L.in.k (xquyen)

Race #52790

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Official speed 101.91 wpm (101.74 seconds elapsed during race)
Without ending ping 102.15 wpm (239 ms delay sending score to TypeRacer’s server)
Timerless 102.20 wpm (51 ms elapsed before first character typed; 101.45 seconds elapsed during race)
Timerless minus one 102.08 wpm, ignoring the first character typed
Race Start November 25, 2023 3:58:37am UTC
Race Finish November 25, 2023 4:00:18am UTC
Outcome Win (1 of 5)
Opponents 2. flamingfingers69 (92.09 wpm)
Accuracy 98.0%
Points 275.16
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 to a change in another. How does the speed of a falling object change as a function of time? How doe sths the level of water in a barrel change as a function of the amount of ullliquid 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 instantanoeous rates off change, and show that they aer re closely realterelated to the slope foof a curve at a point P on the curve. We give precise developmetns onts of these important concepts in the next chapter, but for now we use an informal approach s oyso wyouyou will see how they lead naturally to hte mthe main idea of this chapter, the limtiit. The idea of a limit plays a foundational 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 51 408 182 176 96 276 208 113 80 70 70 80 225 221 169 97 161 197 70 60 100 30 60 19 131
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 79 81 171 79 80 100 158 92 160 111 69 151 79 149 20 147 144 79 39 112 69 80 40 90 60
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 120 80 85 99 76 69 60 31 100 100 574 106 49 50 134 149 98 118 460 94 107 151 78 102 89
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 39 115 55 111 80 59 61 173 37 112 88 99 31 166 94 120 315 156 105 63 91 39 144 148 119
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 79 90 70 80 80 49 123 68 170 90 80 120 121 89 91 79 9 108 43 121 0 275 96 356 153
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 178 80 102 48 50 101 69 81 99 19 153 119 70 90 50 129 121 120 88 197 168 57 174 104 95
Character n g e a s a f u n c t i o n o f t i m e
Milliseconds 124 20 115 118 110 70 90 100 121 59 369 123 99 151 569 138 72 80 100 49 60 130 50 132 58
Character ? H o w d o e s t h -s -t -h - s t h e l e
Milliseconds 281 150 150 110 90 80 91 89 99 71 9 105 66 429 0 0 224 106 50 100 121 69 21 119 49
Character v e l o f w a t e r i n a b a r r e l
Milliseconds 107 63 105 96 135 85 49 239 102 70 90 70 80 49 105 66 71 99 80 78 135 122 64 121 59
Character c h a n g e a s a f u n c t i o n o f t
Milliseconds 129 91 70 141 19 128 221 96 125 83 56 121 39 110 91 70 131 48 116 105 50 108 62 39 161
Character h e a m o u n t o f u l -l l -l -u l i q u i d
Milliseconds 39 92 27 111 30 104 95 174 66 81 70 155 105 326 203 317 321 431 144 220 191 136 90 150 101
Character p o u r e d i n t o i t ? W e s e e c
Milliseconds 79 154 175 91 18 50 144 48 39 91 80 60 100 208 100 212 80 139 81 90 380 90 63 330 176
Character h a n g e o c c u r r i n g i n n e a r l y
Milliseconds 111 60 130 29 70 71 89 121 131 196 125 139 88 100 50 39 91 71 60 123 56 70 30 132 88
Character e v e r y t h i n g w e o b s e r v e i n
Milliseconds 80 90 131 164 105 99 95 96 72 98 50 28 71 70 80 175 76 198 30 82 173 114 72 49 70
Character t h e w o r l d a n d u n i v e r s e ,
Milliseconds 71 90 99 30 61 90 70 59 101 69 50 71 89 50 41 100 76 137 46 180 130 121 49 134 65
Character - -, - , a n d p o w e r f u l m o d e r n
Milliseconds 51 357 148 632 233 79 29 92 39 50 91 141 59 19 80 150 50 141 58 132 134 4 230 81 140
Character i n s t r u m e n t s h e l p u s s e e
Milliseconds 59 165 116 19 59 144 47 180 60 132 17 92 59 121 100 59 164 87 134 36 70 99 81 137 73
Character m o r e a n d m o r e . I n t h i s s e
