안녕하세요 (noogie13)

Race #5233

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Official speed 106.12 wpm (97.70 seconds elapsed during race)
Without ending ping 106.32 wpm (182 ms delay sending score to TypeRacer’s server)
Timerless 106.59 wpm (246 ms elapsed before first character typed; 97.27 seconds elapsed during race)
Timerless minus one 106.46 wpm, ignoring the first character typed
Race Start March 20, 2024 3:01:43pm UTC
Race Finish March 20, 2024 3:03:20pm UTC
Outcome Win (1 of 2)
Accuracy 96.7%
Points 286.52
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 hleps elps us understand how a change in one quantity is related to a chang ein achange in ahotnother. How does the speed of a falfalling object change as a function of time? How does the leve of ollevel of water in a barrel, chnange as a function of the amount of liquid poruured into it? We see change iocucurinring in nearly everything we observe in teh woteh he world asnd suniverse, and powerfulmo modern instruments help us see more and more. Itn this section we introduce the ideas of average and instantsanoueous rates of change, and show that ethhey are closely related tot he o the slop oe of a curve at a point P on the curve. We give precise developments of these important concepts in the next chapter, but forno now we use an informal approach so wilyou will se e how they lead naturally to themaihe main idea of this chatperhapter, the limit. The idea of a limit plays a foundaltitional 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 246 88 25 98 122 88 95 175 122 0 103 180 168 135 44 53 109 119 117 0 63 45 51 63 133
Character l e p s -l -e -p -s - e l p s u s u n d e r s t
Milliseconds 75 7 123 87 75 451 0 0 0 0 111 17 125 103 82 70 134 112 54 147 69 139 73 82 106
Character a n d h o w a c h a n g e i n o n e q
Milliseconds 104 35 111 111 21 58 73 106 137 100 63 71 75 40 96 36 74 31 83 79 44 87 36 176 111
Character u a n t i t y i s r e l a t e d t o a c
Milliseconds 73 91 81 110 15 114 60 150 39 141 155 21 53 70 83 66 82 124 111 8 39 147 8 169 162
Character h a n g e i n a -c -h -a -n -g - -e -i -n - -a c h a n
Milliseconds 45 67 70 81 48 0 61 72 120 0 360 0 0 0 0 0 0 0 0 0 0 57 74 48 82
Character g e i n a h o t -t -o -h n o t h e r . H o w
Milliseconds 62 31 117 44 61 122 0 70 97 32 154 112 346 139 38 73 66 45 49 66 138 114 109 91 109
Character d o e s t h e s p e e d o f a f a l -f -a
Milliseconds 35 56 79 61 108 14 75 24 130 20 65 72 223 401 121 55 59 131 0 135 133 23 32 452 0
Character -l f a l l i n g o b j e c t c h a n g e a s
Milliseconds 0 51 48 40 112 34 70 58 93 44 113 65 68 130 123 151 78 69 56 81 68 37 171 0 48
Character a f u n c t i o n o f t i m e ? H o w
Milliseconds 147 0 122 38 57 57 20 119 37 66 72 98 28 48 140 37 34 56 27 185 753 95 132 82 130
Character d o e s t h e l e v e o f -l -e -v -e - -o -f -
Milliseconds 31 65 91 19 123 15 46 68 96 29 36 67 88 110 0 99 106 454 0 0 0 0 0 0 0
Character o l -l -o l e v e l o f w a t e r i n a b
Milliseconds 34 333 152 100 166 59 76 89 207 197 47 67 132 0 34 31 103 44 103 27 73 87 14 149 17
Character a r r e l , - -, c h n -n a n g e a s a f
Milliseconds 86 70 114 91 146 235 150 192 106 188 51 69 142 312 124 63 145 39 177 52 54 154 0 122 64
Character u n c t i o n o f t h e a m o u n t o f
Milliseconds 5 60 59 108 54 53 61 115 42 90 148 25 68 44 140 47 62 101 59 133 102 40 73 101 54
Character l i q u i d p o r u -u -r u r e d i n t o i t
Milliseconds 126 75 136 88 58 137 179 61 29 129 23 251 98 110 80 54 135 85 45 62 70 54 143 54 73
Character ? W e s e e c h a n g e i -i o c u -u c u r
Milliseconds 162 204 180 166 186 0 46 117 144 120 48 44 76 74 24 118 15 233 151 87 160 405 88 77 121
Character i n -n -i r i n g i n n e a r l y e v e r y t
Milliseconds 48 52 379 98 269 56 45 110 99 45 43 133 79 68 73 17 96 81 91 22 90 120 59 59 76
Character h i n g w e o b s e r v e i n t e h w o
Milliseconds 88 59 64 92 149 10 66 119 61 140 154 78 61 163 104 132 25 69 86 0 69 0 163 0 65
Character -t -e -h - -w -o t e h -e -h - h e w o r l d a s -s
Milliseconds 377 0 0 0 0 0 12 78 0 208 425 0 0 100 47 163 17 110 51 103 57 127 38 100 280
