Michael (michaelam99)

Race #26

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Official speed 79.45 wpm (130.50 seconds elapsed during race)
Without ending ping 79.58 wpm (215 ms delay sending score to TypeRacer’s server)
Timerless 79.64 wpm (99 ms elapsed before first character typed; 130.18 seconds elapsed during race)
Timerless minus one 79.55 wpm, ignoring the first character typed
Race Start November 11, 2023 4:48:14pm UTC
Race Finish November 11, 2023 4:50:25pm UTC
Outcome Win (1 of 2)
Accuracy 96.7%
Points 214.52
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 up unssus understsand how a chnaange in one quanitity is related to a change in another. hHow does the seppeed of f aa aa falling object change as a function of time>? How does the level of water in a barrel ochange aas sa a a s a function of the amount of liquid poured into it? wWe see channge occurin rin g in nearly everythig ng we ovsbserve in the world and universe, and powerful omofdern instruments help us see more and more// . iIn this section we introduce the ideas of average and instantaneous rates of change, and hsshow that they are closely related to the slope of a curve at a point P on the curve. eWe give precidese developments of these important concepts nin the next chapterm, but for no ww we use an informal approach so you will see how they led ad natruurally to the main idea of this chapter, the limite>. The idea of a limit plays a foundation rolal role throughout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 99 271 116 121 150 162 176 100 42 134 73 113 102 63 99 74 112 153 137 102 96 27 114 124 125
Character e l p s u p u n -n -u - -p -u s -s s -s u s u n d
Milliseconds 75 63 138 99 76 150 174 138 138 86 213 112 101 111 113 72 279 700 501 215 94 89 113 88 37
Character e r s t s -s a n d h o w a c h n a -a -n a n g
Milliseconds 125 88 124 89 37 559 154 101 60 76 164 82 53 89 99 50 163 10 177 226 237 87 138 112 100
Character e i n o n e q u a n i -i t i t y i s r e
Milliseconds 100 63 99 101 97 114 100 39 73 151 49 127 112 300 276 112 75 76 174 263 137 75 100 75 100
Character l a t e d t o a c h a n g e i n a n o t
Milliseconds 46 154 87 150 154 109 75 62 125 114 91 108 112 113 62 112 99 64 113 75 125 37 101 88 48
Character h e r . h -h H o w d o e s t h e s e p -p -e
Milliseconds 113 62 113 112 188 297 427 164 175 137 99 89 62 87 113 75 77 98 47 65 88 174 76 275 87
Character p e e d o f f a -a - a - -a -f a -a a f a l
Milliseconds 125 89 124 113 100 137 100 100 124 11 102 188 100 125 99 300 114 274 351 186 226 186 102 100 85
Character l i n g o b j e c t c h a n g e a s a f
Milliseconds 141 223 88 37 88 112 151 99 63 150 97 102 51 112 100 36 113 100 100 39 112 100 51 100 87
Character u n c t i o n o f t i m e > -> ? H o w d o
Milliseconds 99 88 63 175 48 102 137 126 161 89 111 113 35 166 9 404 486 375 250 463 175 100 62 113 89
Character e s t h e l e v e l o f w a t e r i n
Milliseconds 61 125 138 75 99 100 76 162 63 125 99 88 138 99 38 72 49 104 122 103 99 88 125 100 125
Character a b a r r e l o -o c h a n g e a a s s a
Milliseconds 102 23 175 89 149 151 149 113 149 184 316 138 100 100 47 103 100 110 62 103 38 46 41 75 72
Character - -a -s - -s -a a a - -a - -a s a f u n c t i o
Milliseconds 228 105 95 125 112 124 139 87 138 62 262 114 87 110 151 164 90 110 150 126 112 74 338 75 112
Character n o f t h e a m o u n t o f l i q u i d
Milliseconds 112 126 100 76 61 126 99 75 113 212 88 125 163 100 49 89 137 125 49 113 175 99 163 138 150
Character p o u r e d i n t o i t ? w -w W e s e e
Milliseconds 62 163 163 374 138 88 137 111 127 99 60 103 149 138 76 400 311 126 275 138 325 137 150 175 126
Character c h a n -n n g e o c c u r i n - -n -i r i n
Milliseconds 98 136 77 189 0 286 425 109 103 63 113 59 128 125 75 87 101 126 185 139 87 100 140 98 125
Character - g i n n e a r l y e v e r y t h i g - -g
Milliseconds 350 71 91 125 88 112 163 63 100 86 214 76 136 687 125 113 125 63 174 88 88 124 88 299 114
Character n g w e o v -v s -s b s e r v e i n t h e
Milliseconds 450 113 87 87 150 112 150 101 274 22 453 201 124 199 101 200 99 64 136 101 127 86 100 24 101
Character w o r l d a n d u n i v e r s e , a n d p
