312211 (312211)

Race #9944

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Official speed 108.14 wpm (95.88 seconds elapsed during race)
Without ending ping 108.34 wpm (174 ms delay sending score to TypeRacer’s server)
Timerless 109.10 wpm (671 ms elapsed before first character typed; 95.03 seconds elapsed during race)
Timerless minus one 108.97 wpm, ignoring the first character typed
Race Start March 18, 2024 2:48:00am UTC
Race Finish March 18, 2024 2:49:36am UTC
Outcome No win (2 of 4)
Opponents 1. sskhynix (110.96 wpm)
Accuracy 98.6%
Points 291.98
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 halpelps us understand how a change in one quantity is realtelated to a change in another. How does the speed of a fealling object change a as a function of time? How does the level of wwaterater in a barrel change as a function of the amount of liquid poured into it? We see change occuringring in nearly everything we observe in the world and universe, and powerful modern instruments help us see more and more. In this section we introduced th the ideas of average and instantaneous rates ocf 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 poiimportant 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 clalculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 671 137 191 143 130 198 137 119 18 134 105 71 115 78 121 86 145 161 41 69 97 57 63 55 152
Character a l p -p -l -a e l p s u s u n d e r s t a n d
Milliseconds 82 118 160 243 150 113 105 103 103 128 80 96 112 83 173 73 64 135 80 104 104 49 88 119 57
Character h o w a c h a n g e i n o n e q u a n t
Milliseconds 71 88 71 97 97 96 87 96 56 104 95 82 8 111 63 48 98 63 81 105 103 95 88 56 120
Character i t y i s r e a l t e -e -t -l -a l a t e d t o
Milliseconds 113 112 94 58 119 80 95 121 65 70 34 118 81 208 144 145 359 192 48 73 86 145 131 62 111
Character a c h a n g e i n a n o t h e r . H o w
Milliseconds 80 296 113 280 94 57 96 120 73 7 96 56 71 105 89 79 39 122 72 63 72 87 138 160 56
Character d o e s t h e s p e e d o f a f e -e a
Milliseconds 135 87 98 62 56 49 89 87 48 111 57 128 89 143 151 74 95 80 89 63 120 256 64 215 161
Character l l i n g o b j e c t c h a n g e a - a -a
Milliseconds 144 129 63 64 48 56 120 81 183 73 119 194 111 113 86 65 104 126 83 134 96 297 479 209 256
Character s a f u n c t i o n o f t i m e ? H o w
Milliseconds 86 104 105 74 111 104 48 95 162 13 80 33 55 104 72 74 113 109 25 87 160 121 192 152 112
Character d o e s t h e l e v e l o f w w a t e r
Milliseconds 81 71 72 128 353 120 79 88 63 64 73 64 137 79 48 96 112 48 104 80 104 17 79 111 83
Character -r -e -t -a -w a t e r i n a b a r r e l c h a
Milliseconds 214 152 159 146 151 57 113 117 64 97 89 56 79 65 86 131 70 104 151 105 88 72 97 71 63
Character n g e a s a f u n c t i o n o f t h e
Milliseconds 96 121 79 129 129 118 41 249 87 88 104 41 56 174 80 58 39 72 119 73 87 160 90 79 39
Character a m o u n t o f l i q u i d p o u r e d i
Milliseconds 130 56 112 87 160 113 64 86 96 89 416 64 89 118 112 96 81 87 65 183 153 167 153 65 136
Character n t o i t ? W e s e e c h a n g e o c c
Milliseconds 71 64 73 95 129 103 288 121 224 175 89 118 89 152 97 102 81 120 82 230 111 129 63 97 136
Character u r i n g -g -n -i r i n g i n n e a r l y e v
Milliseconds 114 103 135 88 97 264 142 114 127 120 63 80 73 73 48 104 119 112 89 96 64 167 81 102 153
Character e r y t h i n g w e o b s e r v e i n t h
Milliseconds 96 129 78 112 112 89 89 48 120 41 86 96 88 112 89 38 88 193 63 50 78 73 49 22 137
Character e w o r l d a n d u n i v e r s e , a n d
Milliseconds 31 129 112 111 65 112 79 90 87 63 129 23 105 96 97 98 95 118 104 80 87 64 89 81 87
Character p o w e r f u l m o d e r n i n s t r u m e
