Kai zheng (nebs_2ge)

Race #3130

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Official speed 82.41 wpm (125.81 seconds elapsed during race)
Without ending ping 82.54 wpm (194 ms delay sending score to TypeRacer’s server)
Timerless 82.78 wpm (367 ms elapsed before first character typed; 125.25 seconds elapsed during race)
Timerless minus one 82.68 wpm, ignoring the first character typed
Race Start March 18, 2024 3:28:30pm UTC
Race Finish March 18, 2024 3:30:36pm UTC
Outcome No win (5 of 5)
Opponents 1. chickenhelmet (113.67 wpm)
2. kelvinjay (104.94 wpm)
3. kingclem (86.29 wpm)
4. sterlingwolf (85.30 wpm)
Accuracy 96.5%
Points 222.51
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 Calculaus is st a tool that heklps us understand how a chhaange in one qutntiantity is related to a change in another. How does the speed of a falling object change as a fucntnction of time? HOw dow does the level of water in a bearrel change as a function of the amount of liquid ourepoured itnto it? We see change occuring rinrrring in cnearly veverything we observe in the world and universe, and piwpowerful modern instruments help us see more and more. In this sections we introdducuce the ideaso of average and instantenaneous rates of change, and hsow wshow that they are closely related to the sloepe of a curve at a point P on the curve. We give perecise developments of these iportpmmportant concetppts int the next cahhapter, but for now we use an informa l appeoaroach so you will see how they lead naturaly ly to hthe main idea of this chapter, the limit. The idea of a limit pallays a foundational role throughout calculu.s.
Timing
Character C a l c u l a -a u s i s s t - -t -s a t o o
Milliseconds 367 82 33 145 112 118 117 443 192 49 92 106 101 67 186 149 83 249 142 134 118 106 65 78 143
Character l t h a t h e k -k l p s u s u n d e r s t
Milliseconds 141 142 141 75 41 57 35 263 154 91 554 220 27 142 66 76 66 75 190 128 75 126 74 117 117
Character a n d h o w a c h h a -a -h a n g e i n o
Milliseconds 123 110 100 109 74 38 50 79 106 78 185 65 124 30 408 188 81 103 116 109 126 22 64 103 261
Character n e q u t -t n t i -i -t -n a n t i t y i s r e
Milliseconds 55 32 62 167 67 280 332 172 107 65 431 129 142 197 113 184 90 397 120 67 133 75 85 149 56
Character l a t e d t o a c h a n g e i n a n o t
Milliseconds 78 132 142 134 134 75 89 49 95 142 110 188 83 61 84 49 55 62 54 41 105 71 95 84 100
Character h e r . H o w d o e s t h e s p e e d o
Milliseconds 90 67 49 95 91 224 68 73 67 117 79 81 70 34 136 31 79 66 135 31 129 131 133 85 79
Character f a f a l l i n g o b j e c t c h a n g e
Milliseconds 43 93 64 218 202 65 95 139 102 83 58 40 223 71 267 107 100 166 77 141 66 49 77 73 60
Character a s a f u c n t -t -n -c n c t i o n o f t
Milliseconds 101 139 61 93 79 86 331 86 255 112 133 420 106 497 198 72 141 59 22 42 128 116 75 34 108
Character i m e ? H O w d -d - -w -O o w d o e s t h e
Milliseconds 67 41 49 245 132 209 49 134 57 152 337 134 162 141 220 55 84 275 57 65 49 70 110 66 55
Character l e v e l o f w a t e r i n a b e -e a
Milliseconds 62 83 49 119 55 136 99 181 52 86 55 85 118 100 55 78 37 42 111 74 110 127 245 400 61
Character r r e l c h a n g e a s a f u n c t i o n
Milliseconds 160 134 49 93 100 132 60 90 31 87 41 39 152 42 84 307 94 167 107 134 92 134 55 16 59
Character o f t h e a m o u n t o f l i q u i d
Milliseconds 137 124 99 60 234 56 60 66 169 83 82 108 151 442 118 157 99 42 166 76 114 187 133 57 110
Character o u r e -e -r -u -o p o u r e d i t -t n t o i t ?
