174 76 96 137 190 173 77 185 111 77 77 79 140
Character r e c i s e d e v e l o p m e n t s o f t h
Milliseconds 95 76 261 124 127 95 138 158 171 143 60 125 157 92 190 75 123 80 93 78 79 109 92 109 94
Character s e e -e -e -s e s e i m p o r t a n t c o n c e
Milliseconds 109 97 181 390 157 124 517 283 91 109 140 93 219 62 108 171 77 93 94 65 172 30 108 63 155
Character p t s i n t h e n e x t c h a p t e r ,
Milliseconds 77 93 94 95 64 76 80 76 62 64 63 78 78 171 125 79 174 60 93 110 78 94 93 63 122
Character b u t f o r n o w w e u s e n -n a n i
Milliseconds 123 94 97 91 94 79 93 62 79 61 63 78 124 63 79 108 94 77 264 204 361 109 92 79 78
Character n f o r m a l a p p r o a c h s o y o u w
Milliseconds 76 82 199 436 139 125 124 124 171 139 127 124 157 109 94 110 124 91 96 46 140 78 111 79 95
Character i l l s e e h o w t h e y l e a d n a r
Milliseconds 76 77 126 123 47 109 171 141 111 63 60 47 97 59 109 46 78 110 78 63 125 93 140 78 63
Character t u -u -t -r t u r a l l y t o t h e m a i n
Milliseconds 186 126 345 159 138 77 120 67 80 46 141 139 78 113 123 16 95 94 61 62 93 80 56 101 46
Character i d e a o f t h i s c h a p t e r , t h e
Milliseconds 250 93 171 62 77 95 109 92 110 78 63 48 47 156 110 64 124 83 104 93 93 124 109 79 78
Character l i m i t . T h e i d e a o f a l i m
Milliseconds 47 172 109 108 108 202 172 147 258 144 45 77 154 78 171 64 61 92 78 94 78 77 155 94 188
Character i t e p l -l -p - -e p l a y e -e s a f o u n
Milliseconds 62 94 64 124 111 156 358 157 170 142 187 124 155 126 63 92 435 126 109 123 76 139 92 79 204
Character d a t i o n a l r o l e t h r o u g o u t -t -u
Milliseconds 127 109 124 62 76 16 251 109 138 161 78 188 77 77 95 109 62 79 94 93 343 79 81 434 157
Character -o h o u t c a l c u l u s .
Milliseconds 124 172 156 91 77 79 156 62 62 109 93 170 174 109 128
WPM Timing
Seconds WPM
2.45 4.89
4.91 24.46
7.36 26.09
9.81 44.03
12.26 54.79
14.72 47.29
17.17 53.12
19.62 58.1
22.08 54.9
24.53 55.28
26.98 58.71
29.43 62.38
31.89 65.86
34.34 63.25
36.79 65.23
39.24 68.49
41.7 70.8
44.15 70.12
46.6 69.27
49.06 69.72
51.51 70.36
53.96 68.49
56.41 70.41
58.87 72.57
61.32 74.17
63.77 74.33
66.23 76.1
68.68 75.66
71.13 77.1
73.58 76.32
76.04 76.54
78.49 77.82
80.94 79.61
83.4 80.29
85.85 80.93
88.3 81.54
90.75 81.98
93.21 81.11
95.66 81.79
98.11 82.93
100.56 83.29
103.02 83.4
105.47 84.42
107.92 84.17
110.38 85.24
112.83 85.51
115.28 85.04
117.73 84.8
120.19 84.87
122.64 84.54