Mach (mach1_speed)

Race #728

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Official speed 105.41 wpm (98.36 seconds elapsed during race)
Without ending ping 105.63 wpm (209 ms delay sending score to TypeRacer’s server)
Timerless 105.94 wpm (287 ms elapsed before first character typed; 97.86 seconds elapsed during race)
Timerless minus one 105.82 wpm, ignoring the first character typed
Race Start July 14, 2024 7:56:16am UTC
Race Finish July 14, 2024 7:57:55am UTC
Outcome Win (1 of 3)
Opponents 2. strongly_typed_meteorite (89.94 wpm)
Accuracy 98.9%
Points 284.61
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 CacCaclculus is a tool that helps us understand how a change in one quantity is related to a change in another. How does sthe 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 amoutn nt of liquid poruured into it? We see change occruuring ring in nearly everything we observe in the mworld 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 slop ofe of a curve at a point P on the curve. We give precise developments of these important concepts in the nect xt 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.
Timing
Character C a c -c -a -C C a c -c l c u l u s i s a t o o
Milliseconds 287 235 345 1130 156 188 440 141 172 393 188 94 126 126 126 93 31 63 79 79 61 110 63 79 125
Character l t h a t h e l p s u s u n d e r s t a n
Milliseconds 141 79 79 78 47 47 31 63 94 63 156 126 78 330 125 78 63 126 63 141 48 124 581 126 62
Character d h o w a c h a n g e i n o n e q u a
Milliseconds 94 64 63 109 31 94 47 94 79 79 78 78 78 48 78 95 62 32 125 0 94 94 126 109 79
Character n t i t y i s r e l a t e d t o a c h a
Milliseconds 156 141 78 95 173 219 110 125 48 124 48 94 16 125 110 126 78 93 32 141 0 110 299 94 125
Character n g e i n a n o t h e r . H o w d o e s
Milliseconds 47 266 78 95 78 63 63 47 78 125 220 141 125 31 79 94 157 157 392 188 110 79 63 31 78
Character s -s t h e s p e e d o f a f a l l i n g
Milliseconds 94 377 78 94 47 95 109 126 126 110 156 314 109 95 63 94 47 94 63 46 126 142 47 110 94
Character o b j e c t c h a n g e a s a f u n c t i
Milliseconds 407 267 126 94 156 126 63 110 93 126 63 126 47 172 94 48 93 63 63 78 94 157 63 110 47
Character o n o f t i m e ? H o w d o e s t h e
Milliseconds 33 76 32 109 63 47 110 78 94 95 565 203 204 79 110 47 141 79 78 47 126 110 63 62 63
Character l e v e l o f w a t e r i n a b a r r e
Milliseconds 125 48 125 47 47 94 95 31 95 31 140 64 125 16 63 94 62 63 110 47 125 126 110 126 141
Character l c h a n g e a s a f u n c t i o n o f
Milliseconds 94 94 79 94 93 80 47 61 110 48 64 93 78 64 77 79 158 62 126 30 48 94 16 313 94
Character t h e a m o u t n - -n -t n t o f l i q u
Milliseconds 80 62 78 63 62 189 78 142 63 156 0 188 283 157 156 173 94 63 78 110 17 109 141 94 109
Character i d p o r u -u -r u r e d i n t o i t ? W e
Milliseconds 142 78 48 109 126 78 156 299 141 158 78 140 126 32 109 48 125 78 125 64 109 377 204 376 204
Character s e e c h a n g e o c c r u -u -r u r i n g
Milliseconds 93 95 157 109 63 94 126 298 78 110 48 93 110 95 125 235 110 376 157 267 125 80 46 110 78
Character - -g -n -i r i n g i n n e a r l y e v e r y t
Milliseconds 251 173 157 157 204 110 47 124 79 266 79 110 94 78 79 46 64 141 62 94 158 94 62 79 93
Character h i n g w e o b s e r v e i n t h e m -m
Milliseconds 315 360 63 79 93 64 78 62 110 63 141 110 31 126 94 63 95 78 47 62 111 93 63 109 298
Character w o r l d a n d u n i v e r s e , a n d p
Milliseconds 95 109 94 95 63 94 62 80 62 47 832 141 125 78 110 48 109 63 47 79 63 62 63 94 172
Character o w e r f u l m o d e r n i n s t r u m e n t
