λ (yambda)

Race #10079

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Official speed 122.84 wpm (84.40 seconds elapsed during race)
Without ending ping 123.18 wpm (230 ms delay sending score to TypeRacer’s server)
Timerless 123.73 wpm (378 ms elapsed before first character typed; 83.79 seconds elapsed during race)
Timerless minus one 123.59 wpm, ignoring the first character typed
Race Start November 5, 2023 10:11:46pm UTC
Race Finish November 5, 2023 10:13:11pm UTC
Outcome No win (2 of 5)
Opponents 1. rayer (132.64 wpm)
4. reiner24 (98.12 wpm)
Accuracy 98.9%
Points 331.67
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 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 poruApooured 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 chagne,hange, and show that they are closely related to the slope of a curve at a point P on the curve. We give precise developementseevevelopments of these imporatnmportant 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.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 378 94 97 93 126 80 97 125 48 79 96 95 110 77 128 63 130 140 78 95 95 47 48 65 95
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 78 78 96 64 64 110 157 188 80 190 17 144 95 94 80 47 108 61 97 96 48 47 77 110 48
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 140 32 140 0 128 92 65 64 62 80 97 64 91 82 93 111 94 110 113 64 126 63 79 64 112
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 93 142 80 108 63 46 80 128 95 92 46 94 31 107 96 81 63 95 64 95 65 96 94 63 157
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 77 62 80 80 64 49 81 48 158 158 96 142 79 94 80 64 48 95 64 95 111 110 142 110 126
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 159 64 77 97 64 95 93 112 64 128 109 126 81 126 46 123 109 111 48 141 161 80 142 80 65
Character n g e a s a f u n c t i o n o f t i m e
Milliseconds 109 78 93 64 98 78 238 62 113 79 79 143 46 158 62 49 31 97 96 32 428 140 48 62 66
Character ? H o w d o e s t h e l e v e l o f w
Milliseconds 205 131 347 61 142 176 93 65 96 48 30 113 63 63 80 46 79 142 81 77 65 96 80 110 80
Character a t e r i n a b a r r e l c h a n g e a
Milliseconds 78 48 93 83 77 80 62 64 80 65 124 145 127 122 77 113 47 96 112 33 96 64 96 144 0
Character s a f u n c t i o n o f t h e a m o u n
Milliseconds 113 174 47 126 79 143 161 112 176 47 65 32 80 495 94 95 81 64 48 112 48 94 112 80 129
Character t o f l i q u i d p o r u A p o -o -r -u -A -p -o
Milliseconds 96 77 79 97 63 110 95 61 124 47 111 62 94 49 143 64 366 177 49 553 0 0 0 0 0
Character o u r e d i n t o i t ? W e s e e c h a
Milliseconds 29 66 96 61 162 79 78 49 109 30 108 96 112 193 80 348 63 92 157 144 112 49 146 62 79
Character n g e o c c u r r i n g i n n e a r l y e
Milliseconds 79 94 94 46 126 94 128 98 94 144 64 62 113 16 96 49 111 129 111 80 49 63 81 49 79
Character v e r y t h i n g w e o b s e r v e i n t
Milliseconds 143 64 127 113 111 81 32 96 80 94 64 64 97 95 97 127 80 49 159 80 62 65 62 79 17
Character h e w o r l d a n d u n i v e r s e , a n
Milliseconds 96 32 96 64 79 63 97 33 92 97 31 126 16 145 142 64 62 123 79 79 31 144 32 65 80
Character d p o w e r f u l m o d e r n i n s t r u m
Milliseconds 61 81 208 46 62 47 46 159 80 63 112 159 63 80 176 61 78 48 142 94 32 49 127 143 128
Character e n t s h e l p u s s e e m o r e a n d
Milliseconds 15 146 44 94 79 112 124 16 112 63 128 79 94 144 127 112 129 79 64 96 16 96 129 94 95
Character m o r e . I n t h i s s e c t i o n w e
Milliseconds 81 64 48 62 32 96 32 143 63 80 130 78 33 111 49 112 50 175 173 32 64 16 80 127 93
