M (springfield12)

Race #9605

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Official speed 123.10 wpm (84.22 seconds elapsed during race)
Without ending ping 123.47 wpm (255 ms delay sending score to TypeRacer’s server)
Timerless 123.98 wpm (340 ms elapsed before first character typed; 83.63 seconds elapsed during race)
Timerless minus one 123.83 wpm, ignoring the first character typed
Race Start March 12, 2024 7:48:21am UTC
Race Finish March 12, 2024 7:49:45am UTC
Outcome Win (1 of 5)
Accuracy 98.6%
Points 332.36
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 uffunction 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 hneanearly everything we observe in the world and univeerse, and powerful modern instruments help us see more and more. In this section we introduce the ideas of average and instantaneous rates oc f change, and show that they are closel yrelaty 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 informationl approach so you will see how they lead naturally to the main idea of this capahapter, the limit. The diidea 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 340 172 78 118 78 176 93 95 89 59 102 66 93 114 86 56 144 157 54 79 52 78 88 44 26
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 125 72 59 72 78 41 93 98 122 191 32 159 55 133 35 78 86 68 63 83 67 31 66 95 109
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 131 45 77 100 49 76 81 22 53 120 22 75 95 75 104 83 96 114 201 105 76 110 111 90 102
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 72 111 76 73 102 54 74 155 39 108 43 91 98 93 128 33 106 70 78 78 84 156 48 114 83
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 99 73 69 70 76 74 39 68 146 151 39 81 111 59 108 80 15 107 82 71 78 91 31 129 177
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 469 180 99 81 83 72 113 113 58 57 155 66 63 36 57 90 86 89 70 170 140 84 145 106 96
Character n g e a s a u f -f -u f u n c t i o n o f
Milliseconds 115 46 75 82 79 73 70 111 94 220 131 210 119 89 80 162 49 170 16 21 88 32 108 50 70
Character t i m e ? H o w d o e s t h e l e v e l
Milliseconds 110 25 79 24 182 112 160 141 34 104 95 44 120 51 52 86 88 71 85 102 69 160 37 104 27
Character o f w a t e r i n a b a r r e l c h a n
Milliseconds 153 64 76 57 118 78 134 54 51 72 76 66 100 90 125 81 116 151 79 78 70 164 58 65 115
Character g e a s a f u n c t i o n o f t h e a
Milliseconds 33 88 88 78 77 96 101 105 216 86 173 21 198 25 35 66 43 110 60 72 115 52 89 75 69
Character m o u n t o f l i q u i d p o u r e d i n
Milliseconds 41 99 81 157 75 68 88 107 36 102 48 107 107 70 75 65 128 106 69 97 450 270 173 76 52
Character t o i t ? W e s e e c h a n g e o c c u
Milliseconds 99 76 72 125 82 176 91 133 189 76 98 70 147 86 121 78 53 136 31 52 85 48 151 166 93
Character r r i n g i n h n e a -a -e -n -h n e a r l y e
Milliseconds 112 145 177 76 82 76 114 69 82 106 5 81 67 222 129 128 131 174 43 63 81 41 120 62 94
Character v e r y t h i n g w e o b s e r v e i n t
Milliseconds 145 145 35 58 127 53 48 141 33 83 50 61 92 133 100 160 64 56 190 50 90 41 51 107 48
Character h e w o r l d a n d u n i v e e -e r s e ,
Milliseconds 54 85 96 44 80 59 94 93 67 68 88 67 56 83 160 38 59 116 253 328 94 125 73 85 91
Character a n d p o w e r f u l m o d e r n i n s t r
Milliseconds 63 84 64 68 53 55 74 41 22 185 21 66 66 99 48 57 166 60 35 100 87 60 75 46 152
Character u m e n t s h e l p u s s e e m o r e a
Milliseconds 38 179 53 89 66 92 80 88 89 74 41 56 103 83 72 105 70 164 50 61 74 20 64 87 53
