Mika (micaroni)

Race #701

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Official speed 84.67 wpm (122.45 seconds elapsed during race)
Without ending ping 85.03 wpm (242 ms delay sending score to TypeRacer’s server)
Timerless 85.09 wpm (87 ms elapsed before first character typed; 122.12 seconds elapsed during race)
Timerless minus one 85.00 wpm, ignoring the first character typed
Race Start February 9, 2024 5:54:28am UTC
Race Finish February 9, 2024 5:56:30am UTC
Outcome Win (1 of 5)
Opponents 3. rajnishkumar31 (82.22 wpm)
4. mohamedabdelfattah005 (77.24 wpm)
Accuracy 96.2%
Points 228.60
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 CCalculusu is a tool that helps us understand how a chagenge in one quantity is relate tod to a change in another. How oddoes the speed of a falling object changes as as a function of time? How does the level of water in a bearrel change ssas a function toof the amount of liquid poured inot oto it? We see change occuring inring in nearly everyhttginhing we obsere ve in the world and universe an, and wpowerful modern instruments help us see more and more. In this section we introduce the ideas of average and instantaneous rates of chagne, nnge, and show that they are aclosely related to the slope of a curve at a point P on the curve. We hggive precise developments of thseese imporanttant concenrpprtts in the next chatppter, but for mnow we use an informal appracoach so you will se he ohow they lead naturally to the main idea of this chapter , the limit. The idea of a limit plays of a fojundational frole throught ouout calculus.
Timing
Character C C -C a l c u l u s u - -u i s a t o o l
Milliseconds 87 268 419 243 58 387 65 179 149 62 120 51 248 120 180 0 386 94 87 94 86 92 112 161 86
Character t h a t h e l p s u s u n d e r s t a n d
Milliseconds 24 159 55 94 24 127 21 30 98 56 89 121 94 94 144 56 30 91 118 94 61 89 89 64 91
Character h o w a c h a g e -e -g n g e i n o n e q
Milliseconds 89 92 55 90 60 93 182 64 85 149 214 239 121 532 63 152 149 56 59 63 182 60 116 59 273
Character u a n t i t y i s r e l a t e t o -o -t - d
Milliseconds 95 118 57 119 125 143 68 91 89 55 91 91 60 87 94 93 60 206 60 92 209 148 90 119 61
Character t o a c h a n g e i n a n o t h e r . H
Milliseconds 27 98 145 57 155 241 53 93 121 455 118 54 94 53 63 34 88 99 51 150 60 26 96 88 123
Character o w o d -d -o d o e s t h e s p e e d o f
Milliseconds 147 26 101 416 393 120 148 93 59 88 85 185 58 238 27 124 124 91 88 150 116 516 89 57 123
Character a f a l l i n g o b j e c t c h a n g e s
Milliseconds 27 158 201 57 61 126 150 60 22 66 93 114 121 94 93 31 116 204 27 70 120 0 89 89 87
Character a s -s -a - -s a s a f u n c t i o n o f t
Milliseconds 124 81 246 151 122 82 213 56 153 180 151 91 448 180 60 90 28 454 90 58 126 88 89 153 264
Character i m e ? H o w d o e s t h e l e v e l o
Milliseconds 63 59 124 142 248 144 213 118 120 331 149 89 65 68 81 151 87 0 158 82 120 63 83 93 131
Character f w a t e r i n a b e $a r r e l c h a n
Milliseconds 21 91 94 84 56 94 119 98 84 54 70 25 123 180 88 511 296 214 25 153 213 175 61 65 126
Character g e s s -s -s a s a f u n c t i o n t o -o -t
Milliseconds 0 78 92 88 159 537 85 150 57 94 88 125 89 180 86 120 25 100 23 62 149 181 91 180 153
Character o f t h e a m o u n t o f l i q u i d p
Milliseconds 128 82 54 94 152 24 61 94 55 123 180 27 97 88 91 95 51 96 144 359 111 133 476 128 52
Character o u r e d i n o t - -t -o o -o t o i t ? W e
Milliseconds 61 186 239 58 184 115 0 58 215 85 120 331 155 119 233 273 62 57 97 383 92 146 183 121 208
Character s e e c h a n g e o c c u r i n g i n -n -i
Milliseconds 59 512 116 123 127 142 62 59 128 26 58 57 89 118 159 93 84 186 48 71 84 98 54 180 176
Character - -g -n -i r i n g i n n e a r l y e v e r y h
Milliseconds 123 149 121 275 178 85 59 122 428 150 53 26 189 92 85 54 94 89 126 87 92 115 25 151 212
Character t -t -h t g i n -n -i -g h i n g w e o b s e r e
Milliseconds 59 221 115 92 236 25 62 398 147 89 181 120 0 53 94 124 117 57 304 119 238 57 100 748 51
Character - -e v e i n t h e w o r l d a n d u n i
Milliseconds 573 123 211 60 89 88 66 54 91 210 88 117 93 216 414 148 95 123 62 87 91 0 115 92 122