Character i n t r o d u c e t h e i d e a s o f a
Milliseconds 79 175 77 50 155 81 96 80 96 78 33 126 16 111 65 97 47 144 48 64 97 79 80 94 81
Character v e r a g e a n d i n s t a n t a n e o u s
Milliseconds 80 94 112 48 111 64 81 95 111 142 112 158 49 79 49 111 97 254 202 188 97 66 63 109 66
Character r a t e s o f c h a g n e , -h -a -g -n -e -, h a n
Milliseconds 170 78 80 33 95 80 76 66 63 112 64 64 78 15 173 82 440 0 0 0 0 0 97 48 94
Character g e , a n d s h o w t h a t t h e y a r
Milliseconds 64 95 33 63 79 64 78 110 77 125 48 81 48 64 112 31 33 79 94 48 95 32 93 63 47
Character e c l o s e l y r e l a t e d t o t h e
Milliseconds 47 62 127 15 160 16 49 81 95 64 48 63 143 96 32 80 144 47 112 33 79 63 60 49 112
Character s l o p e o f a c u r v e a t a p o i
Milliseconds 111 93 124 82 142 97 79 111 48 94 47 97 96 80 128 66 92 113 64 93 96 114 94 34 63
Character n t P o n t h e c u r v e . W e g i v
Milliseconds 64 79 31 269 127 96 50 79 31 98 0 127 64 112 48 272 78 96 33 175 65 96 348 112 80
Character e p r e c i s e d e v e l o p e m e n t s -e -v
Milliseconds 48 63 96 96 80 175 65 79 34 98 96 183 96 80 142 159 46 144 80 82 92 62 108 479 0
Character -e -l -o -p -e -m -e -n -t -s e e v e -e -v -e v e l o p m e n
Milliseconds 0 0 0 0 0 0 0 0 0 0 15 239 145 91 361 112 158 144 47 191 156 78 160 79 524
Character t s o f t h e s e i m p o r a t n -m -p -o -r -a
Milliseconds 144 92 48 112 64 79 79 94 0 113 66 94 128 64 64 48 48 143 0 128 522 0 0 0 0
Character -t -n m p o r t a n t c o n c e p t s i n t h
Milliseconds 0 0 64 80 16 96 139 77 94 80 97 160 64 63 95 51 141 47 93 64 92 33 109 48 80
Character e n e x t c h a p t e r , b u t f o r n
Milliseconds 48 112 97 48 144 140 110 80 113 47 127 16 125 96 79 48 80 80 96 64 111 47 113 79 111
Character o w w e u s e a n i n f o r m a l a p p
Milliseconds 47 96 116 109 63 81 126 48 48 79 96 63 81 112 47 112 46 111 48 124 82 63 139 144 96
Character r o a c h s o y o u w i l l s e e h o w
Milliseconds 82 111 63 126 48 61 128 46 94 204 80 64 64 81 50 30 126 96 79 126 140 111 96 62 96
Character t h e y l e a d n a t u r a l l y t o t
Milliseconds 47 64 111 49 143 79 112 130 25 127 62 142 94 49 110 78 48 33 143 64 47 77 64 81 47
Character h e m a i n i d e a o f t h i s c h a p
Milliseconds 96 46 110 33 110 48 78 64 96 32 126 79 48 79 81 61 97 77 62 64 111 80 112 48 126
Character t e r , t h e l i m i t . T h e i d e a
Milliseconds 124 126 110 30 63 94 63 65 80 78 79 65 78 65 127 31 143 92 94 97 111 97 158 157 97
Character o f a l i m i t p l a y s a f o u n d a
Milliseconds 78 110 92 49 127 78 81 64 80 80 32 126 0 112 111 63 95 62 95 80 63 47 143 16 64
Character t i o n a l r o l e t h r o u g h o u t c a
Milliseconds 95 62 49 46 80 96 32 143 80 124 79 49 112 61 112 15 78 113 47 80 95 64 79 143 93
Character l c u l u s .
Milliseconds 97 94 77 64 109 96 96
WPM Timing
Seconds WPM
1.69 99.52
3.38 113.74
5.06 123.22
6.75 126.18
8.44 129.38
10.13 130.33
11.82 129.99
13.5 128.85
15.19 127.17
16.88 125.11
18.57 124.73
20.26 126.18
21.94 126.32
23.63 124.4
25.32 124.64
27.01 119.07
28.7 117.92
30.38 118.48
32.07 119.73
33.76 121.56
35.45 122.88
37.14 123.11
38.83 123.63
40.51 124.4
42.2 124.83
43.89 125.22
45.58 125.59
47.27 124.91
48.95 123.06
50.64 124.64
52.33 125.67
54.02 125.96
55.71 126.45
57.39 125.45
59.08 124.3
60.77 121.05
62.46 119.12
64.15 118.6
65.83 117.75
67.52 118.36
69.21 118.94
70.9 119.5
72.59 119.86
74.27 120.04
75.96 121.01
77.65 121.47
79.34 121.76
81.03 122.18
82.71 122.74
84.4 122.84