Raymond (rng9512)

Race #233

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Official speed 107.93 wpm (96.06 seconds elapsed during race)
Without ending ping 108.20 wpm (236 ms delay sending score to TypeRacer’s server)
Timerless 108.53 wpm (294 ms elapsed before first character typed; 95.53 seconds elapsed during race)
Timerless minus one 108.40 wpm, ignoring the first character typed
Race Start October 18, 2023 2:42:36am UTC
Race Finish October 18, 2023 2:44:12am UTC
Outcome Win (1 of 5)
Opponents 2. abishiek_a (105.87 wpm)
Accuracy 97.9%
Points 291.42
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 Calculuiss is a toool that helps us undderstand how a chance geange in one quanitytity is realted trelated to a change in another. How does the speed of a falling object hcange 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 occcurring in nearly everything we observe in the world and universe, and powerful modern intstruments help us see more and more. In this section we introduce the ideas of average and instantaneous rates of change, adnd show that they are closely reallated to the slope of a curve a a pot a point P on the curve. We give precise developments of these important concepts in the next chatpter, but for now we use an infroormal approach so wyyou will see how they lead naturally to the main idea if of this cahpthapter, the limit. The idea of a limit plays a foundational role throughout calculus.
Timing
Character C a l c u l u i s -s -i s i s a t o o o -o l
Milliseconds 294 203 125 96 347 155 157 598 34 265 140 109 62 110 64 123 79 94 80 46 157 175 647 190 63
Character t h a t h e l p s u s u n d -d d e r s t a n
Milliseconds 47 94 32 63 47 31 109 47 126 93 30 46 109 79 46 220 0 296 587 143 63 96 77 78 16
Character d h o w a c h a n c e - -e -c -n g e -e -g -a a
Milliseconds 94 48 63 80 30 79 95 95 80 0 125 16 80 62 47 268 142 143 156 33 76 254 141 143 534
Character n g e i n o n e q u a n i t y -y -t -i t i t y
Milliseconds 48 78 82 46 94 63 111 63 63 62 64 481 47 144 109 113 76 143 300 141 160 141 79 93 82
Character i s r e a l t e d t -t - -d -e -t -l -a -e -r r e l
Milliseconds 91 126 110 78 64 63 47 30 110 64 159 47 110 109 520 31 32 31 31 32 31 33 202 78 95
Character a t e d t o a c h a n g e i n a n o t h
Milliseconds 124 110 156 204 96 94 94 47 300 94 93 64 78 64 94 78 48 62 47 92 80 32 94 31 80
Character e r . H o w d o e s t h e s p e e d o f
Milliseconds 63 50 76 65 153 156 16 109 81 79 93 47 77 64 17 79 94 47 94 64 157 126 48 93 62
Character a f a l l i n g o b j e c t h c a n g e
Milliseconds 94 78 125 110 62 93 157 78 48 61 62 93 94 142 63 80 175 47 142 0 109 32 64 61 63
Character - -e -g -n -a -c -h c h a n g e a s a f u n c t i
Milliseconds 223 516 31 31 31 33 46 95 96 77 63 32 79 47 95 66 78 109 143 17 125 141 32 176 12
Character o n o f t i m e ? H o w d o e s t h e
Milliseconds 49 77 78 79 94 77 63 67 44 65 234 126 128 125 158 78 94 62 124 82 75 62 31 95 79
Character l e v e l o f w a t e r i n a b a r r e
Milliseconds 31 93 142 61 96 80 124 50 109 126 78 64 109 50 45 79 47 79 190 94 110 205 124 157 94
Character l c h a n g e a s a f u n c t i o n o f
Milliseconds 46 99 88 48 127 15 77 48 647 94 78 64 125 124 47 95 155 77 156 32 31 64 64 93 80
Character t h e a m o u n t o f l i q u i d p o u
Milliseconds 63 95 0 110 32 157 143 130 90 127 47 46 95 79 78 63 93 127 95 79 109 124 157 455 91
Character r e d i n t o i t ? W e s e e c h a n g
Milliseconds 109 80 142 48 61 47 79 64 79 94 77 208 92 96 156 81 94 47 174 47 94 15 140 15 64
Character e o c c c -c u r r i n g i n n e a r l y e
Milliseconds 93 63 111 125 157 220 406 156 79 140 66 43 47 62 48 49 97 92 32 48 79 47 79 83 91
Character v e r y t h i n g w e o b s e r v e i n t
Milliseconds 109 127 62 96 62 109 95 79 32 62 95 79 80 109 125 313 65 78 172 142 81 78 62 95 64
Character h e w o r l d a n d u n i v e r s e , a n
Milliseconds 89 21 93 63 62 16 142 15 76 82 29 79 63 61 144 75 16 124 64 93 79 61 47 77 64
Character d p o w e r f u l m o d e r n i n t -t s t r
Milliseconds 94 46 47 155 48 15 79 124 79 126 110 345 48 96 142 48 66 89 64 77 79 315 49 45 62
Character u m e n t s h e l p u s s e e m o r e a
Milliseconds 111 157 93 66 63 62 80 63 110 47 111 108 47 111 95 78 77 143 30 96 46 32 46 64 79
Character n d m o r e . I n t h i s s e c t i o n
Milliseconds 47 95 62 30 63 62 64 79 63 517 157 78 47 79 48 47 94 83 56 63 173 47 15 48 62
Character w e i n t r o d u c e t h e i d e a s o f
Milliseconds 94 78 79 16 78 76 47 109 107 80 125 63 80 62 80 77 62 16 140 109 77 94 95 95 95
Character a v e r a g e a n d i n s t a n t a n e o u
Milliseconds 76 93 111 113 79 141 64 63 62 78 63 79 64 46 64 47 80 126 141 534 115 213 143 157 64
Character s r a t e s o f c h a n g e , a d -d n d
Milliseconds 95 78 158 94 94 78 77 47 95 92 77 97 75 77 77 220 66 123 17 80 156 518 171 48 31
Character s h o w t h a t t h e y a r e c l o s e l
Milliseconds 82 92 62 48 62 62 63 95 47 81 95 47 126 17 77 92 63 79 92 79 62 140 32 46 127
Character y r e a l -l -a l a t e d t o t h e s l o p
Milliseconds 79 48 46 77 48 43 394 142 219 47 47 78 141 47 80 44 94 46 31 94 78 63 392 155 139
Character e o f a c u r v e a a p o -o -p - -a - t
Milliseconds 128 44 110 78 82 92 109 79 79 47 93 94 62 108 122 112 107 95 31 266 157 141 155 160 106
Character a p o i n t P o n t h e c u r v e .
