d.phuong (juliap)

Race #1484

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Official speed 92.61 wpm (111.95 seconds elapsed during race)
Without ending ping 92.43 wpm (-481 ms delay sending score to TypeRacer’s server)
Timerless 92.81 wpm (463 ms elapsed before first character typed; 111.97 seconds elapsed during race)
Timerless minus one 92.70 wpm, ignoring the first character typed
Race Start March 17, 2024 3:00:02am UTC
Race Finish March 17, 2024 3:01:54am UTC
Outcome Win (1 of 4)
Accuracy 97.0%
Points 250.04
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 understan dhow d how a change in one quantity is related to a chagne in hangein in another. how HOw ow does the psespeed of a fallingob object change as a function of time? How does the level of water in a barrel change as a function of the amount of liuid iquid poured in to to it? We see chnge oxhchange occuring ring in nearly everything we observe in the world and universe, and powerful modern intsstruments help us see more and more. IN thisn this section we introduce the ideas of average and instanteaneous tarates of change, and show that they are closely related to the slope of a curve at a point P on the cruurve. We give precised developemtnments of these important concpeepts in the next chapter, but for now we use an informal appraooach so you will see how they lead naturally to th emain he main idea of this chapter, the limit. The idea of a limit plays a foundatinoal onal role thorroughout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 463 102 138 115 100 152 172 41 95 87 99 53 118 67 116 60 153 164 57 84 113 83 49 17 81
Character e l p s u s u n d e r s t a n d h o w - -w
Milliseconds 182 93 47 132 83 114 71 98 93 74 32 84 103 59 105 47 117 133 0 87 126 19 96 1391 82
Character -o -h -d - d h o w a c h a n g e i n o n e
Milliseconds 169 121 114 146 168 135 95 83 50 100 105 65 134 88 92 117 116 56 81 86 80 54 99 80 52
Character q u a n t i t y i s r e l a t e d t o a
Milliseconds 118 76 88 131 85 133 68 202 127 139 158 101 93 94 51 122 194 99 53 81 119 87 42 38 111
Character c h a g n e i n -h -a -g -n -e - -i -n - h a n g e
Milliseconds 71 87 90 78 183 0 85 28 96 80 39 520 0 0 0 0 0 0 0 0 113 71 115 49 54
Character i n -n -i i n a n o t h e r . h o w $H -o -w -
Milliseconds 149 118 300 110 172 94 85 71 47 117 62 76 95 95 57 96 74 196 101 81 88 709 0 0 0
Character O w - -w -O o w d o e s t h e p s e -e -s -p s
Milliseconds 58 207 201 290 77 135 220 48 121 42 106 66 77 49 283 122 215 150 70 69 177 323 99 130 40
Character p e e d o f a f a l l i n g o b -b -o o b j
Milliseconds 128 51 128 120 130 58 80 120 64 115 97 69 107 112 159 60 62 216 135 312 102 113 94 78 150
Character e c t c h a n g e a s a f u n c t i o n
Milliseconds 65 181 189 101 102 77 68 97 87 60 122 84 96 42 148 68 118 326 59 76 201 31 33 53 78
Character o f t i m e ? H o w d o e s t h e l e v
Milliseconds 83 54 96 76 61 80 87 198 189 185 149 49 125 90 97 81 56 71 108 36 130 192 79 51 82
Character e l o f w a t e r i n a b a r r e l c
Milliseconds 99 199 84 153 100 81 99 56 98 112 98 36 92 93 233 470 158 168 138 163 121 110 84 152 85
Character h a n g e a s a f u n c t i o n o f t h
Milliseconds 155 79 131 65 53 83 137 65 14 167 0 300 272 59 70 181 51 49 23 109 84 74 85 78 71
Character e a m o u n t o f l i u i d -i -u -i -d - i q
Milliseconds 82 134 62 100 79 88 51 120 134 146 155 43 36 147 246 44 111 97 735 0 0 0 0 214 123
Character u i d p o u r e d i n t o - -o -t - t o i
Milliseconds 85 63 118 65 107 361 320 110 73 98 182 62 92 74 140 65 123 295 98 122 111 116 82 69 79
Character t ? W e s e e c h n g e o $x -h -n -g -e - -o h
Milliseconds 109 200 232 478 186 136 63 72 161 80 100 107 177 42 79 84 70 595 0 0 0 0 0 0 136
Character -h -x c h a n g e o c c u r i n g - -g -n -i r i n
Milliseconds 282 100 99 105 44 146 26 75 59 78 100 116 102 98 71 65 98 106 328 84 131 122 95 117 83
Character g i n n e a r l y e v e r y t h i n g w e
Milliseconds 40 80 93 56 66 130 85 70 117 132 103 97 112 55 166 65 67 161 35 76 99 33 159 69 74
Character o b s e r v e i n t h e w o r l d a n d
Milliseconds 90 359 117 174 104 183 204 65 65 118 44 73 48 101 49 113 73 63 90 113 83 114 80 102 102
