Viro (cbengs)

Race #265

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Official speed 90.81 wpm (114.17 seconds elapsed during race)
Without ending ping 91.07 wpm (197 ms delay sending score to TypeRacer’s server)
Timerless 91.31 wpm (296 ms elapsed before first character typed; 113.68 seconds elapsed during race)
Timerless minus one 91.20 wpm, ignoring the first character typed
Race Start March 23, 2025 5:55:16am UTC
Race Finish March 23, 2025 5:57:10am UTC
Outcome No win (3 of 3)
Opponents 1. _ehsaas_gupta (127.08 wpm)
Accuracy 95.7%
Points 245.18
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 understand how a change in one quantity is realtelated to a change in another. how How does the speed of a falling object change as faf fucntionnction of time? Hodw w does the leve ofl of water in a barrel change as a function of the amoun tt of liquied poured into it? We see change occuring inring in nearly everhytiything we observe in tehe wthe world and unviverse, an powerd powerful modern niinstruments hel p use see see more and more. In this ecsection we trinintrudcoduce the ieas oddeaseas of average and instante=aenous reous rates of change, and show that they are closely related to the slope of a curve at ap apoint P on the surcurvel W. We give preiccise delvvelopment sts of those im=ese important concepts in the next chapter, but for now we use an informal approach so you will show ee how they lead naturally in to the main idea of this chapter, the limitt. The idea of a limit plays a fuoundational roule 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 296 150 98 112 117 98 104 118 348 125 56 76 49 111 63 76 410 139 77 49 104 27 58 34 48
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 85 68 132 76 8 97 90 173 238 140 33 133 76 69 106 82 78 104 54 57 82 44 61 62 139
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 113 82 84 97 85 89 79 53 70 62 153 76 112 97 125 153 125 105 133 47 119 69 77 118 63
Character r e a l t e -e -t -l -a l a t e d t o a c h a
Milliseconds 49 119 89 69 14 167 77 152 126 125 118 174 28 78 75 152 49 98 55 63 90 77 90 78 83
Character n g e i n a n o t h e r . h o w - -w -o -h H
Milliseconds 97 76 78 68 55 70 56 55 98 118 69 104 57 55 99 75 146 69 14 174 159 126 118 139 285
Character o w d o e s t h e s p e e d o f a f a
Milliseconds 98 56 119 54 118 56 70 42 97 56 48 181 97 203 75 160 162 89 104 15 103 35 132 7 70
Character l l i n g o b j e c t c h a n g e a s f -f
Milliseconds 118 153 90 84 41 49 90 77 167 62 56 187 77 91 69 85 61 105 62 49 69 98 41 419 195
Character a f - -f f u c n t i o n -n -o -i -t -n -c n c t i o
Milliseconds 346 278 63 293 124 76 77 113 81 98 112 48 62 42 181 118 139 132 153 111 175 76 181 48 63
Character n o f t i m e ? H o d w - -w -d w d o e s
Milliseconds 21 85 96 41 91 69 63 76 49 243 120 200 84 62 174 97 181 125 125 70 21 153 28 104 63
Character t h e l e v e o f -f -o - l o f w a t e r
Milliseconds 41 113 33 107 33 62 70 84 75 91 187 105 139 132 125 181 92 116 49 77 76 70 76 98 69
Character i n a b a r r e l c h a n g e a s a
Milliseconds 42 56 76 56 34 105 56 48 76 139 59 101 70 118 91 48 112 62 56 90 56 76 85 61 98
Character f u n c t i o n o f t h e a m o u n t -t -
Milliseconds 159 112 125 77 173 42 91 13 84 98 55 98 76 76 63 69 70 83 98 90 125 113 19 335 119
Character t o f l i q u i e -e d p o u r e d i n t o
Milliseconds 88 56 126 83 42 69 69 146 105 83 84 362 86 48 241 0 619 71 75 159 37 54 70 76 63
Character i t ? W e s e e c h a n g e o c c u r i
Milliseconds 84 90 77 318 153 169 111 62 159 77 147 69 97 77 76 83 70 57 41 90 69 125 105 111 69
Character n g i n -n -i - -g -n -i r i n g i n n e a r l y
Milliseconds 84 104 28 49 69 201 133 132 132 155 151 97 119 42 84 61 70 69 63 201 70 56 70 55 90
Character e v e r h y t i -i -t -y -h y t h i n g w e o b
Milliseconds 56 56 111 90 97 79 6 82 112 215 125 132 119 180 56 111 35 105 27 98 55 56 91 152 84
Character s e r v e i n t e h e w -w - -e -h -e -t t h e
Milliseconds 90 56 76 167 118 126 69 63 62 35 83 35 97 28 28 236 126 132 133 110 160 459 70 76 83
Character w o r l d a n d u n v -v i v e r s e , a n
Milliseconds 71 89 77 104 91 55 70 83 502 90 110 153 77 328 160 41 125 90 104 91 119 68 56 91 118
Character p o w e r -r -e -w -o -p - d p o w e r f u l m o d
Milliseconds 112 145 42 21 111 76 132 132 126 146 145 29 91 118 173 98 27 91 167 41 84 62 111 105 48