Character n d s -s u n i v e r s e , a n d p o w e r f
Milliseconds 306 74 121 28 338 144 65 113 62 117 45 104 85 60 155 51 86 78 124 29 33 73 39 27 126
Character u l m o -o -m m o d e r n i n s t r u m e n t s
Milliseconds 68 66 173 107 308 98 155 43 38 143 153 61 89 204 58 83 67 81 44 58 166 69 75 70 67
Character h e l p u s s e e m o r e a n d m o r
Milliseconds 123 48 89 51 111 80 50 142 177 47 69 111 131 29 50 27 50 106 4 72 55 97 46 45 45
Character e . I t -t n t h i s s e c t i o n w e i
Milliseconds 34 104 136 90 176 320 124 95 27 50 21 79 142 13 60 161 119 49 66 60 105 31 138 175 55
Character n t r o d u c e t h e i d e a s o f a v e
Milliseconds 61 61 32 63 139 89 65 141 106 27 25 56 144 0 33 134 35 104 154 0 78 126 22 128 111
Character r a g e a n d i n s t a n t s -s a n o u -u -o e
Milliseconds 64 61 91 40 199 0 82 77 136 24 84 68 92 79 133 98 175 268 234 183 122 59 324 113 97
Character o u s r a t e s o f c h a n g e , a n d
Milliseconds 66 51 115 142 142 97 194 54 39 135 18 38 146 114 78 59 92 117 63 374 134 24 36 74 152
Character s h o w t h a t e t h -e -h h e y a r e c l
Milliseconds 60 75 33 72 137 16 64 41 64 99 29 62 6 622 0 74 69 56 104 15 54 43 155 56 77
Character o s e l y r e l a t e d t o t h e -o -t - -h
Milliseconds 113 46 50 44 95 115 76 40 77 73 29 75 115 139 10 56 88 46 58 23 147 484 0 0 0
Character -e - o t h e s l o p o -o - e o f a c u
Milliseconds 0 0 60 124 32 52 55 151 0 72 111 118 135 39 221 92 89 123 13 73 142 6 156 259 105
Character r v e a t a p o i n t P o n t h e c
Milliseconds 66 159 69 213 0 219 151 0 130 100 32 47 171 60 110 115 209 91 52 131 20 62 49 146 54
Character u r v e . W e g i v e p r e c i s e d e v
Milliseconds 85 66 164 25 92 131 257 278 289 76 91 90 32 144 37 76 72 187 102 82 133 557 152 114 172
Character e l o p m e n t s o f t h e s e i m p o r t
Milliseconds 47 72 469 198 244 166 0 465 83 167 61 63 92 43 31 49 88 75 113 28 94 81 27 60 110
Character a n t c o n c e p t s i n t h e n e x t
Milliseconds 66 27 95 118 74 59 32 101 146 63 84 92 81 31 68 134 37 41 98 108 32 44 78 62 163
Character c h a p t e r , b u t f o r n o -o -n n o w
Milliseconds 23 60 58 82 41 102 65 135 184 222 55 523 161 0 200 511 275 101 255 104 180 52 37 100 142
Character w e u s e a n i n f o r m a l a p p r o a
Milliseconds 23 57 142 53 68 59 166 0 94 167 35 59 84 75 61 85 84 85 262 73 61 106 97 73 147
Character c h s o w i l -w -i -l y o u w i l l s e -
Milliseconds 100 116 168 197 36 129 25 80 43 444 0 0 533 77 90 174 47 46 46 130 131 0 52 251 297
Character e h o w t h e y l e a d n a t u r a l l y
Milliseconds 77 120 25 44 110 129 137 65 54 61 98 52 27 55 88 172 73 16 92 119 24 72 54 105 30
Character t o t h e m a i -h -e -m -a -i h e m a i n i d
Milliseconds 139 79 21 160 0 78 34 178 84 83 473 0 0 0 0 152 104 108 71 86 71 55 251 278 50
Character e a o f t h i s c h a t p e r -h -a -t -p -e -r h
Milliseconds 116 51 125 70 79 119 12 72 32 53 170 91 72 71 63 11 124 30 441 0 0 0 0 0 63
Character a p t e r , t h e l i m i t . T h e i d e
Milliseconds 72 49 68 102 52 42 121 30 23 81 108 21 49 61 92 96 80 218 85 100 55 118 61 21 142
Character a o f a l i m i t p l a y s a f o u n
Milliseconds 41 172 28 64 180 0 138 31 60 66 86 139 123 30 29 76 111 67 142 262 173 44 63 39 133
Character d a l t i -i -t -l t i o n a l r o l e t h r o u
Milliseconds 62 51 54 124 99 193 107 127 140 71 64 74 129 52 182 77 68 102 112 175 44 49 88 28 61
Character g h o u t c a l c u l u s .
Milliseconds 146 350 166 58 104 170 144 28 57 92 83 58 106 193 70
WPM Timing
Seconds WPM
1.95 104.4
3.91 98.26
5.86 110.54
7.82 121.29
9.77 109.31
11.72 109.52
13.68 110.54
15.63 110.54
17.59 116
19.54 114.84
21.49 106.08
23.45 110.03
25.4 105.35
27.36 109.23
29.31 108.09
31.26 108.62
33.22 106.93
35.17 106.79
37.13 108.28
39.08 105.01
41.03 103.23
42.99 104.12
44.94 104.67
46.9 107.22
48.85 107.35
50.8 108.89
52.76 109.4
54.71 107.47
56.67 108
58.62 108.29
60.57 107.97
62.53 107.85
64.48 107.75
66.44 107.83
68.39 107.03
70.34 105.94
72.3 107.22
74.25 108.44
76.21 107.08
78.16 106.55
80.11 106.8
82.07 105.86
84.02 105.97
85.98 105.66
87.93 105.9
89.88 105.6
91.84 106.36
93.79 106.45
95.75 106.41
97.7 106.12