Milliseconds 141 47 31 48 156 64 141 109 78 111 63 140 33 61 32 94 79 78 126 157 110 282 78 110 16
Character s h e l p u s s e e m o r e a n d m o
Milliseconds 157 78 361 125 48 156 94 94 110 79 111 155 110 63 157 78 47 47 48 94 47 94 32 93 63
Character r e . I n t h i s s e c t i o n w e i n
Milliseconds 109 16 94 79 157 95 109 157 62 47 94 126 78 204 142 109 63 31 47 47 110 63 93 173 126
Character t r o d u c e t h e i d e a s o f a v e r
Milliseconds 62 126 62 267 141 94 158 78 78 94 15 64 93 31 158 94 78 79 93 49 93 46 110 141 32
Character a g e a n d i n s t a n t a n e o u s r a t
Milliseconds 126 15 63 78 126 298 126 94 109 63 79 126 94 46 79 439 94 126 110 125 141 33 108 95 94
Character e s o f c h a n g e , a n d s h o w t h
Milliseconds 32 204 125 110 79 94 392 125 79 78 62 64 47 93 64 94 46 78 80 46 94 48 109 79 110
Character a t t h e y a r e c l o s e l y r e l a t
Milliseconds 31 31 62 110 32 110 78 94 173 78 31 111 109 79 142 46 47 94 142 78 141 267 157 109 95
Character e d t o t h e s l o p o f -f -o - e o f
Milliseconds 93 157 63 126 31 142 78 109 31 94 64 78 172 78 142 125 110 220 141 172 157 79 140 110 63
Character a c u r v e a t a p o i n t P o n t
Milliseconds 94 47 110 220 189 140 47 158 46 95 125 220 94 188 172 79 78 110 94 158 94 109 94 63 78
Character h e c u r v e . W e g i v e p r e c i s e
Milliseconds 94 63 47 109 63 79 266 63 125 95 188 141 94 110 94 48 93 47 111 62 314 160 91 78 63
Character d e v e l o p m e n t s o f t h e s e i m
Milliseconds 79 110 141 110 63 46 142 94 125 48 141 16 250 142 109 125 32 141 78 63 110 78 47 110 141
Character p o r t a n t c o n c e p t s i n t h e n
Milliseconds 125 126 32 157 62 63 109 79 110 47 31 329 188 79 78 110 62 79 79 47 63 94 62 78 143
Character e c t - -t -c x t c h a p t e r , b u t f o
Milliseconds 0 203 109 126 282 157 157 141 125 63 125 94 63 95 93 126 47 47 79 172 94 79 78 297 111
Character r n o w w e u s e a n i n f o r m a l
Milliseconds 79 63 109 31 63 94 94 63 94 63 78 47 79 94 16 126 77 80 62 251 188 94 110 63 125
Character a p p r o a c h s o y o u w i l l s e e
Milliseconds 78 78 94 126 94 16 251 79 94 63 63 109 126 124 48 78 141 48 156 157 79 109 157 94 63
Character h o w t h e y l e a d n a t u r a l l y t
Milliseconds 126 63 46 220 157 47 126 47 94 126 47 62 126 16 110 94 299 125 219 94 63 126 125 109 79
Character o t h e m a i n i d e a o f t h i s c
Milliseconds 63 94 63 94 47 78 110 47 110 47 62 94 63 142 94 63 110 63 77 95 47 62 32 110 93
Character h a p t e r , t h e l i m i t . T h e i d
Milliseconds 95 31 298 126 125 33 93 62 95 31 78 79 78 156 126 95 78 93 95 188 125 64 94 93 32
Character e a o f a l i m i t p l a y s a f o u
Milliseconds 157 95 46 140 95 62 95 62 95 126 124 143 0 155 158 157 78 125 95 78 94 78 94 79 78
Character n d a t i o n a l r o l e t h r o u g h o u t
Milliseconds 141 64 94 62 16 31 16 110 78 95 78 47 172 31 95 140 111 0 235 156 346 93 110 79 94
Character c a l c u l u s .
Milliseconds 79 110 109 125 110 110 157 78 110 47
WPM Timing
Seconds WPM
1.97 0
3.93 15.25
5.9 56.93
7.87 62.53
9.84 81.74
11.8 87.43
13.77 89.76
15.74 89.21
17.7 90.15
19.67 90.28
21.64 94.83
23.61 94.04
25.57 99.01
27.54 101.52
29.51 101.26
31.47 100.27
33.44 99.04
35.41 97.26
37.38 95.03
39.34 92.11
41.31 92.66
43.28 94.55
45.25 93.36
47.21 95.06
49.18 95.89
51.15 96.9
53.11 98.05
55.08 98.69
57.05 99.71
59.02 99.84
60.98 100.55
62.95 101.8
64.92 102.04
66.88 100.83
68.85 100.74
70.82 100.99
72.79 101.39
74.75 101.78
76.72 102.14
78.69 101.26
80.65 101.92
82.62 102.54
84.59 102.85
86.56 103.29
88.52 103.7
90.49 104.23
92.46 104.74
94.42 104.97
96.39 105.57
98.36 105.41