Character e r n n i -i -n i n s t r u m e n t s h e l -
Milliseconds 125 91 139 139 279 453 151 127 283 56 56 76 126 69 146 76 77 70 55 42 62 84 90 299 348
Character p u s e s e e -e -e -s - -e s e e m o r e a
Milliseconds 355 86 80 63 62 77 105 34 167 153 119 131 140 131 84 98 55 160 55 91 76 42 50 75 90
Character n d m o r e . I n t h i s e c -c -e s e c t
Milliseconds 91 91 34 104 105 21 55 119 77 145 57 54 35 98 76 55 58 82 188 214 127 62 22 82 224
Character i o n w e t r i n -n -i -r -t i n t r u d c -c -d -u
Milliseconds 47 49 62 104 35 49 125 78 137 70 56 167 132 139 118 155 40 42 138 92 89 153 160 119 131
Character o d u c e t h e i e a s o -o - -s -a -e d d e a
Milliseconds 230 91 173 77 97 98 479 77 69 56 93 227 56 118 70 82 188 133 139 146 138 35 63 70 69
Character s -s -a -e -d e a s o f a v e r a g e a n d i
Milliseconds 146 195 118 139 155 124 396 140 71 122 85 49 450 84 125 91 125 76 90 63 91 41 90 57 48
Character n s t a n t e $= -= a e -e n o u s r -r - -s -u -o e o
Milliseconds 69 44 68 76 49 111 445 396 266 151 160 329 278 69 125 83 84 104 132 125 139 132 153 28 161
Character u s r a t e s o f c h a n g e , a n d s
Milliseconds 89 70 69 56 108 88 82 55 91 97 90 58 130 70 111 42 104 56 84 62 48 84 83 49 153
Character h o w t h a t t h e y a r e c l o s e l y
Milliseconds 56 71 69 76 83 78 34 70 54 201 70 104 56 63 35 69 76 49 125 63 139 35 35 97 83
Character r e l a t e d t o t h e s l o p e o f
Milliseconds 57 55 56 82 105 84 90 166 63 105 42 62 49 76 83 37 179 63 138 141 82 14 120 54 69
Character a c u r v e a t a p - -p a -a p o i n t
Milliseconds 64 111 62 125 83 299 77 84 63 91 47 91 125 153 223 131 147 159 335 618 278 90 72 40 97
Character P o n t h e s u r -r -u -s c u r v e l W -W -
Milliseconds 125 91 159 63 77 62 85 69 41 112 138 99 165 133 138 42 120 69 187 83 99 35 116 174 119
Character -l . W e g i v e p r e i c -c -i c i s e d e
Milliseconds 132 232 87 105 63 70 193 105 91 55 50 68 112 63 48 111 259 137 487 86 88 50 96 173 167
Character l v -v -l v e l o p m e n t - -t s -s t s o f t
Milliseconds 91 104 320 125 63 90 294 179 139 175 152 70 118 97 432 138 56 321 103 90 70 112 77 75 105
Character h o s e i m -m = -= -i - -e -s -o e s e i m p o r t
Milliseconds 76 76 49 35 63 104 111 167 15 97 145 146 139 146 314 111 69 118 84 83 91 83 125 42 153
Character a n t c o n c e p t s i n t h e n e x t
Milliseconds 69 84 77 96 91 43 42 75 69 105 91 83 21 104 65 60 35 97 56 42 83 42 160 63 69
Character c h a p t e r , b u t f o r n o w w e u
Milliseconds 118 63 83 104 56 92 82 62 56 104 160 43 56 116 56 98 64 54 78 55 110 90 56 91 263
Character s e a n i n f o r m a l a p p r o a c h s
Milliseconds 77 35 70 104 64 69 90 76 29 110 58 110 77 61 106 96 83 119 97 62 84 69 56 90 28
Character o y o u w i l l s h o w - -w -o -h e e h o
Milliseconds 83 63 69 70 77 55 63 84 48 125 90 57 77 83 62 63 277 132 133 145 43 152 83 105 49
Character w t h e y l e a d n a t u r a l l y i n
Milliseconds 69 78 90 64 83 82 55 91 34 57 117 42 57 89 84 125 56 83 63 126 89 78 89 76 90
Character - -n -i t o t h e m a i n i d e a o f t h
Milliseconds 153 112 368 111 98 97 16 110 70 42 96 69 91 49 83 125 49 125 56 58 116 50 96 125 55
Character i s c h a p t e r , t h e l i m i t -t t .
Milliseconds 91 42 111 55 77 69 91 598 152 51 103 77 140 68 71 75 41 63 98 97 146 293 346 98 77
Character T h e i d e a o f a l i m i t p l a y s
Milliseconds 153 76 83 56 76 63 126 55 62 91 55 70 42 111 63 97 125 111 111 70 76 139 35 223 125
Character a f u -u o u n d a t i o n a l r o u -u l e
Milliseconds 7 153 104 264 112 445 167 69 154 14 131 104 112 62 56 146 70 90 167 90 125 633 203 96 77
Character t h r o u g h o u t c a l c u l u s .
Milliseconds 166 56 111 28 78 110 56 62 91 22 82 105 69 111 57 103 90 368 84 111
WPM Timing
Seconds WPM
2.28 84.08
4.57 107.73
6.85 115.61
9.13 107.73
11.42 113.51
13.7 107.73
15.98 111.11
18.27 103.79
20.55 98.1
22.83 96.7
25.12 96.98
27.4 101.16
29.68 101.87
31.97 100.22
34.25 101.25
36.54 98.54
38.82 97.69
41.1 98.39
43.39 96.53
45.67 95.38
47.95 94.59
50.24 92.92
52.52 91.39
54.8 92.19
57.09 92.28
59.37 90.55
61.65 88.56
63.94 86.9
66.22 87.35
68.5 84.78
70.79 86.8
73.07 89.01
75.35 90.13
77.64 88.72
79.92 88.44
82.2 88.32
84.49 87.21
86.77 86.02
89.05 84.89
91.34 85.79
93.62 87.54
95.9 88.71
98.19 88.97
100.47 90.06
102.76 90.27
105.04 90.82
107.32 91.02
109.61 90.65
111.89 90.41
114.17 90.81