Diego (divarela)

Race #72601

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Official speed 108.36 wpm (95.68 seconds elapsed during race)
Without ending ping 108.52 wpm (140 ms delay sending score to TypeRacer’s server)
Timerless 108.85 wpm (294 ms elapsed before first character typed; 95.25 seconds elapsed during race)
Timerless minus one 108.73 wpm, ignoring the first character typed
Race Start December 15, 2023 6:52:36pm UTC
Race Finish December 15, 2023 6:54:12pm UTC
Outcome Win (1 of 2)
Accuracy 98.2%
Points 292.56
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 Calcususlus is a tool that helps uds udnderstand how a change in one quantity is related to a change in another. How does the speed of a falling object hanchange 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 occuring ring in naerly early everything we obeserve in the world and universe, and powerful modern instruments help us see more and mor. e. In this section we introduce the idea s of average and instanataneous rateess of change, and show that they are closely related to the slope of a cruvurve at a point P on the curve. We give precise developments of these important oconcepts in the next chapter, but for now uwewe use an informal approach so you will see how they lead naturally to the main idea of this cahapter, the limit. The idea of a limit plays a foundational role throughout calculus.
Timing
Character C a l c u s u s -s -u -s l u s i s a t o o l
Milliseconds 294 202 293 160 90 402 74 126 298 102 106 186 43 129 0 100 160 35 148 46 143 25 145 240 95
Character t h a t h e l p s u d -d s u d -d n d e r s t
Milliseconds 75 78 43 53 37 120 87 70 141 115 67 81 162 323 82 46 115 93 411 150 59 145 0 94 93
Character a n d h o w a c h a n g e i n o n e q
Milliseconds 95 0 131 79 102 67 40 101 82 108 80 81 89 88 47 77 29 68 63 52 264 93 89 87 101
Character u a n t i t y i s r e l a t e d t o a c
Milliseconds 82 121 51 178 63 134 73 76 79 61 82 139 83 168 76 107 33 162 78 140 63 69 101 125 92
Character h a n g e i n a n o t h e r . H o w d o e
Milliseconds 40 118 53 87 82 0 60 68 40 87 76 100 47 88 49 56 105 58 169 82 95 94 81 61 74
Character s t h e s p e e d o f a f a l l i n g
Milliseconds 59 48 89 52 112 0 127 80 80 158 160 47 88 69 80 59 170 168 35 81 148 63 100 190 50
Character o b j e c t h a n -n -a -h c h a n g e a s a
Milliseconds 136 111 81 51 150 95 37 207 89 87 262 121 82 203 50 156 82 88 65 72 105 142 53 385 152
Character f u n c t i o n o f t i m e ? H o w d o e
Milliseconds 181 47 174 151 115 0 17 53 83 96 140 81 230 53 62 46 196 56 208 223 160 216 163 41 122
Character s t h e l e v e l o f w a t e r i n a
Milliseconds 59 46 111 24 132 0 73 338 174 64 50 83 140 96 63 47 72 74 90 82 50 63 66 71 172
Character b a r r e l c h a n g e a s a f u n c t
Milliseconds 110 79 95 148 169 34 114 76 101 52 69 87 40 69 71 99 57 104 75 106 81 81 147 150 130
Character i o n o f t h e a m o u n t o f l i q u
Milliseconds 0 19 74 81 94 63 93 76 23 83 46 143 109 48 147 150 92 52 111 134 83 248 52 170 55
Character i d p o u r e d i n t o i t ? W e s e e
Milliseconds 47 115 89 255 74 39 130 53 138 17 116 88 101 67 143 115 81 208 61 153 143 90 86 101 109
Character c h a n g e o c c u r i n g - -g -n -i r i n g
Milliseconds 122 100 63 72 81 33 74 46 150 81 135 77 153 122 42 86 73 272 107 108 126 69 111 38 67
Character i n n a e r l y - -y -l -r -e -a e a r l y e v
Milliseconds 52 69 62 75 337 197 0 57 21 91 75 253 124 119 114 109 176 135 28 53 41 76 81 264 112
Character e r y t h i n g w e o b e -e s e r v e i n
Milliseconds 78 85 75 80 65 63 115 86 82 109 85 76 224 276 303 338 255 29 72 177 48 68 120 298 57
Character t h e w o r l d a n d u n i v e r s e , a
Milliseconds 130 121 46 104 176 101 87 96 101 72 60 65 115 72 87 129 52 36 75 80 94 76 47 80 163
Character n d p o w e r f u l m o d e r n i n s t r u
Milliseconds 73 90 38 78 46 45 43 72 128 19 63 357 142 48 52 196 82 25 64 73 67 62 58 143 46
Character m e n t s h e l p u s s e e m o r e a n
Milliseconds 163 104 92 143 70 69 103 148 46 165 106 102 81 100 123 73 177 87 84 49 70 33 52 238 75
Character d m o r . - -. e . I n t h i s s e c t i
Milliseconds 101 38 90 48 58 267 88 282 114 68 121 81 128 156 67 81 61 41 66 101 476 113 188 101 40
Character o n w e i n t r o d u c e t h e i d e a
Milliseconds 23 68 72 197 53 95 141 95 62 250 0 350 108 94 148 26 158 45 110 0 81 101 114 46 163
Character - s o f a v e r a g e a n d i n s t a n a
Milliseconds 351 53 70 81 77 83 109 168 95 121 88 101 75 40 87 90 86 40 82 80 46 136 84 81 289
Character -a t a n e o u s r a t e e s -s -e s o f c h a
Milliseconds 391 52 42 75 188 129 51 123 95 264 69 97 90 75 74 311 107 67 76 86 47 73 117 45 75
Character n g e , a n d s h o w t h a t t h e y a
Milliseconds 82 46 88 345 63 79 53 96 56 206 53 76 87 110 93 55 46 75 47 103 25 89 51 89 64
Character r e c l o s e l y r e l a t e d t o t h e
Milliseconds 66 74 41 168 0 141 57 45 55 93 80 273 43 82 113 46 88 149 38 130 35 85 66 42 41
Character s l o p e o f a c r u v -v -u -r u r v e a
Milliseconds 68 114 82 167 245 106 95 58 64 82 38 115 74 162 0 196 236 115 109 168 88 140 81 77 87
Character t a p o i n t P o n t h e c u r v e .