Milliseconds 74 119 63 55 49 97 152 39 87 104 96 56 26 159 71 64 56 186 71 64 104 143 90 166 88
Character n t s h e l p u s s e e m o r e a n d
Milliseconds 81 96 97 63 280 216 104 143 120 116 100 88 97 83 141 73 104 64 70 90 41 118 90 111 48
Character m o r e . I n t h i s s e c t i o n w e
Milliseconds 86 64 73 97 57 86 143 137 87 83 70 73 56 87 288 79 152 178 64 70 56 90 158 72 122
Character i n t r o d u c e d t h -h -t - -d t h e i d e
Milliseconds 135 55 48 153 71 122 118 82 56 134 82 104 79 223 162 126 168 105 129 70 91 77 97 49 151
Character a s o f a v e r a g e a n d i n s t a n t
Milliseconds 64 111 49 120 96 81 222 168 144 98 95 162 87 103 73 127 104 97 96 86 90 231 192 231 192
Character a n e o u s r a t e s o c -c f c h a n g e ,
Milliseconds 281 255 161 177 111 119 73 160 114 77 74 64 22 112 137 344 129 110 129 88 64 87 112 82 64
Character a n d s h o w t h a t t h e y a r e c
Milliseconds 78 105 65 112 56 118 41 87 89 63 136 81 47 81 48 135 74 97 69 90 95 57 86 41 151
Character l o s e l y r e l a t e d t o t h e s l o
Milliseconds 129 160 74 55 70 137 71 65 80 64 81 56 86 152 104 97 97 70 41 96 50 77 122 58 148
Character p e o f a c u r v e a t a p o i n t
Milliseconds 129 120 55 96 82 94 74 104 87 104 87 194 50 92 128 104 146 152 103 152 24 48 49 56 134
Character P o n t h e c u r v e . W e g i v e p
Milliseconds 178 126 138 78 57 40 119 64 81 128 127 90 167 79 66 71 160 160 36 148 72 111 57 15 130
Character r e c i s e d e v e l o p m e n t s o f t h
Milliseconds 70 96 152 98 79 55 89 104 159 128 88 48 145 97 151 104 96 47 104 96 128 48 81 89 95
Character e s e p o i -i -o -p i m p o r t a n t c o n c e
Milliseconds 39 120 89 71 144 64 10 287 127 136 177 65 56 57 77 153 96 72 97 96 297 119 70 104 89
Character p t s i n t h e n e x t c h a p t e r ,
Milliseconds 168 97 144 113 182 81 22 33 119 75 85 82 71 223 178 111 145 63 79 104 82 126 83 77 64
Character b u t f o r n o w w e u s e a n i n f
Milliseconds 128 80 82 78 97 81 79 72 71 96 97 87 114 342 105 144 79 57 72 153 64 78 128 64 105
Character o r m a l a p p r o a c h s o y o u w i l
Milliseconds 96 113 78 104 128 72 130 70 145 167 139 103 112 111 89 335 31 90 118 88 72 40 96 73 169
Character l s e e h o w t h e y l e a d n a t u r
Milliseconds 119 82 45 73 159 42 111 80 73 78 84 69 90 62 79 185 55 72 105 73 96 64 79 104 81
Character a l l y t o t h e m a i n i d e a o f
Milliseconds 70 49 151 112 186 135 71 66 56 96 63 79 96 96 65 81 56 104 22 152 73 73 103 57 55
Character t h i s c h a p t e r , t h e l i m i t .
Milliseconds 176 88 41 79 88 98 69 82 104 104 113 77 74 78 97 79 67 77 145 89 56 111 112 159 98
Character T h e i d e a o f a l i m i t p l a y s
Milliseconds 134 136 65 72 87 74 142 66 31 328 113 78 104 73 114 62 63 121 74 95 103 169 86 123 302
Character a f o u n d a t i o n a l r o l e t h r o
Milliseconds 136 79 104 96 161 73 166 90 127 81 126 56 56 90 103 49 105 69 169 136 104 105 96 70 57
Character u g h o u t c l -l a l c u l u s .
Milliseconds 72 81 71 129 55 71 112 96 145 410 224 125 178 127 192 153 150 96
WPM Timing
Seconds WPM
1.92 62.58
3.84 78.23
5.75 85.53
7.67 100.13
9.59 97.63
11.51 92.83
13.42 97.45
15.34 102.48
17.26 100.82
19.18 97
21.09 98.99
23.01 98.57
24.93 96.28
26.85 97.89
28.76 99.71
30.68 100.13
32.6 100.87
34.52 100.13
36.43 97.82
38.35 99.19
40.27 101.32
42.19 102.69
44.1 104.21
46.02 104.04
47.94 105.14
49.86 105.42
51.77 103.84
53.69 103.93
55.61 103.58
57.53 103.26
59.44 103.16
61.36 104.24
63.28 105.06
65.2 105.47
67.11 106.03
69.03 106.56
70.95 107.06
72.87 105.89
74.78 106.23
76.7 106.7
78.62 106.69
80.54 106.54
82.45 107.26
84.37 107.81
86.29 108.61
88.21 108.84
90.12 109.05
92.04 108.86
93.96 109.33
95.88 108.14