Kai حيادي (famboy32)

Race #1198

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Official speed 135.64 wpm (76.44 seconds elapsed during race)
Without ending ping 135.94 wpm (171 ms delay sending score to TypeRacer’s server)
Timerless 135.98 wpm (18 ms elapsed before first character typed; 76.25 seconds elapsed during race)
Timerless minus one 135.82 wpm, ignoring the first character typed
Race Start November 12, 2023 3:43:03am UTC
Race Finish November 12, 2023 3:44:19am UTC
Outcome Win (1 of 5)
Opponents 2. viscoseoce (125.07 wpm)
3. davidbird764 (115.90 wpm)
4. bb__ (109.07 wpm)
Accuracy 97.6%
Points 366.22
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 CAlalculus is a tool that helps us understand how a change in one quantity is related to caacha change in another. How does the speed of a falling object change as af u function of time? How does the lefvevel 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 powefulrful modern instruments help us sees moresee more and more. In this asection we introduce the ideas of average and instnaaanteaneous rates of change, and show that they are closely relate d to the slope of a scucurve at a point P on the curve. We giev cpve pcrerecise developments of these important occoncept s in the next chapter, but for now we use an informam l approach so you will see how they lead naturally to the main indedea of this chapter, the limit. The idea of a limilt t plays a funoundational role throughout calculus.
Timing
Character C A l -l -A a l c u l u s i s a t o o l t h
Milliseconds 18 314 140 266 140 95 78 94 127 169 234 77 47 78 62 47 46 78 30 111 125 159 109 47 64
Character a t h e l p s u s u n d e r s t a n d h o
Milliseconds 16 62 47 64 96 78 33 78 46 62 63 47 140 128 62 139 30 109 46 62 110 46 62 110 32
Character w a c h a n g e i n o n e q u a n t i t
Milliseconds 63 47 64 109 45 34 93 31 79 32 31 94 32 47 96 32 32 63 110 64 140 78 249 171 158
Character y i s r e l a t e d t o c a -a -c a c h a -a
Milliseconds 109 92 60 111 46 77 47 77 63 79 31 110 46 47 63 62 78 47 234 111 45 330 63 61 218
Character -h -c c h a n g e i n a n o t h e r . H o w
Milliseconds 125 141 46 31 63 15 95 47 32 47 61 32 63 31 62 16 81 93 30 78 64 63 109 93 31
Character d o e s t h e s p e e d o f a f a l l
Milliseconds 124 63 63 93 47 47 62 78 32 109 48 48 79 124 110 16 110 62 48 31 95 16 93 78 124
Character i n g o b j e c t c h a n g e a s a f u
Milliseconds 63 46 32 31 79 46 142 48 121 96 31 109 46 47 63 31 31 63 46 48 78 46 96 15 158
Character -u - -f f u n c t i o n o f t i m e ? H o w
Milliseconds 189 141 126 94 48 78 110 32 126 63 15 31 78 65 61 48 61 61 32 32 202 108 140 139 79
Character d o e s t h e l e f v e -e -v -f v e l o f
Milliseconds 93 62 48 107 47 31 63 47 62 31 93 46 111 15 30 281 123 111 46 62 124 236 94 79 30
Character w a t e r i n a b a r r e l c h a n g e
Milliseconds 63 76 46 95 48 47 61 48 48 33 110 94 95 79 94 95 47 125 110 32 48 63 63 15 64
Character a s a f u n c t i o n o f t h e a m o u
Milliseconds 62 47 78 46 110 93 77 94 47 127 64 32 16 62 65 61 47 48 49 46 62 48 61 62 78
Character n t o f l i q u i d p o u r e d i n t o
Milliseconds 127 62 32 63 79 45 47 16 93 125 33 157 125 110 33 61 94 92 110 62 47 16 94 46 93
Character i t ? W e s e e c h a n g e o c c u r r i
Milliseconds 47 60 299 280 159 186 78 279 141 188 112 60 76 16 94 48 16 78 109 47 111 110 47 126 157
Character n g i n n e a r l y e v e r y t h i n g w
Milliseconds 31 31 63 77 16 79 77 46 62 64 77 33 62 32 108 79 47 96 76 125 61 62 15 78 62
Character e o b s e r v e i n t h e w o r l d a n
Milliseconds 46 63 63 30 47 61 285 138 79 16 94 30 62 62 47 17 108 32 48 17 109 46 63 16 79
Character d u n i v e r s e , a n d p o w e f u l -l -u
Milliseconds 46 47 61 137 48 47 79 61 78 62 111 62 31 79 16 61 79 33 48 31 156 111 31 247 141
Character -f r f u l m o d e r n i n s t r u m e n t s
