Luke (lukell)

Race #7227

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Official speed 99.12 wpm (104.60 seconds elapsed during race)
Without ending ping 99.17 wpm (53 ms delay sending score to TypeRacer’s server)
Timerless 99.45 wpm (290 ms elapsed before first character typed; 104.26 seconds elapsed during race)
Timerless minus one 99.33 wpm, ignoring the first character typed
Race Start March 25, 2024 12:36:43am UTC
Race Finish March 25, 2024 12:38:28am UTC
Outcome Win (1 of 3)
Opponents 2. andzer0 (87.59 wpm)
Accuracy 96.9%
Points 267.63
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 haelps uss usnderstand how a change in one quantity is ralelated to a change in another. How does the speed of a afalling onjbject change as a function of time? Howw does the level of water in a barrel change as a funtionction of the amount of liquid poured into it? We see change occurring in nearly everythign we ng we observe in the world and universe, and powerful modern instruments help us wsee more and more. In this section we intrudoduce the ides as of average and instatnntaneous rates of hdchange, and show the4at at they are closely related to the sloeop oe of a curve at a point P on the curve. We igigive precise developments of these important concdeptsepts in the next chapter, fbut for new weow we use an informal approach so you will s3e hee how they lead naturally to the main idea of this chapter, the limit. The idea of a limity p plays a foundations ral role throguuighoghout clcaalculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 290 135 109 106 157 240 165 88 20 122 91 25 121 32 141 76 95 178 157 157 35 83 41 28 105
Character a -a e l p s u s s -s u s -s n d e r s t a n d
Milliseconds 130 265 87 62 113 73 44 92 94 192 247 114 75 91 463 135 54 128 51 93 97 76 76 76 100
Character h o w a c h a n g e i n o n e q u a n t
Milliseconds 197 122 78 37 75 36 180 105 94 42 153 146 98 106 121 95 117 96 227 310 24 121 67 87 115
Character i t y i s r a l -l -a e l a t e d t o a c
Milliseconds 66 74 107 116 89 95 48 156 117 278 186 103 94 80 54 85 116 122 56 110 29 92 33 84 134
Character h a n g e i n a n o t h e r . H o w d o e
Milliseconds 79 81 44 113 108 74 128 147 91 81 53 130 64 73 109 48 49 101 127 95 85 60 101 60 50
Character s t h e s p e e d o f a a -a f a l l i n
Milliseconds 100 48 113 27 95 16 167 73 69 125 124 83 74 78 72 59 66 268 237 50 78 53 116 115 90
Character g o n j -j -n b j e c t c h a n g e a s a
Milliseconds 52 52 90 83 132 202 106 162 141 60 123 162 43 187 85 53 88 73 101 70 88 67 71 69 61
Character f u n c t i o n o f t i m e ? H o w w - -w
Milliseconds 81 91 112 53 154 34 41 67 100 93 55 70 107 58 142 7 296 331 232 108 378 110 112 216 102
Character d o e s t h e l e v e l o f w a t e r
Milliseconds 132 112 73 60 100 41 124 40 93 46 93 50 142 93 74 68 100 19 79 50 117 65 146 72 44
Character i n a b a r r e l c h a n g e a s a f
Milliseconds 83 100 99 74 58 112 46 106 101 135 51 89 128 73 56 66 86 96 84 96 60 68 53 77 131
Character u n t i o n -n -o -i -t c t i o n o f t h e a m
Milliseconds 70 110 80 87 60 56 249 104 139 99 45 143 35 39 28 131 82 73 57 150 81 48 47 148 92
Character o u n t o f l i q u i d p o u r e d i n t
Milliseconds 158 68 121 66 67 94 45 66 106 132 154 123 107 93 74 191 200 147 456 147 129 49 84 67 91
Character o i t ? W e s e e c h a n g e o c c u r
Milliseconds 49 110 68 32 238 119 142 102 79 141 193 83 257 104 82 62 72 73 110 107 154 104 105 114 91
Character r i n g i n n e a r l y e v e r y t h i g n
Milliseconds 149 154 115 75 73 158 108 93 73 44 98 59 112 163 90 86 130 123 64 57 47 96 147 80 8
Character w e - -e -w - -n -g n g w e o b s e r v e i
Milliseconds 99 57 61 72 170 122 117 127 139 130 382 56 66 92 62 56 114 82 109 63 98 158 133 83 81
Character n t h e w o r l d a n d u n i v e r s e ,
Milliseconds 89 105 35 105 16 80 76 60 44 114 44 65 40 72 39 50 101 128 132 43 133 56 108 60 107
Character a n d p o w e r f u l m o d e r n i n s t
Milliseconds 103 82 85 56 43 145 133 83 52 46 165 62 145 102 172 123 70 145 38 71 110 270 117 80 113
Character r u m e n t s h e l p u s w -w s e e m o r