Milliseconds 34 90 110 581 46 47 51 75 50 156 768 80 30 96 75 31 63 93 64 49 108 94 111 47 109
Character W e g i v e p r e c i s e d e v e l o p m e
Milliseconds 155 93 62 95 80 93 46 66 140 80 62 171 111 79 46 79 93 162 58 95 15 190 30 190 48
Character n t s o f t h e s e i m p o r t a n t c o
Milliseconds 126 94 46 158 312 33 94 78 50 46 109 94 51 168 96 155 171 48 63 78 78 61 77 126 79
Character n c e p t s i n t h e n e x t c h a t -t p
Milliseconds 49 77 63 141 79 95 93 51 77 63 46 62 78 63 77 62 172 53 87 111 92 62 94 530 186
Character t e r , b u t f o r n o w w e u s e a
Milliseconds 78 94 79 95 94 79 63 47 80 62 95 32 93 61 66 76 124 392 62 49 96 45 78 65 63
Character n i n f r o -o -r o r m a l a p p r o a c h s
Milliseconds 77 93 64 77 32 254 138 264 159 173 51 77 95 63 48 109 95 157 142 139 110 107 80 109 126
Character o w y -y -w y o u w i l l s e e h o w t h
Milliseconds 62 30 92 126 328 124 203 93 63 49 76 64 155 127 45 62 63 156 80 63 47 78 48 79 50
Character e y l e a d n a t u r a l l y t o t h e
Milliseconds 92 62 96 63 33 92 80 79 109 95 78 113 63 110 109 125 110 94 78 80 79 170 346 78 78
Character m a i n i d e a i f - -f -i o f t h i s c
Milliseconds 46 111 78 79 93 80 93 159 44 46 110 49 92 312 140 172 189 61 64 62 48 79 47 79 79
Character a h p t -t -p -h -a h a p t e r , t h e l i m i t
Milliseconds 95 65 108 173 268 142 173 174 187 82 61 112 111 78 47 96 61 63 79 63 48 62 79 126 143
Character . T h e i d e a o f a l i m i t p l a
Milliseconds 110 84 138 125 46 62 111 79 125 63 63 63 78 108 31 157 15 79 125 95 111 47 62 141 76
Character y s a f o u n d a t i o n a l r o l e t h
Milliseconds 64 111 94 63 141 31 111 46 141 47 62 92 79 31 48 206 141 141 141 128 184 78 62 64 92
Character r o u g h o u t c a l c u l u s .
Milliseconds 61 48 46 47 109 95 79 49 93 159 94 32 110 93 112 110 141 49
WPM Timing
Seconds WPM
1.92 43.72
3.84 53.09
5.76 72.87
7.68 81.2
9.61 64.96
11.53 70.79
13.45 67.81
15.37 63.24
17.29 70.09
19.21 78.07
21.13 83.47
23.05 80.16
24.98 84.56
26.9 88.34
28.82 90.36
30.74 90.96
32.66 94.06
34.58 94.73
36.5 96.32
38.42 96.81
40.35 98.15
42.27 100.79
44.19 102.11
46.11 102.8
48.03 104.93
49.95 106.42
51.87 107.34
53.79 107.52
55.72 107.9
57.64 107.64
59.56 108.4
61.48 108.13
63.4 107.7
65.32 106.18
67.24 106
69.16 106.53
71.09 106.86
73.01 107.82
74.93 107.3
76.85 108.05
78.77 107.55
80.69 106.63
82.61 107.78
84.53 107.74
86.46 106.88
88.38 105.77
90.3 106.58
92.22 107.22
94.14 107.46
96.06 107.93