Milliseconds 580 129 99 91 255 122 139 121 316 8 88 85 83 205 89 99 67 477 174 117 141 114 170 125 208
Character W e s e e c h a n g e o c c u r i n g -
Milliseconds 125 364 195 66 167 158 108 94 154 84 33 102 47 61 42 152 108 125 116 64 137 58 117 100 276
Character -g -n -i -r r i n -n r -r r -r -i r i n g i n c -c n e
Milliseconds 140 148 119 117 134 108 47 372 97 82 299 187 437 122 254 35 77 67 134 38 68 237 268 183 106
Character a r l y v -v e v e r y t h i n g w e o b s e
Milliseconds 108 41 179 86 77 374 323 85 100 169 66 265 136 92 91 66 66 85 124 57 69 204 63 116 127
Character r v e i n t h e w o r l d a n d u n i v
Milliseconds 116 193 41 117 54 67 71 108 38 66 52 117 76 149 23 163 66 117 100 66 67 239 52 154 148
Character e r s e , a n d p i w -w -i -p p o w e r f u l
Milliseconds 108 66 117 66 475 118 115 121 44 68 161 21 207 291 115 124 423 75 83 144 57 182 5 90 162
Character m o d e r n i n s t r u m e n t s h e l p u
Milliseconds 138 83 125 142 16 85 109 62 78 39 129 124 82 193 101 73 24 161 92 256 179 268 199 116 175
Character s s e e m o r e a n d m o r e . I n t
Milliseconds 63 69 134 174 161 47 215 52 101 48 85 133 31 129 50 36 43 58 44 85 126 178 62 85 122
Character h i s s e c t i o n s - -s w e i n t r o d
Milliseconds 68 77 47 94 186 158 107 159 64 8 47 97 91 394 99 142 45 68 95 62 69 152 16 56 345
Character d u c -c -u -d u c e t h e i d e a s o -o o f
Milliseconds 57 110 126 377 377 137 212 55 55 45 117 48 74 50 101 331 166 71 93 159 490 135 158 83 102
Character a v e r a g e a n d i n s t a n t e n -n -e a n
Milliseconds 44 433 98 91 108 73 66 95 352 72 114 78 31 56 51 137 82 68 93 204 383 282 115 331 125
Character e o u s r a t e s o f c h a n g e , a n d
Milliseconds 505 427 79 133 101 364 75 100 67 415 154 133 65 60 290 86 75 56 77 33 101 108 90 110 47
Character h s o w -h -s -o -w - w -w s h o w t h a t t h
Milliseconds 61 136 7 56 91 85 659 0 0 0 0 583 349 158 77 49 76 92 212 39 91 47 70 356 77
Character e y a r e c l o s e l y r e l a t e d t o
Milliseconds 41 67 206 249 137 67 71 138 90 160 23 118 77 82 67 157 60 158 70 181 125 141 67 114 78
Character t h e s l o e -e p e o f a c u r v e a
Milliseconds 100 66 108 49 67 127 125 221 156 460 182 90 50 87 70 66 99 86 80 128 67 160 57 143 212
Character t a p o i n t P o n t h e c u r v e .
Milliseconds 113 73 110 83 150 16 206 45 66 50 280 155 150 49 68 105 77 49 51 160 81 94 168 54 128
Character W e g i v e p e -e r e c i s e d e v e l o
Milliseconds 100 184 167 99 132 68 100 39 61 72 118 314 53 43 150 109 82 93 100 234 133 133 74 127 158
Character p m e n t s o f t h e s e i p o r t -t -r -o -p
Milliseconds 75 454 140 96 128 150 117 87 68 61 140 66 84 176 117 118 25 184 46 94 142 300 141 346 147
Character p m -m -p m p o r t a n t c o n c e t p -p -t p t s
Milliseconds 314 68 376 217 301 50 91 159 150 55 60 102 90 176 84 185 107 108 150 100 413 111 182 18 197
Character i n t -t t h e n e x t c a h -h -a h a p t e
Milliseconds 114 70 61 85 445 254 118 32 85 49 38 84 154 151 23 196 72 38 488 108 215 76 59 133 117
Character r , b u t f o r n o w w e u s e a n
Milliseconds 50 83 108 281 68 83 68 150 64 79 49 99 75 27 91 97 51 78 158 82 76 57 144 125 102
Character i n f o r m a - l a p p e o a -a -o -e r o a c h
Milliseconds 90 54 79 133 39 249 138 260 385 198 100 114 9 237 189 215 92 355 140 148 118 58 100 125 56
Character s o y o u w i l l s e e h o w t h e y
Milliseconds 163 81 92 31 145 106 15 68 150 48 147 166 67 88 119 142 92 213 35 94 66 133 57 77 101
Character l e a d n a t u r a l y - -y l y t o h -h
Milliseconds 49 81 75 68 101 93 139 77 386 89 109 100 50 238 36 363 542 253 240 171 177 30 135 141 513
Character t h e m a i n i d e a o f t h i s c h a
Milliseconds 247 70 61 76 64 78 90 42 52 142 102 115 75 58 132 66 84 109 33 56 62 49 133 83 178
Character p t e r , t h e l i m i t . T h e i d e a
Milliseconds 132 134 82 66 84 83 151 48 84 60 429 290 99 122 101 110 100 204 70 93 33 89 93 108 94
Character o f a l i m i t p a -a l l -l a y s a f
Milliseconds 85 132 83 87 41 126 4 72 145 109 106 60 123 111 562 254 168 453 129 84 73 95 64 102 141
Character o u n d a t i o n a l r o l e t h r o u g h o
Milliseconds 76 33 134 91 100 109 88 4 81 111 100 151 116 65 144 73 58 167 93 72 153 47 128 100 218
Character u t c a l c u l u . -. s .
Milliseconds 49 73 77 186 148 56 135 100 135 98 287 317 106 144
WPM Timing
Seconds WPM
2.52 57.23
5.03 62
7.55 79.48
10.06 78.69
12.58 67.72
15.1 77.9
17.61 85.16
20.13 87.63
22.65 85.31
25.16 84.89
27.68 84.98
30.19 86.24
32.71 88.78
35.23 89.25
37.74 85.84
40.26 84.06
42.78 83.04
45.29 80.01
47.81 79.07
50.32 81.31
52.84 81.98
55.36 81.07
57.87 82.11
60.39 83.66
62.9 84.13
65.42 83.28
67.94 82.49
70.45 81.93
72.97 80.91
75.49 80.92
78 80.46
80.52 81.22
83.03 81.51
85.55 82.48
88.07 82.85
90.58 83.06
93.1 81.72
95.62 81.33
98.13 80.95
100.65 80.72
103.16 81.66
105.68 80.62
108.2 81.52
110.71 81.29
113.23 80.76
115.75 81.9
118.26 82.29
120.78 81.67
123.29 82.63
125.81 82.41