Khoa (khoanguyendang_1234)

Race #1185

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Official speed 76.75 wpm (135.09 seconds elapsed during race)
Without ending ping 77.03 wpm (181 ms delay sending score to TypeRacer’s server)
Timerless 77.19 wpm (285 ms elapsed before first character typed; 134.62 seconds elapsed during race)
Timerless minus one 77.10 wpm, ignoring the first character typed
Race Start October 15, 2023 1:49:44pm UTC
Race Finish October 15, 2023 1:51:59pm UTC
Outcome Win (1 of 5)
Opponents 2. debugraghav (63.55 wpm)
Accuracy 95.4%
Points 207.22
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 Callcuculus ia s a tolool that helps uns undersattand how a change in one wuaquantity is realtelated to ca change in anotyheehrrther. How does the speed of a falling ojebject hangchange as a function of time? How does thtee level of water in a braarrel change as a function of the amount of liquid pioured into it? We see change ocrcruurring ainin nreaaly early everything were observer in ti in the world an und unicverse, and powerful modenrrn instruments help us see more and more. In this essection we intrdoduce sthe ideas of average and instantaneous rates of change, and sho whtaw aththat they are closely realtelated to the slope of a curve at a pointt P P on the couruvrve. We lgive precseise developments of these important concepts in the nesxxt, chapetter, but for now eewe euuse an informal apoproach so you will see how they lead unnnnaturally to the manin in idea of this chapter, the limit. The idea of a limit plays a foundational role thorrooughughout calculus.
Timing
Character C a l l c u -u -c -l c u l u s i a - -a s a t
Milliseconds 285 116 57 118 101 116 237 105 95 64 83 82 124 45 98 85 146 103 358 114 62 89 91 111 142
Character o l o -o -l o l t h a t h e l p s u n -n s u
Milliseconds 82 169 187 184 113 88 161 130 75 98 32 69 61 53 83 82 169 81 311 122 213 331 45 111 101
Character n d e r s a t -t $t a n d h o w a c h a n g e
Milliseconds 169 17 78 119 144 293 76 255 124 38 101 101 54 85 39 35 98 90 118 153 72 86 54 128 68
Character i n o n e w u a -a -u $q u a n t i t y i s
Milliseconds 132 89 75 109 83 117 78 94 113 60 118 189 112 102 170 300 99 263 218 155 67 141 131 99 111
Character r e a l t e -e -t -l -a l a t e d t o c -c a c h
Milliseconds 323 86 68 20 127 66 218 111 101 320 128 75 51 75 166 91 146 38 119 197 232 71 93 92 102
Character a n g e i n a n o t y h e -e -h -y e h r r -r -r -h
Milliseconds 115 130 103 22 74 55 115 69 77 86 64 153 0 39 143 151 117 109 171 18 69 119 126 134 102
Character -e -t t h e r . H o w d o e s t h e s p e e
Milliseconds 208 125 586 85 85 80 35 187 126 134 127 135 229 104 62 50 81 54 109 45 120 97 90 105 150
Character d o f a f a l l i n g o j e -e -j b j e c t
Milliseconds 44 43 86 54 136 212 160 542 75 79 140 126 99 46 33 364 298 156 148 132 121 179 60 77 204
Character h a n g -g -n -a -h c h a n g e a s a f u n c
Milliseconds 148 375 96 82 101 176 114 110 139 71 79 54 124 42 72 128 203 81 93 191 120 130 92 383 135
Character t i o n o f t i m e ? H o w d o e s t h
Milliseconds 204 59 63 113 107 97 61 112 94 89 92 78 227 138 148 211 61 117 75 92 49 88 64 89 91
Character t e -e -t e l e v e l o f w a t e r i n a
Milliseconds 76 112 265 110 93 110 80 46 139 54 83 121 122 98 146 336 122 78 97 123 58 115 77 126 33
Character b r a -a -r a r r e l c h a n g e a s a f
Milliseconds 142 154 93 140 219 145 39 49 145 83 119 168 141 62 89 80 28 69 117 81 85 127 188 136 143
Character u n c t i o n o f t h e a m o u n t o f
Milliseconds 58 73 159 195 59 44 122 94 52 76 118 78 114 438 136 116 148 213 115 178 58 101 75 100 105
Character l i q u i d p i -i o u r e d i n t o i t ?