Character u n i v e r s e , a n d p o w e r f u l m
Milliseconds 49 149 334 68 102 228 106 88 75 88 51 110 85 35 138 42 84 55 31 49 178 38 147 75 95
Character o d e r n i n t s -s -t s t r u m e n t s h e l
Milliseconds 62 50 139 105 124 85 73 94 48 118 334 151 84 114 53 84 267 149 99 89 64 64 163 121 95
Character p u s s e e m o r e a n d m o r e . I
Milliseconds 26 134 113 44 105 115 156 176 67 35 62 56 51 70 75 73 77 54 65 66 72 48 114 67 196
Character N t h i s -N - -t -h -i -s n t h i s s e c t i o
Milliseconds 67 87 67 115 52 51 917 0 0 0 0 0 199 179 0 107 66 50 95 79 44 191 208 47 69
Character n w e i n t r o d u c e t h e i d e a s
Milliseconds 62 102 152 48 102 131 69 102 0 58 125 132 150 62 69 103 85 49 100 46 96 184 23 80 150
Character o f a v e r a g e a n d i n s t a n t e -e a
Milliseconds 70 99 95 156 133 84 116 79 118 72 64 148 31 119 120 108 89 20 80 65 107 196 145 354 80
Character n e o u s t a -a -t r a t e s o f c h a n g e
Milliseconds 103 350 104 101 117 82 374 26 299 115 35 47 100 67 67 49 69 82 70 209 108 97 161 43 37
Character , a n d s h o w t h a t t h e y a r e
Milliseconds 119 52 116 98 58 113 39 134 74 22 150 70 117 30 81 467 85 115 51 98 80 34 64 75 61
Character c l o s e l y r e l a t e d t o t h e s l
Milliseconds 123 84 150 33 68 118 77 105 114 51 100 87 61 37 94 134 81 37 72 82 69 75 103 85 113
Character o p e o f a c u r v e a t a p o i n t
Milliseconds 379 138 449 119 167 131 91 175 19 101 132 75 165 64 113 84 62 44 127 57 93 83 186 70 48
Character P o n t h e c r u -u -r u r v e . W e g
Milliseconds 116 130 118 103 96 53 37 128 36 131 195 184 171 236 114 186 64 186 79 107 113 432 214 115 89
Character i v e p r e c i s e d - -d d e v e l o p e m
Milliseconds 99 117 78 54 72 82 60 191 130 103 67 163 0 477 104 100 64 166 185 72 81 182 50 103 81
Character t n -n -t -m -e m e n t s o f t h e s e i m p o
Milliseconds 149 89 261 346 253 642 175 88 94 87 52 65 70 81 82 99 79 87 97 88 51 67 86 82 79
Character r t a n t c o n c p e -e -p e p t s i n t h e
Milliseconds 67 164 40 144 119 98 124 140 71 156 130 16 454 97 129 99 115 56 47 83 73 49 91 75 84
Character n e x t c h a p t e r , b u t f o r n o
Milliseconds 63 69 66 162 153 97 101 86 101 101 132 181 51 61 102 121 50 99 84 96 73 112 24 126 31
Character w w e u s e a n i n f o r m a l a p p r
Milliseconds 70 117 84 72 56 159 81 63 81 103 90 63 98 87 66 98 68 115 85 118 95 135 88 111 233
Character a o -o -a o a c h s o y o u w i l l s e e
Milliseconds 101 36 365 85 276 120 86 85 101 159 56 81 110 70 38 104 67 64 177 105 98 68 53 156 40
Character h o w t h e y l e a d n a t u r a l l y t
Milliseconds 114 118 0 55 109 69 105 85 60 106 78 49 86 106 71 59 292 183 89 79 123 99 96 135 135
Character o t h e m a i n -h - -e -m -a -i -n - h e m a i
Milliseconds 49 65 85 70 175 0 71 84 83 86 80 482 0 0 0 0 0 0 0 75 94 65 52 86 84
Character n i d e a o f t h i s c h a p t e r , t
Milliseconds 79 66 71 62 165 26 109 89 101 96 82 113 31 20 121 69 93 85 112 94 151 60 7 72 104
Character h e l i m i t . T h e i d e a o f a l
Milliseconds 57 99 46 31 66 170 81 430 220 120 149 83 86 81 197 50 149 56 101 79 66 103 84 80 84
Character i m i t p l a y s a f o u n d a t i n o a l
Milliseconds 65 153 80 88 80 39 110 71 165 68 100 78 108 121 92 48 56 50 80 130 47 103 19 97 134
Character - -l -a -o -n o n a l r o l e t h o r -r -o r o u
Milliseconds 83 336 133 119 117 128 190 67 128 102 131 135 79 134 86 99 117 67 97 52 435 84 227 107 103
Character g h o u t c a l c u l u s .
Milliseconds 128 118 318 109 88 137 164 82 98 136 33 163 60 377 90
WPM Timing
Seconds WPM
2.24 91.11
4.48 112.55
6.72 75.03
8.96 87.09
11.2 92.18
13.43 84.86
15.67 84.22
17.91 79.05
20.15 76.82
22.39 77.17
24.63 79.9
26.87 84.41
29.11 86.16
31.35 86.13
33.59 88.61
35.83 86.08
38.06 85.75
40.3 83.37
42.54 80.95
44.78 80.12
47.02 82.69
49.26 83.8
51.5 84.82
53.74 85.97
55.98 86.61
58.22 87.19
60.45 87.14
62.69 88.81
64.93 89.26
67.17 88.43
69.41 89.9
71.65 90.94
73.89 90.95
76.13 91.74
78.37 91.26
80.61 91.11
82.85 89.81
85.08 89.28
87.32 89.19
89.56 90.17
91.8 91.37
94.04 90.98
96.28 91.98
98.52 92.45
100.76 92.18
103 92.86
105.24 93.39
107.48 93.34
109.71 92.75
111.95 92.5