Milliseconds 38 113 111 127 87 275 148 101 76 74 238 112 87 75 126 88 149 200 113 262 122 104 25 113 111
Character o w e r f u l o -o m o f -f d e r n i n s t r u
Milliseconds 137 76 163 60 199 140 150 99 252 271 116 99 187 214 100 137 125 122 128 113 99 76 137 149 112
Character m e n t s h e l p u s s e e m o r e a n
Milliseconds 176 113 90 73 162 400 197 90 125 112 128 136 87 150 122 240 126 124 163 75 62 75 113 75 88
Character d m o r e / -/ / - -/ . i -i I n t h i s s
Milliseconds 75 75 149 87 73 104 148 476 187 262 248 128 159 292 299 475 226 173 113 139 99 76 86 38 99
Character e c t i o n w e i n t r o d u c e t h e i
Milliseconds 163 138 201 86 125 100 100 175 151 162 225 88 314 198 125 162 60 141 137 124 126 76 46 94 159
Character d e a s o f a v e r a g e a n d i n s t a
Milliseconds 34 101 115 112 188 150 99 64 75 161 123 116 126 58 115 60 64 126 100 113 199 126 125 112 113
Character n t a n e o u s r a t e s o f c h a n g e ,
Milliseconds 177 384 89 151 88 196 164 139 102 110 101 137 89 148 126 99 75 72 141 25 99 72 79 101 98
Character a n d h s -s -h s h o w t h a t t h e y a
Milliseconds 163 101 59 59 69 239 148 200 100 126 100 99 85 53 124 64 60 77 88 125 74 25 88 97 49
Character r e c l o s e l y r e l a t e d t o t h e
Milliseconds 115 89 62 113 59 127 22 742 100 137 113 150 137 50 99 215 224 150 112 75 63 125 24 126 9
Character s l o p e o f a c u r v e a t a p o
Milliseconds 127 101 113 123 152 125 112 162 76 101 86 63 112 113 76 173 89 450 137 151 86 51 88 161 163
Character i n t P o n t h e c u r v e . e -e W e
Milliseconds 149 140 48 86 202 187 101 87 124 76 108 26 79 137 62 163 212 124 514 199 313 311 313 187 200
Character g i v e p r e c i d e -e -d s e d e v e l o p m
Milliseconds 73 100 91 97 65 150 39 99 150 163 86 164 200 100 137 189 70 200 129 112 100 60 152 125 151
Character e n t s o f t h e s e i m p o r t a n t c
Milliseconds 137 100 88 149 163 138 112 75 100 49 164 162 149 64 153 87 122 123 49 152 77 88 59 93 175
Character o n c e p t s n -n i n t h e n e x t c h a
Milliseconds 109 179 113 161 136 398 426 151 236 274 202 86 102 112 99 47 103 111 37 190 161 102 99 62 126
Character p t e r m -m , b u t f o r n o w -w - w w
Milliseconds 99 150 124 101 588 447 140 226 162 92 108 100 75 85 103 87 137 100 175 11 252 99 112 74 79
Character e u s e a n i n f o r m a l a p p r o a c
Milliseconds 135 140 124 59 166 87 75 75 126 124 100 63 113 86 88 124 86 128 150 100 113 225 284 140 125
Character h s o y o u w i l l s e e h o w t h e
Milliseconds 150 112 64 99 125 113 86 138 113 76 126 160 100 101 73 165 121 91 175 100 71 104 96 91 47
Character y l e d - -d a d n a t r u -u -r u r a l l y
Milliseconds 90 114 136 22 254 137 300 100 138 125 110 128 62 175 150 16 321 88 211 100 100 126 112 97 166
Character t o t h e m a i n i d e a o f t h i s
Milliseconds 175 113 137 59 116 51 87 177 85 125 88 100 163 74 123 113 76 124 65 137 187 100 111 76 88
Character c h a p t e r , t h e l i m i t e -e > -> . T
Milliseconds 88 88 124 86 388 129 74 110 176 110 89 11 102 162 201 50 249 188 112 360 315 488 187 264 187
Character h e i d e a o f a l i m i t p l a y s
Milliseconds 200 75 59 139 112 90 112 112 114 87 100 123 113 164 250 112 138 76 136 150 63 135 112 149 101
Character a f o u n d a t i o n r o l -l -o -r - a l r o
Milliseconds 62 102 73 84 579 149 88 125 100 60 115 101 135 141 45 128 413 114 110 113 163 112 138 136 89
Character l e t h r o u g h o u t c a l c u l u s .
Milliseconds 125 88 98 101 113 87 75 200 87 101 187 149 100 101 188 100 59 125 150 164 152 113 124
WPM Timing
Seconds WPM
2.61 101.15
5.22 68.97
7.83 61.3
10.44 67.82
13.05 71.73
15.66 80.46
18.27 80.13
20.88 74.71
23.49 74.08
26.1 79.08
28.71 75.65
31.32 79.7
33.93 79.58
36.54 75.54
39.15 77.24
41.76 78.16
44.37 76.81
46.98 75.86
49.59 75.5
52.2 74.71
54.81 74
57.42 75.24
60.03 75.16
62.64 75.29
65.25 76.69
67.86 74.27
70.47 74.76
73.08 75.21
75.69 76.1
78.3 77.09
80.91 77.87
83.52 77.88
86.13 79
88.74 79.51
91.35 78.43
93.96 78.55
96.57 79.16
99.18 78.89
101.79 79.11
104.4 78.51
107.01 79.17
109.62 79.48
112.23 79.55
114.84 79.52
117.45 80
120.06 79.56
122.67 79.53
125.28 79.6
127.89 79.19
130.5 79.45