Character v e r s e a n -n -a - , a n d w -w p o w e r f
Milliseconds 57 93 51 160 57 454 26 91 207 150 122 123 149 26 122 55 65 125 236 269 54 125 27 96 215
Character u l m o d e r n i n s t r u m e n t s h e l
Milliseconds 53 181 89 95 53 155 120 57 96 146 90 52 92 59 91 29 63 154 51 97 60 125 234 91 25
Character p u s s e e m o r e a n d m o r e . I
Milliseconds 94 121 124 115 93 292 61 151 101 48 30 67 64 52 64 89 66 78 72 87 51 40 120 413 187
Character n t h i s s e c t i o n w e i n t r o d u
Milliseconds 233 92 90 151 94 55 60 118 92 179 545 179 0 56 514 184 56 125 182 19 159 17 185 214 115
Character c e t h e i d e a s o f a v e r a g e a
Milliseconds 91 56 128 86 181 54 32 191 49 98 88 95 114 124 210 176 90 152 91 88 118 95 85 90 94
Character n d i n s t a n t a n e o u s r a t e s o f
Milliseconds 89 53 62 123 26 132 148 207 150 538 89 212 87 121 94 110 128 148 54 126 57 124 0 118 58
Character c h a g n e , - -, -e -n n -n -g n g e , a n d
Milliseconds 94 214 49 36 123 0 85 117 126 118 155 144 98 296 215 90 177 62 49 71 89 90 83 91 121
Character s h o w t h a t t h e y a r e a -a c l o s
Milliseconds 121 149 89 92 299 241 179 59 94 87 150 182 54 95 54 94 58 58 63 61 299 150 93 90 25
Character e l y r e l a t e d t o t h e s l o p e
Milliseconds 63 240 90 121 120 88 92 85 93 57 179 66 55 91 124 24 154 56 61 157 86 90 151 156 120
Character o f a c u r v e a t a p o i n t P o
Milliseconds 124 30 84 20 155 185 91 94 75 96 129 51 56 162 89 116 118 91 205 93 154 173 304 277 80
Character n t h e c u r v e . W e h g -g $g i v e p
Milliseconds 99 55 53 191 53 64 181 95 15 127 89 25 252 202 239 95 181 208 245 147 144 64 56 151 185
Character r e c i s e d e v e l o p m e n t s o f t h
Milliseconds 50 132 49 190 91 89 210 237 89 91 122 23 123 35 211 61 87 56 178 245 89 116 59 215 180
Character s e -e -s e s e i m p o r a n t -t -n -a t a n t c
Milliseconds 122 145 185 115 154 153 325 189 167 214 125 87 22 245 91 92 209 119 153 179 50 100 58 58 209
Character o n c e n r p -p -r -n p r t -t -r t s i n t h e
Milliseconds 0 99 87 51 123 69 111 272 123 119 88 95 173 242 152 92 51 334 182 58 62 90 213 49 0
Character n e x t c h a t p -p -t p t e r , b u t f o r
Milliseconds 126 96 49 74 145 180 151 52 188 148 206 94 183 50 242 27 93 184 180 55 101 49 128 90 92
Character m -m n o w w e u s e a n i n f o r m a l
Milliseconds 80 65 295 185 55 94 54 95 55 103 172 119 96 239 126 113 88 120 62 59 122 87 126 57 267
Character a p p r a c -c -a o a c h s o y o u w i l l
Milliseconds 178 99 61 112 60 125 179 296 119 118 121 93 418 150 122 93 58 179 28 121 89 151 87 150 118
Character s e h -h - e o -o h o w t h e y l e a d
Milliseconds 63 122 61 120 94 326 120 88 91 122 209 62 86 94 92 178 148 93 55 57 126 118 33 149 95
Character n a t u r a l l y t o t h e m a i n i d e
Milliseconds 141 100 53 92 52 88 95 120 57 98 90 85 99 53 155 18 95 96 28 122 49 62 128 52 95
Character a o f t h i s c h a p t e r - , t h e
Milliseconds 57 120 150 61 90 89 152 127 64 48 188 51 58 127 56 123 93 267 240 118 92 59 157 46 30
Character l i m i t . T h e i d e a o f a l i m i
Milliseconds 99 149 91 88 0 174 65 126 148 54 91 119 62 212 55 125 118 93 123 50 129 53 124 123 50
Character t p l a y s o f - -f -o a f o j -j u n d a t
Milliseconds 31 93 91 154 178 62 119 88 93 121 84 362 92 147 180 62 116 395 184 328 208 93 52 61 91
Character i o n a l f -f r o l e t h r o u g h t o u -u
Milliseconds 55 65 54 100 88 117 152 240 92 88 57 121 62 55 191 145 26 98 54 120 32 95 54 59 248
Character -o - -t o u t c a l c u l u s .
Milliseconds 120 173 269 151 93 0 95 176 27 55 120 73 143 153 236 23
WPM Timing
Seconds WPM
2.45 39.2
4.9 78.4
7.35 86.56
9.8 85.75
12.25 87.22
14.69 91.46
17.14 87.5
19.59 90.04
22.04 86.56
24.49 86.24
26.94 87.31
29.39 88.2
31.84 87.07
34.29 87.85
36.74 87.54
39.18 84.52
41.63 85.03
44.08 82.21
46.53 82.27
48.98 81.09
51.43 79.33
53.88 80.18
56.33 79.04
58.78 81.05
61.23 82.51
63.67 82.17
66.12 82.94
68.57 83.82
71.02 84.14
73.47 82.97
75.92 83.61
78.37 84.22
80.82 85.23
83.27 85.46
85.72 85.26
88.17 85.61
90.61 84.75
93.06 83.81
95.51 83.67
97.96 83.42
100.41 83.78
102.86 83.18
105.31 83.18
107.76 83.74
110.21 84.93
112.66 85.32
115.1 86.01
117.55 84.83
120 85.3
122.45 84.67