Milliseconds 277 94 108 118 66 80 132 214 81 325 151 67 64 127 108 110 121 46 129 81 129 127 72 318 146
Character W e s e e c h a n g e o c r -r c r u -u -r u r
Milliseconds 154 216 133 184 200 122 15 158 115 51 118 36 90 145 82 76 229 240 101 165 123 232 121 62 43
Character r i n g a i n -n -i -a i n n r e a a l y - -y -l
Milliseconds 147 37 43 107 101 116 41 92 289 118 93 148 52 117 73 115 33 67 53 102 273 260 289 128 95
Character -a -a -e -r e a r l y e v e r y t h i n g w e r -r
Milliseconds 137 130 127 114 66 15 58 76 168 86 221 207 107 335 107 140 66 59 153 42 138 69 271 86 367
Character -e e o b s e r v e r i n t -t - -n -i - -r i -i
Milliseconds 128 125 456 336 128 180 165 63 171 125 89 12 63 93 110 21 209 108 123 129 119 116 249 295 102
Character i n t h e w o r l d a n u n -n -u - d u n
Milliseconds 120 82 92 90 77 66 95 86 88 154 141 103 141 63 99 133 179 84 232 120 119 52 51 120 55
Character i c -c v e r s e , a n d p o w e r f u l m o
Milliseconds 146 79 336 90 67 116 75 119 171 152 65 108 95 90 52 89 112 87 52 306 106 87 140 52 83
Character d e n r -r -n r n i n s t r u m e n t s h e l p
Milliseconds 82 136 115 129 216 128 67 102 226 123 79 138 149 88 47 183 94 69 95 149 134 312 147 37 157
Character u s s e e m o r e a n d m o r e . I n
Milliseconds 103 46 93 115 530 117 178 62 103 61 78 72 90 328 100 65 109 88 53 27 58 148 145 106 151
Character t h i s e s -s -e s e c t i o n w e i n t r
Milliseconds 157 0 164 36 67 127 73 313 98 265 82 50 114 264 28 90 127 150 42 143 133 107 33 75 76
Character d -d o d u c e s -s t h e i d e a s o f a v
Milliseconds 395 268 123 63 202 184 57 188 91 253 51 91 58 69 142 67 77 87 575 119 77 109 136 460 154
Character e r a g e a n d i n s t a n t a n e o u s r
Milliseconds 207 85 117 213 62 145 55 121 73 38 126 63 118 149 98 129 86 442 112 181 393 37 167 136 487
Character a t e s o f c h a n g e , a n d s h o w
Milliseconds 47 125 33 119 93 240 138 87 204 100 41 123 55 19 136 112 60 116 109 85 164 50 41 101 25
Character h t a -a -t -h -w - w a t h -h -t -a t h a t t h e y
Milliseconds 117 58 87 201 134 114 123 124 35 91 97 116 70 267 86 136 41 102 69 38 77 60 90 80 61
Character a r e c l o s e l y r e a l t e -e -t -l -a l a
Milliseconds 98 37 107 34 109 162 117 148 49 84 108 192 123 218 80 77 38 153 36 220 119 121 123 110 44
Character t e d t o t h e s l o p e o f a c u r
Milliseconds 136 0 635 129 99 64 113 90 294 164 211 172 94 470 84 136 186 132 54 138 45 166 59 141 67
Character v e a t a p o i n t t P -P - -t P o n
Milliseconds 252 104 36 138 111 56 205 148 85 151 181 84 68 34 111 134 254 125 110 74 134 135 267 122 136
Character t h e c o u r -r -u -o u v -v r v e . W e l -l g