Character n d m o r e . I n t h i s s e c t i o n
Milliseconds 58 82 56 55 52 65 54 83 47 151 143 61 68 57 43 50 79 82 45 157 181 43 50 76 17
Character w e i n t r o d u c e t h e i d e a s o f
Milliseconds 78 57 91 151 74 25 160 60 106 87 84 61 94 91 41 59 103 61 78 142 75 115 75 71 94
Character a v e r a g e a n d i n s t a n t a n e o u
Milliseconds 61 208 134 165 47 119 81 66 63 76 94 60 88 89 73 119 67 92 106 156 137 247 101 86 86
Character s r a t e s o c - -c f c h a n g e , a n
Milliseconds 50 63 164 107 87 62 77 52 52 151 21 377 159 131 87 289 102 91 81 48 81 86 47 107 75
Character d s h o w t h a t t h e y a r e c l o s
Milliseconds 90 67 81 75 43 64 67 65 76 57 95 10 146 62 84 116 53 82 99 51 94 125 56 139 37
Character e l y r e l a t -t -a -l -e -r -y - y r e l a t e d
Milliseconds 60 67 83 11 77 71 53 111 53 209 127 130 140 143 139 136 187 84 74 63 41 112 47 83 154
Character t o t h e s l o p e o f a c u r v e
Milliseconds 21 102 23 98 49 60 94 86 64 43 152 7 110 35 119 84 87 79 119 148 90 90 168 40 76
Character a t a p o i n t P o n t h e c u r v e
Milliseconds 74 118 99 90 107 57 40 83 45 47 53 123 132 122 23 105 79 36 90 84 101 85 86 166 49
Character . W e g i v e p r e c i s e d e v e l o p
Milliseconds 96 86 242 277 127 111 82 110 53 95 61 74 64 182 58 99 64 50 143 171 141 36 90 210 114
Character m e n t s o f t h e s e i m p o r t a n t
Milliseconds 199 96 75 82 85 69 135 105 99 104 48 79 128 92 64 89 46 73 20 91 147 62 65 64 81
Character c o n c e p t s i n t h e n e x t c h a p
Milliseconds 156 16 56 94 76 37 137 106 66 78 54 78 130 6 227 150 115 84 196 121 109 131 134 96 104
Character t e r , b u t f o r n o w w e u s e a
Milliseconds 125 123 66 76 52 115 48 123 86 100 92 73 76 54 66 17 96 128 69 113 171 73 59 83 78
Character n i n f o r m a t i o n -n -o -i -t l a p p r o a
Milliseconds 109 55 138 71 94 116 76 132 84 73 58 59 109 245 128 143 135 194 84 53 110 130 86 80 83
Character c h s o y o u w i l l s e e h o w t h
Milliseconds 89 82 96 105 54 90 78 90 66 37 56 67 42 149 72 40 75 165 114 99 62 90 43 112 83
Character e y l e a d n a t u r a l l y t o t h e
Milliseconds 88 86 63 111 74 78 110 59 50 74 72 87 101 66 32 135 39 73 76 60 90 44 68 92 64
Character m a i n i d e a o f t h i s c a p a -a -p -a
Milliseconds 53 95 75 80 29 135 23 155 71 114 17 200 85 148 74 63 51 79 197 101 25 232 154 130 133
Character h a p t e r , t h e l i m i t . T h e d i
Milliseconds 200 81 81 88 114 67 50 66 86 67 72 73 44 45 201 54 80 127 69 113 85 65 74 129 95
Character -i -d i d e a o f a l i m i t p l a y s a
Milliseconds 198 123 161 43 156 74 109 63 76 76 63 124 9 88 275 58 110 106 138 155 46 112 64 90 71
Character f o u n d a t i o n a l r o l e t h r o u g
Milliseconds 120 62 42 54 155 58 36 126 31 9 69 72 84 51 35 104 163 55 72 88 43 131 19 45 118
Character h o u t c a l c u l u s .
Milliseconds 53 127 62 105 257 160 52 68 95 94 213 76 110 103
WPM Timing
Seconds WPM
1.68 99.73
3.37 121.11
5.05 130.6
6.74 130.01
8.42 132.5
10.11 132.98
11.79 128.23
13.48 129.12
15.16 125.85
16.84 126.09
18.53 126.93
20.21 127.64
21.9 127.13
23.58 128.74
25.27 126.8
26.95 126
28.64 125.3
30.32 121.9
32.01 122.98
33.69 124.31
35.37 122.8
37.06 124.67
38.74 125.44
40.43 127.64
42.11 127.94
43.8 127.68
45.48 127.44
47.17 125.94
48.85 126.26
50.53 126.8
52.22 123.17
53.9 124.44
55.59 124.78
57.27 124.67
58.96 124.57
60.64 123.88
62.33 124.76
64.01 124.48
65.69 124.58
67.38 124.67
69.06 122.84
70.75 123.48
72.43 123.92
74.12 124.83
75.8 123.32
77.49 123.58
79.17 122.92
80.86 123.03
82.54 123.72
84.22 123.1