Shrubber (shrubber)

Race #7221

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Official speed 69.55 wpm (149.07 seconds elapsed during race)
Without ending ping 69.67 wpm (256 ms delay sending score to TypeRacer’s server)
Timerless 69.68 wpm (28 ms elapsed before first character typed; 148.79 seconds elapsed during race)
Timerless minus one 69.60 wpm, ignoring the first character typed
Race Start January 9, 2024 8:22:54pm UTC
Race Finish January 9, 2024 8:25:23pm UTC
Outcome No win (3 of 5)
Opponents 1. teemoh (92.23 wpm)
2. ningg (73.80 wpm)
Accuracy 95.6%
Points 187.79
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 toa a a chainnge in another. How does the speed of a falling object change as a functino oon of time? how How does the level of water in a abarrel change as a function of the amount of liquid oporeured into it? We see change occurring in nearly everything we observe in teh eh wohe world and univers,e, and pwerfwoerowerful modern instruments help us see mroeor ere and more. I n this section we introduce the idea of s of aveagerage and isntnstanteaaneous trates of change, and show that they are closely related to teh ehs he slpe ope of a curve at a POipointP P on the curve. We give precise develpopments of these important concetpspts int he n the next chapter, abubut for now we use an informal apparoroach so wyou will see how they lead natuallrally to the main idea of this chatperpter, the limit. The idea fof a lmitimit plays afou foundational role throughout caulculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 28 126 110 182 136 168 316 184 170 129 61 128 106 62 148 85 173 190 100 109 106 63 64 62 109
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 84 128 165 129 85 87 122 150 195 209 310 170 108 103 149 104 193 83 127 129 85 80 109 148 85
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 164 86 108 105 110 81 65 87 106 84 105 129 164 107 212 108 143 87 253 211 147 127 128 190 124
Character r e l a t e d t o a a -a - - -a a c h a
Milliseconds 165 152 212 106 104 107 81 151 148 86 86 124 0 150 127 256 168 168 168 39 85 128 147 87 186
Character i n -n -i n g e i n a n o t h e r . H o w d
Milliseconds 171 192 297 147 146 83 127 84 63 87 83 107 84 128 148 106 103 65 107 62 215 85 123 486 293
Character o e s t h e s p e e d o f a f a l l i n
Milliseconds 126 106 171 63 85 85 61 108 41 127 128 168 168 107 65 104 128 105 65 316 168 128 143 89 84
Character g o b j e c t c h a n g e a s a f u n c
Milliseconds 106 108 64 207 129 167 192 148 103 211 107 146 65 128 62 148 86 105 149 62 87 147 106 184 91
Character t i n o o -o - -o -n o n o f t i m e ? h o w
Milliseconds 148 42 127 23 63 149 359 148 169 169 205 68 82 128 166 129 169 106 64 81 260 119 218 85 103
Character - -w -o -h H o w d o e s t h e l e v e l o
Milliseconds 127 320 146 169 171 208 42 126 105 191 65 124 145 90 41 128 60 90 65 81 148 122 112 85 126
Character f w a t e r i n a a -a b a r r e l c h a
Milliseconds 42 107 168 189 108 104 107 62 88 105 85 83 86 189 258 123 146 128 169 144 110 106 183 92 124
Character n g e a s a f u n c t i o n o f t h e
Milliseconds 107 42 85 128 188 128 127 105 86 82 172 232 190 188 107 41 85 86 149 82 106 127 87 104 81
Character a m o u n t o f l i q u i d o -o p o r e -e -r
Milliseconds 107 131 127 104 212 40 170 129 100 89 169 128 166 130 125 607 126 172 649 255 62 104 168 299 148
Character u r e d i n t o i t ? W e s e e c h a n
Milliseconds 273 145 106 188 86 87 84 101 132 210 148 106 277 80 170 106 127 148 190 147 65 211 107 145 87
Character g e o c c u r r i n g i n n e a r l y e v
Milliseconds 63 83 128 86 167 149 129 145 565 130 63 127 86 43 105 106 127 84 147 65 85 149 83 84 150
Character e r y t h i n g w e o b s e r v e i n t e
Milliseconds 124 86 105 170 108 146 107 82 149 42 127 81 218 40 356 128 103 211 129 107 105 106 62 24 190
Character h - -h -e e h w o -o -w - -h -e h e w o r l d a
Milliseconds 43 147 362 147 145 186 4 147 62 145 261 166 171 169 168 167 59 131 83 108 105 106 126 107 128
Character n d u n i v e r s , -, e , a n d p w e r f -f
Milliseconds 85 82 85 129 274 126 127 204 64 321 402 380 98 131 85 148 84 84 86 88 417 85 84 189 278
Character -r -e -w w o e r -r -e -o -w o w e r f u l m o d e r n
Milliseconds 143 173 169 203 25 168 107 172 168 166 297 230 104 24 82 192 87 83 147 380 122 102 195 148 149
Character i n s t r u m e n t s h e l p u s s e e
Milliseconds 106 127 170 81 85 191 87 190 144 89 104 124 129 250 129 85 169 148 317 228 109 250 189 148 87