Milliseconds 30 119 20 40 50 81 59 81 39 81 70 79 20 121 80 111 107 50 80 80 80 9 83 89 89
Character c t i o n w e i n t r o d u c e t h e i d
Milliseconds 149 165 7 99 111 18 101 71 80 182 120 17 136 95 176 122 72 153 56 61 109 30 81 120 29
Character e a s o f a v e r a g e a n d i n s t a n
Milliseconds 160 81 70 79 102 48 48 122 123 194 92 91 130 99 49 81 119 42 30 90 71 49 90 120 204
Character t a n o -o e o u s r a t e s o f f - -f c h
Milliseconds 390 383 167 171 364 117 126 57 110 30 160 70 100 42 89 99 80 111 82 79 460 147 122 50 136
Character a n g e , a n d s h o w t h a t t h e y
Milliseconds 89 149 25 101 129 51 60 101 8 121 110 100 61 80 59 101 130 109 71 38 91 50 30 159 41
Character a e r - -r -e r e c l o s e l y r e a l t e -r
Milliseconds 30 119 9 111 436 150 151 33 29 72 124 54 164 36 40 157 144 215 170 76 149 99 100 30 431
Character -e -a -l -t -e r e l a t e d t o t h e s l o p e
Milliseconds 0 0 0 0 0 128 42 100 80 69 60 149 61 91 68 50 101 40 49 102 110 48 167 168 76
Character f o -f -o o f a c u r v e a t a p o i n
Milliseconds 49 121 40 470 0 195 25 70 39 121 141 109 99 157 139 84 83 187 101 80 89 49 162 48 142
Character t P o n t h e c u r v e . W e g i v e
Milliseconds 99 80 200 171 99 60 81 50 90 30 90 106 105 99 188 155 149 88 230 80 110 123 135 60 126
Character p r e c i s e d e v e l o p m e t n s o -o -
Milliseconds 75 106 34 71 175 172 93 39 80 513 245 211 71 140 165 188 180 47 121 30 90 59 70 334 158
Character -s -n -t n t s o f t h e s e i m p o r t a n t
Milliseconds 171 300 208 251 415 132 41 143 77 40 131 70 70 128 41 60 70 110 163 158 49 153 68 140 19
Character c o n c e p t s i n t h e n e x t c h a
Milliseconds 50 141 59 91 69 169 112 80 79 61 60 58 71 61 80 19 89 107 24 185 139 86 140 90 79
Character p t e r , b u t f o r n o w w e u s e
Milliseconds 81 80 89 61 149 70 91 68 118 32 172 80 120 60 59 102 196 185 129 89 69 141 70 29 120
Character a n i n f o r m a l a p p r o a c h s o y
Milliseconds 119 121 60 90 69 81 70 120 99 81 310 144 116 110 139 81 99 40 179 122 80 164 86 39 240
Character -o -y - s -s o w y o u -w -y -o -u y o u w i l l s
Milliseconds 330 0 147 165 506 186 75 50 90 91 100 320 0 0 0 368 106 55 81 120 48 161 145 65 71
Character e e h o w t h e y l e a d n a t u r a l l
Milliseconds 89 140 80 200 89 61 39 80 70 70 92 39 130 30 40 140 59 73 78 100 100 80 80 80 153
Character y t o h t e m -m -h -t -e - t h e m a i n i
Milliseconds 65 60 102 38 91 108 11 91 112 48 350 151 0 0 0 89 142 58 40 132 38 123 47 96 103
Character d e a o f t h i s c h a p t e r , t h e
Milliseconds 72 151 48 80 111 165 125 239 71 90 59 50 121 105 66 99 70 100 60 97 52 101 69 79 62
Character l i m t i -i -t i t . T h e i d e a o f a
Milliseconds 61 99 166 329 84 312 160 234 44 166 53 111 81 57 50 81 61 143 77 69 91 69 49 77 65
Character l i m i t p l a y s a f o u n d a t i o n a
Milliseconds 48 100 159 136 127 69 121 153 77 113 87 80 80 60 59 91 70 204 36 81 99 49 83 108 376
Character l r o l e t h r o u g h o u t c a l c u l u
Milliseconds 164 101 91 98 163 38 40 99 72 79 49 71 87 73 132 57 92 58 153 107 31 194 96 165 170
Character s .
Milliseconds 111 130
WPM Timing
Seconds WPM
2.03 70.77
4.07 91.41
6.1 104.19
8.14 100.26
10.17 103.8
12.21 105.17
14.24 105.31
16.28 106.89
18.31 106.81
20.35 104.39
22.38 100.79
24.42 104.19
26.45 105.25
28.49 107.42
30.52 100.65
32.56 101.73
34.59 100.95
36.63 102.55
38.66 103.36
40.69 105.57
42.73 102.79
44.76 103.74
46.8 105.39
48.83 107.38
50.87 108.04
52.9 108.65
54.94 106.59
56.97 105.74
59.01 106.77
61.04 105.37
63.08 104.82
65.11 104.13
67.15 104.19
69.18 104.25
71.22 103.63
73.25 101.57
75.29 101.22
77.32 102.28
79.35 102.83
81.39 103.35
83.42 102.7
85.46 100.54
87.49 100.67
89.53 101.33
91.56 101.05
93.6 101.67
95.63 101.01
97.67 101.61
99.7 101.82
101.74 101.91