Milliseconds 127 80 110 61 32 79 94 15 63 110 16 77 62 77 30 64 45 111 62 125 94 78 93 79 0
Character h e l p u s s e e s m o r e -m -o -r -e -s -e -e -s
Milliseconds 110 48 78 15 95 63 47 188 94 47 108 0 62 64 48 30 62 201 0 0 0 112 0 0 0
Character - s e e m o r e a n d m o r e . I n t h
Milliseconds 0 314 33 123 62 46 31 47 31 49 31 79 48 31 64 48 46 0 109 31 142 127 91 47 32
Character i s a -a s e c t i o n w e i n t r o d u c e
Milliseconds 31 47 63 92 219 62 31 127 109 62 31 17 45 62 47 78 78 16 63 109 48 110 47 109 111
Character t h e i d e a s o f a v e r a g e a n d
Milliseconds 61 34 60 46 47 47 78 140 46 63 94 77 79 31 78 126 94 62 93 62 63 78 63 111 47
Character i n s t n a -a -n a -a a n t e -e a n e o u s r a
Milliseconds 62 78 32 48 46 139 47 252 111 64 265 359 93 63 249 299 171 77 77 94 63 62 78 125 64
Character t e s o f c h a n g e , a n d s h o w t
Milliseconds 77 47 76 49 93 79 31 249 48 30 94 47 32 93 94 16 77 95 155 63 61 32 46 63 31
Character h a t t h e y a r e c l o s e l y r e l a
Milliseconds 79 16 62 63 63 46 32 78 78 32 79 46 64 79 32 113 60 32 93 47 46 47 32 109 108
Character t e - d t o t h e s l o p e o f a s
Milliseconds 77 33 189 262 78 62 47 47 93 32 63 62 125 94 93 109 62 46 48 77 46 48 31 110 94
Character c u -u -c -s c u r v e a t a p o i n t P o
Milliseconds 204 79 140 156 125 48 47 80 156 188 127 62 94 48 47 108 95 16 15 31 48 124 156 142 280
Character n t h e c u r v e . W e g i e v c p -p -c
Milliseconds 47 78 30 77 16 77 140 76 78 123 47 79 78 93 236 64 63 78 77 0 78 108 0 220 139
Character - -v -e v e p c r e -e -r -c r e c i s e d e v e l
Milliseconds 126 142 108 79 31 62 93 63 123 47 189 125 94 47 31 124 77 206 33 108 46 157 80 62 47
Character o p m e n t s o f t h e s e i m p o r t a n
Milliseconds 94 31 109 77 77 31 94 15 94 46 62 63 63 16 93 78 79 47 46 111 16 47 110 81 29
Character t o c -c -o c o n c e p t - s i n t h e n
Milliseconds 78 48 155 0 301 188 80 105 0 48 235 108 79 94 265 78 63 63 15 79 17 62 31 47 66
Character e x t c h a p t e r , b u t f o r n o w
Milliseconds 126 106 79 33 171 32 48 94 63 93 47 79 0 94 93 31 62 94 48 62 48 64 16 62 48
Character w e u s e a n i n f o r m a m - -m l a p
Milliseconds 221 15 109 111 61 16 63 79 78 92 63 46 47 108 47 109 30 143 188 156 110 124 63 47 77
Character p r o a c h s o y o u w i l l s e e h o
Milliseconds 109 62 95 94 109 80 78 79 49 77 47 63 62 48 62 64 31 94 94 32 46 110 93 234 30
Character w t h e y l e a d n a t u r a l l y t o
Milliseconds 30 62 47 31 63 46 49 77 47 46 77 47 62 232 95 108 47 63 77 126 31 49 28 80 62
Character t h e m a i n i n d e -e -d -n d e a o f t h
Milliseconds 31 79 32 79 62 63 95 78 15 125 16 63 94 217 126 111 46 126 15 64 79 63 46 62 63
Character i s c h a p t e r , t h e l i m i t . T h
Milliseconds 31 79 63 111 47 32 107 77 62 78 63 62 93 48 46 63 46 32 62 95 77 93 33 109 95
Character e i d e a o f a l i m i l t - -t -l t p
Milliseconds 78 48 95 78 125 16 48 108 64 17 61 110 31 47 48 126 16 79 30 235 109 109 61 16 93
Character l a y s a f u n -n -u o u n d a t i o n a l r
Milliseconds 16 62 110 80 16 63 109 79 80 110 235 110 171 18 106 48 188 128 93 15 31 65 93 190 169
Character o l e t h r o u g h o u t c a l c u l u s .
Milliseconds 32 94 47 76 16 64 93 62 32 125 0 267 48 31 63 78 78 77 125 109 188 124 108 16
WPM Timing
Seconds WPM
1.53 47.1
3.06 102.04
4.59 122.98
6.12 133.44
7.64 136.58
9.17 117.74
10.7 127.84
12.23 133.44
13.76 137.8
15.29 137.37
16.82 137.01
18.35 133.44
19.87 136.46
21.4 139.61
22.93 141.82
24.46 137.86
25.99 137.6
27.52 140.42
29.05 142.12
30.58 144.82
32.1 142.04
33.63 143.08
35.16 139.59
36.69 140.64
38.22 142.23
39.75 142.8
41.28 139.26
42.81 137.37
44.33 138.04
45.86 140.77
47.39 139.77
48.92 138.35
50.45 138.2
51.98 137.83
53.51 135.46
55.04 133.88
56.56 135.35
58.09 134.06
59.62 134.25
61.15 135.01
62.68 134.4
64.21 135.31
65.74 135.82
67.27 136.65
68.79 136.23
70.32 137.03
71.85 136.62
73.38 135.9
74.91 136.01
76.44 135.64