Character m r o e -e -o -r o r e -e - r -r e a n d m o r e
Milliseconds 86 167 0 104 300 166 149 208 105 106 19 428 162 81 366 123 123 129 87 104 44 127 108 39 106
Character . I - n t h i s s e c t i o n w e i n
Milliseconds 109 125 214 188 318 208 83 107 64 40 129 85 100 216 190 168 43 43 107 64 145 108 85 212 146
Character t r o d u c e t h e i d e a o f - -f -o - s
Milliseconds 148 189 129 105 129 104 166 127 86 128 65 103 123 130 148 147 170 43 149 125 341 147 168 170 144
Character o f a v e a g e -e -g -a r a g e a n d i s n
Milliseconds 104 111 186 128 207 152 146 165 216 105 191 171 148 59 149 107 104 65 105 105 106 86 128 39 46
Character t -t -n -s n s t a n t e a -a -e a n e o u s t -t r a
Milliseconds 212 234 166 150 145 60 88 147 103 130 253 253 193 167 41 149 143 170 341 121 130 464 400 101 126
Character t e s o f c h a n g e , a n d s h o w t
Milliseconds 111 59 130 106 45 84 105 297 84 124 67 147 62 170 85 273 126 105 87 105 126 45 103 171 64
Character h a t t h e y a r e c l o s e l y r e l a
Milliseconds 145 60 89 42 130 0 126 109 84 104 106 105 67 249 89 338 145 167 130 148 106 208 106 65 147
Character t e d t o t e h - -h -e e h s - -s -h -e h e
Milliseconds 85 105 163 133 107 64 84 64 104 4 207 342 147 169 123 65 145 5 461 150 168 274 267 88 86
Character s l p e - -e -p o p e o f a c u r v e a t
Milliseconds 126 87 211 209 125 297 170 148 231 232 123 88 208 107 85 103 66 189 88 118 217 84 126 106 125
Character a P O i -i -O -P p o i n t P - -P P o n t
Milliseconds 87 127 107 254 85 211 253 191 296 504 60 128 21 101 345 318 231 127 186 253 105 319 147 18 109
Character h e c u r v e . W e g i v e p r e c i s e
Milliseconds 85 59 88 169 66 145 213 83 189 64 359 169 87 146 147 105 84 85 130 82 126 234 22 650 145
Character d e v e l p -p o p m e n t s o f t h e s e
Milliseconds 108 482 187 150 109 148 233 568 250 190 189 121 88 149 378 105 125 61 90 82 110 60 149 86 41
Character i m p o r t a n t c o n c e t p s -s -p -t p t s
Milliseconds 172 108 167 20 127 189 170 107 104 129 253 85 83 103 401 205 90 190 340 169 147 251 83 129 129
Character i n t h e n -n - -e -h - -t t h e n e x t c
Milliseconds 63 125 84 0 149 17 89 169 214 169 168 168 171 166 210 169 107 104 42 150 103 232 167 129 187
Character h a p t e r , a b u -u -b -a b u t f o r n o w
Milliseconds 88 83 110 144 127 65 83 64 85 166 134 231 142 152 19 194 121 129 190 86 103 87 105 62 125
Character w e u s e a n i n f o r m a l a p p a r
Milliseconds 105 88 106 126 109 82 62 172 126 107 83 171 60 172 103 149 87 145 84 108 126 88 126 335 86
Character o -o -r -a r o a c h s o w -w y o u w i l l s
Milliseconds 125 342 127 147 124 128 105 211 401 182 322 191 147 103 448 226 129 108 19 82 299 209 129 126 103
Character e e h o w t h e y l e a d n a t u a l l -l
Milliseconds 191 147 84 104 108 62 151 147 105 62 129 108 106 103 126 86 86 103 129 85 108 82 167 152 293
Character -l -a r a l l y t o t h e m a i n i d e a
Milliseconds 151 146 82 106 63 172 84 104 191 63 62 87 104 64 67 126 167 66 103 89 106 103 189 42 234
Character o f t h i s c h a t p e r -r -e -p -t p t e r ,
Milliseconds 22 145 108 105 64 63 106 64 179 114 130 127 23 210 86 212 169 170 143 256 124 85 104 171 85
Character t h e l i m i t . T h e i d e a f -f o f
Milliseconds 126 87 81 87 64 127 85 127 146 275 106 254 125 103 148 174 146 145 128 149 210 529 208 84 126
Character a l m i t -t -i -m i m i t p l a y s a f o u -u
Milliseconds 84 64 129 188 106 148 234 148 147 210 84 148 62 146 152 148 122 172 82 129 84 211 129 62 355
Character -o -f f o u n d a t i o n a l r o l e t h r o
Milliseconds 153 148 501 169 86 62 170 125 147 64 128 41 88 145 151 105 249 149 171 125 164 154 107 208 107
Character u g h o u t c a u -u l c u l u s .
Milliseconds 86 187 64 191 65 144 107 254 147 171 568 188 146 108 142 133 162 133
WPM Timing
Seconds WPM
2.98 92.57
5.96 90.56
8.94 92.57
11.93 86.54
14.91 82.91
17.89 83.85
20.87 84.52
23.85 83.01
26.83 79.16
29.81 81.71
32.8 82.33
35.78 84.19
38.76 81.12
41.74 79.92
44.72 79.96
47.7 82.01
50.68 80.02
53.67 79.16
56.65 77.53
59.63 75.06
62.61 75.32
65.59 74.28
68.57 73.67
71.55 74.12
74.54 73.57
77.52 73.07
80.5 72.15
83.48 71.87
86.46 73.28
89.44 73.52
92.43 71.8
95.41 71.44
98.39 70.5
101.37 70.44
104.35 70.26
107.33 69.76
110.31 70.38
113.3 69.27
116.28 69.46
119.26 69.63
122.24 69.5
125.22 69.09
128.2 69.92
131.18 70.07
134.17 69.94
137.15 70.44
140.13 69.79
143.11 69.35
146.09 69.74
149.07 69.55