Milliseconds 139 91 68 106 95 61 25 82 63 68 187 144 112 94 30 72 52 58 93 93 89 88 175 65 79
Character W e g i v e p r e c i s e d e v e l o p m
Milliseconds 67 136 167 106 211 74 94 52 42 96 60 46 175 56 102 80 53 129 137 105 62 25 163 63 490
Character e n t s o f t h e s e i m p o r t a n t o
Milliseconds 110 102 50 89 55 74 95 69 66 58 42 198 19 86 74 110 87 52 76 121 92 0 167 79 195
Character -o c o n c e p t s i n t h e n e x t c h a
Milliseconds 372 81 100 48 68 385 176 94 108 357 109 87 27 107 82 130 186 124 57 198 121 68 229 63 121
Character p t e r , b u t f o r n o w u w e -e -w -u w
Milliseconds 60 149 80 75 93 54 103 53 96 52 130 34 93 45 97 83 81 112 209 63 66 296 103 112 76
Character e u s e a n i n f o r m a l a p p r o a c
Milliseconds 42 127 101 88 22 92 277 67 107 69 102 146 69 108 46 118 33 160 95 101 135 96 100 74 191
Character h s o y o u w i l l s e e h o w t h e
Milliseconds 17 123 330 52 70 45 78 80 58 54 47 21 163 77 107 109 135 86 86 48 82 51 98 68 86
Character y l e a d n a t u r a l l y t o t h e m
Milliseconds 46 89 169 95 100 101 46 117 74 109 57 130 78 0 119 117 71 178 67 72 82 61 51 65 216
Character a i n i d e a o f t h i s c a -a h a p t e
Milliseconds 221 72 77 40 100 90 154 46 164 208 63 66 82 39 41 89 58 125 105 418 144 105 102 81 122
Character r , t h e l i m i t . T h e i d e a o f
Milliseconds 74 41 60 110 39 103 44 89 63 158 41 129 106 54 96 97 87 58 83 114 304 129 156 58 83
Character a l i m i t p l a y s a f o u n d a t i
Milliseconds 51 90 116 37 54 158 142 312 108 82 126 53 101 75 101 69 113 68 81 67 130 182 28 91 0
Character o n a l r o l e t h r o u g h o u t c a l c
Milliseconds 30 72 458 103 87 177 59 171 66 81 61 62 126 22 69 100 57 83 77 452 86 243 82 107 154
Character u l u s .
Milliseconds 61 524 77 74 89
WPM Timing
Seconds WPM
1.91 31.35
3.83 65.84
5.74 71.07
7.65 87.79
9.57 95.32
11.48 103.47
13.4 110.19
15.31 110.52
17.22 105.91
19.14 105.98
21.05 104.32
22.96 107.13
24.88 109.02
26.79 111.53
28.7 111.2
30.62 111.31
32.53 109.56
34.45 106.6
36.36 106.27
38.27 103.78
40.19 104.22
42.1 106.32
44.01 107.15
45.93 107.65
47.84 107.11
49.75 106.6
51.67 106.14
53.58 106.83
55.5 105.74
57.41 105.14
59.32 106.81
61.24 107.98
63.15 106.98
65.06 107.16
66.98 107.68
68.89 107.82
70.8 108.81
72.72 107.43
74.63 107.41
76.54 107.39
78.46 107.22
80.37 107.35
82.29 108.06
84.2 108.46
86.11 108.56
88.03 108.79
89.94 108.87
91.85 109.22
93.77 109.16
95.68 108.36