Milliseconds 70 72 156 65 50 51 101 49 176 103 69 117 55 81 111 67 114 324 58 142 86 85 97 116 12
Character e a n d m o r e . I n t h i s s e c t i
Milliseconds 56 81 40 78 38 47 95 110 61 72 84 68 137 98 121 53 86 72 16 99 114 127 136 154 35
Character o n w e i n t r u d -d -u o d u c e t h e i
Milliseconds 42 58 100 86 46 69 142 100 96 48 134 146 216 111 183 85 174 108 121 67 83 39 55 45 65
Character d e s - -s a s o f a v e r a g e a n d i
Milliseconds 68 119 161 69 226 106 99 66 52 97 490 64 82 447 124 53 100 87 88 73 58 70 72 53 85
Character n s t a t n -n -t n t a n e o u s r a t e s o f
Milliseconds 106 310 154 87 93 54 422 105 142 109 138 153 100 417 77 112 81 189 108 81 106 113 24 99 80
Character h d -d -h c h a n g e , a n d s h o w t h e
Milliseconds 28 129 84 239 177 116 73 58 84 88 95 76 81 31 86 33 65 84 51 111 26 99 66 52 132
Character 4 -4 a t - -t -a -e a t t h e y a r e c l o s
Milliseconds 0 285 66 62 60 162 123 125 119 7 75 63 425 86 32 80 69 7 90 63 32 135 27 123 48
Character e l y r e l a t e d t o t h e s l o e -e -o
Milliseconds 49 127 152 71 67 80 70 152 109 148 124 51 102 48 104 48 107 3 108 74 66 150 69 182 130
Character o p o -o - e o f a c u r v e a t a p
Milliseconds 461 127 135 136 274 102 69 35 94 70 38 46 77 597 80 155 175 106 64 227 85 88 46 76 191
Character o i n t P o n t h e c u r v e . W e i
Milliseconds 116 84 73 81 106 140 131 96 101 134 78 77 39 76 96 73 103 189 116 89 97 128 137 39 116
Character g i -i -g -i g i v e p r e c i s e d e v e l o p
Milliseconds 18 107 240 110 136 107 75 43 110 48 131 29 59 206 83 108 67 82 215 114 138 126 58 138 86
Character m e n t s o f t h e s e i m p o r t a n t
Milliseconds 203 97 72 60 140 83 82 84 37 175 72 69 124 35 36 104 149 135 144 39 127 107 81 16 111
Character c o n c d e p t s -s -t -p -e -d e p t s i n t h e
Milliseconds 75 77 73 65 100 37 56 59 104 196 116 133 141 128 103 95 37 91 72 58 77 115 36 73 49
Character n e x t c h a p t e r , f -f b u t f o r
Milliseconds 46 81 35 118 171 45 131 73 88 90 113 119 66 49 88 239 221 98 93 114 320 580 75 50 60
Character n e w w e -e -w - -w -e o w w e u s e a n i
Milliseconds 119 102 59 111 140 70 111 126 117 133 119 161 70 39 148 63 40 105 95 82 85 99 124 112 88
Character n f o r m a l a p p r o a c h s o y o u w
Milliseconds 98 81 52 51 100 123 308 100 220 81 99 117 99 16 172 79 99 148 68 102 152 125 72 27 60
Character i l l s 3 e h -h - -e -3 e e h o w t h e y
Milliseconds 81 126 123 100 43 141 101 55 119 274 115 132 128 77 100 76 72 101 20 80 103 39 73 42 59
Character l e a d n a t u r a l l y t o t h e m a i
Milliseconds 117 31 111 68 94 105 80 147 98 21 139 117 112 178 85 155 52 89 61 71 59 46 114 9 112
Character n i d e a o f t h i s c h a p t e r , t
Milliseconds 98 95 52 65 97 87 119 135 124 17 195 51 73 105 9 163 95 46 130 72 128 64 36 71 58
Character h e l i m i t . T h e i d e a o f a l
Milliseconds 80 39 60 113 67 161 127 80 116 136 108 73 52 65 48 72 107 66 65 94 88 42 79 55 240
Character i m i t y p -p - -y p l a y s a f o u n d a
Milliseconds 133 162 103 73 84 100 121 227 107 128 119 88 107 100 148 144 85 106 94 98 72 64 134 10 138
Character t i o n s r -r - -s a l r o l e t h r o g u -u
Milliseconds 98 73 62 48 76 117 177 149 127 140 176 117 51 441 76 124 79 79 212 73 63 73 51 0 394
Character -g u i g h o -o -h -g -i g h o u t c l -l c a -a -c a l
Milliseconds 107 166 0 56 69 177 226 121 120 125 126 107 304 68 29 88 109 85 489 113 72 250 107 72 478
Character c u l u s .
Milliseconds 212 159 188 151 98 92
WPM Timing
Seconds WPM
2.09 97.51
4.18 91.78
6.28 91.78
8.37 93.21
10.46 92.92
12.55 99.43
14.64 106.53
16.74 101.82
18.83 106.44
20.92 103.25
23.01 104.29
25.1 107.55
27.2 106.34
29.29 107.35
31.38 105.93
33.47 106.12
35.56 106.62
37.66 103.25
39.75 105.97
41.84 106.98
43.93 107.35
46.02 107.94
48.12 109.48
50.21 108.75
52.3 106.46
54.39 105.68
56.48 104.95
58.58 105.5
60.67 103.84
62.76 105.16
64.85 103.06
66.94 102.71
69.04 103.08
71.13 102.58
73.22 102.76
75.31 103.09
77.4 103.09
79.5 102.19
81.59 100.9
83.68 101.24
85.77 101.57
87.86 101.34
89.96 102.05
92.05 102.99
94.14 103.5
96.23 102.75
98.32 102.4
100.42 101.46
102.51 100.21
104.6 99.12