Milliseconds 0 155 38 124 163 76 38 137 216 123 111 106 282 247 74 175 83 236 207 192 199 107 248 226 47
Character i v e p r e c s e -e -s i s e d e v e l o p m e
Milliseconds 76 110 45 69 130 89 93 405 165 110 169 141 83 76 36 120 300 64 173 68 79 133 73 303 82
Character n t s o f t h e s e i m p o r t a n t c o
Milliseconds 125 48 102 120 135 64 127 45 95 41 170 87 112 70 125 136 110 53 162 69 99 294 188 133 94
Character n c e p t s i n t h e n e s x -x -s x t , -
Milliseconds 125 164 254 113 122 103 223 181 51 139 0 126 37 104 47 100 51 201 128 124 113 168 90 134 351
Character -, c h a p e t -t -e t e r , b u t f o r n o
Milliseconds 136 113 144 50 134 45 161 35 331 107 80 55 110 33 128 90 42 106 38 303 86 118 45 171 61
Character w e e -e -e w e e u -u -e u s e a n i n f o r
Milliseconds 66 87 147 236 136 216 106 35 87 156 98 189 127 43 47 33 107 63 110 122 67 107 417 168 123
Character m a l a p o -o p r o a c h s o y o u w i l
Milliseconds 138 120 66 115 114 49 82 475 270 122 168 51 202 71 140 52 125 75 81 60 74 118 82 96 36
Character l s e e h o w t h e y l e a d u n -n n -n
Milliseconds 161 61 108 73 201 138 269 35 52 110 120 48 121 30 71 99 66 42 160 64 135 92 397 167 184
Character n -n -u n a t u r a l l y t o t h e m a n i n
Milliseconds 316 164 362 240 89 88 129 106 59 109 172 178 102 78 84 100 48 103 43 112 77 130 101 30 112
Character - -n -i -n i n i d e a o f t h i s c h a p
Milliseconds 124 181 131 117 128 162 62 101 188 114 67 116 117 117 75 143 57 60 29 101 85 194 56 115 46
Character t e r , t h e l i m i t . T h e i d e a
Milliseconds 157 93 115 68 121 49 85 52 88 112 51 182 69 61 305 205 50 123 113 67 140 102 77 75 162
Character o f a l i m i t p l a y s a f o u n d a
Milliseconds 401 60 160 124 131 77 89 178 70 27 143 75 114 43 210 196 214 198 146 274 52 48 170 72 56
Character t i o n a l r o l e t h o r -r -o r o o u g h -h
Milliseconds 147 44 78 112 100 74 161 159 38 210 95 56 352 22 178 0 325 119 64 107 0 20 72 124 311
Character -g -u -o u g h o u t c a l c u l u s .
Milliseconds 122 112 125 256 84 66 206 66 157 159 138 57 140 158 68 159 397 99 119
WPM Timing
Seconds WPM
2.7 53.3
5.4 68.84
8.11 74.03
10.81 76.62
13.51 71.06
16.21 76.99
18.91 69.8
21.61 74.4
24.32 73.04
27.02 71.51
29.72 73.89
32.42 75.14
35.12 76.87
37.82 78.36
40.53 78.47
43.23 79.12
45.93 79.43
48.63 76
51.33 76.21
54.04 74.4
56.74 73.6
59.44 73.08
62.14 73.77
64.84 74.58
67.54 75.68
70.25 76.02
72.95 75.51
75.65 75.98
78.35 75.81
81.05 76.1
83.75 76.51
86.46 75.65
89.16 75.78
91.86 75.77
94.56 75.13
97.26 75.01
99.97 75.15
102.67 75.86
105.37 75.73
108.07 75.73
110.77 75.72
113.47 75.51
116.18 76.64
118.88 75.71
121.58 75.7
124.28 76.76
126.98 77.11
129.68 77.54
132.39 77.05
135.09 76.75