Mikey (miket349)

Race #67891

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Official speed 117.99 wpm (87.87 seconds elapsed during race)
Without ending ping 118.12 wpm (97 ms delay sending score to TypeRacer’s server)
Timerless 118.40 wpm (208 ms elapsed before first character typed; 87.57 seconds elapsed during race)
Timerless minus one 118.26 wpm, ignoring the first character typed
Race Start March 10, 2024 5:24:02am UTC
Race Finish March 10, 2024 5:25:30am UTC
Outcome No win (2 of 4)
Opponents 4. mouboy (91.55 wpm)
Accuracy 99.2%
Points 318.58
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? GoHow does the level of water in a barrel change as a function of the amount of liquid poured into it? We see change occcurring 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 idaseas of average and instantanoeous 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 concedppts in the next chapter, but for now we use an informatl approach so you will see how they lead naturally to the main idea of this chapter, thie 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 208 199 98 107 104 123 200 169 81 84 58 85 100 92 107 76 133 140 63 107 59 76 42 29 96
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 118 84 191 79 68 323 130 122 112 175 70 169 31 89 131 46 88 92 76 82 35 71 63 81 92
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 105 83 104 85 120 82 30 79 116 77 79 107 52 81 281 73 90 76 98 82 68 85 72 97 64
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 97 50 62 94 64 53 47 135 32 122 48 70 274 152 130 96 68 109 69 47 49 98 131 61 64
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 79 64 92 78 78 80 114 8 186 204 154 110 138 69 88 59 33 109 38 23 87 59 144 131 120
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 135 61 78 84 56 39 130 195 72 84 141 73 154 69 76 71 145 58 109 249 226 67 199 77 91
Character n g e a s a f u n c t i o n o f t i m e
Milliseconds 92 75 46 118 122 58 101 40 136 117 87 175 46 231 42 24 132 73 12 88 68 109 61 156 57
Character ? G o -o -G H o w d o e s t h e l e v e l
Milliseconds 241 51 136 133 304 115 202 129 84 106 81 66 83 60 34 204 48 32 108 74 24 179 65 87 36
Character o f w a t e r i n a b a r r e l c h a n
Milliseconds 132 53 139 122 67 88 93 83 50 84 106 108 74 28 324 161 101 165 177 132 79 209 102 55 110
Character g e a s a f u n c t i o n o f t h e a
Milliseconds 42 62 76 44 63 84 40 135 65 130 179 60 213 27 21 114 85 13 138 62 99 27 41 74 156
Character m o u n t o f l i q u i d p o u r e d i n
Milliseconds 79 180 136 206 56 64 46 94 45 55 46 188 83 58 107 87 358 196 57 82 132 209 71 74 108
Character t o i t ? W e s e e c h a n g e o c c c
Milliseconds 70 39 68 138 80 216 32 103 392 101 96 54 109 63 109 91 80 102 62 48 59 81 141 102 225
Character -c u r r i n g i n n e a r l y e v e r y t h
Milliseconds 331 168 112 128 86 126 73 18 85 110 74 111 75 62 67 83 85 48 78 131 131 61 58 136 46
Character i n g w e o b s e r v e i n t h e w o r
Milliseconds 67 156 68 60 101 95 27 188 102 161 35 81 184 82 72 107 148 86 58 63 23 60 79 36 66
Character l d a n d u n i v e r s e , a n d p o w e
Milliseconds 90 59 86 70 123 56 73 78 166 65 11 128 61 144 51 62 47 41 80 42 112 188 50 12 48
Character r f u l m o d e r n i n s t r u m e n t s h
Milliseconds 64 143 56 47 79 190 58 58 146 72 30 84 74 141 49 73 133 62 177 87 80 86 50 77 111
Character e l p u s s e e m o r e a n d m o r e .
Milliseconds 57 103 165 50 118 110 118 119 51 128 62 119 87 55 39 59 45 86 84 48 115 65 73 28 127
Character I n t h i s s e c t i o n w e i n t r o
Milliseconds 55 169 123 71 87 29 28 88 72 104 50 152 232 34 19 119 60 78 40 127 156 119 167 179 303
Character d u c e t h e i d a s -s -a e a s o f a v e
Milliseconds 244 98 82 100 93 166 26 44 110 77 67 217 46 469 123 73 109 64 163 73 83 69 149 122 145
Character r a g e a n d i n s t a n t a n o -o e o u s
Milliseconds 51 92 100 73 68 47 108 88 91 74 116 80 82 71 12 99 681 87 224 317 45 158 70 85 129
Character r a t e s o f c h a n g e , a n d s h o w
Milliseconds 112 69 114 59 35 68 80 70 79 183 102 117 59 93 53 72 32 39 79 69 81 96 45 42 87
Character t h a t t h e y a r e c l o s e l y r e
Milliseconds 141 133 98 56 56 49 104 34 84 79 39 76 19 54 75 200 56 129 59 59 73 77 57 79 63
Character l a t e d t o t h e s l o p e o f a c
Milliseconds 87 66 62 44 149 107 107 51 58 61 38 21 99 106 76 153 95 251 84 95 78 72 42 118 51
Character u r v e a t a p o i n t P o n t h e
Milliseconds 125 107 198 56 101 106 58 59 75 92 160 33 59 165 60 66 165 101 132 102 60 50 75 37 90
Character c u r v e . W e g i v e p r e c i s e d e
Milliseconds 250 102 116 194 49 121 29 163 214 107 198 99 106 14 98 189 57 83 208 104 88 32 96 203 166
Character v e l o p m e n t s o f t h e s e i m p o r
Milliseconds 147 60 45 146 62 214 92 98 87 71 55 52 94 59 120 50 44 99 84 24 99 189 173 75 100
Character t a n t c o n c e d p -p -d p t s i n t h e
Milliseconds 148 65 62 68 89 116 59 77 74 67 0 119 352 119 260 140 114 92 258 112 81 46 59 67 67
Character n e x t c h a p t e r , b u t f o r n o w
Milliseconds 88 96 201 87 75 161 16 186 92 138 121 58 90 37 117 51 122 62 147 47 138 20 350 78 67
Character w e u s e a n i n f o r m a t -t l a p p
Milliseconds 84 112 57 94 170 70 37 143 169 89 78 108 149 102 77 117 73 156 82 502 202 77 79 125 131
Character r o a c h s o y o u w i l l s e e h o w
Milliseconds 99 137 405 240 95 62 323 85 72 132 82 88 46 99 80 147 130 40 93 23 121 73 94 32 85
Character t h e y l e a d n a t u r a l l y t o t
Milliseconds 63 187 58 169 47 76 239 62 47 145 121 224 180 76 84 97 64 61 157 33 76 109 91 62 76
Character h e m a i n i d e a o f t h i s c h a p
Milliseconds 42 52 33 134 130 33 102 58 99 62 146 61 110 47 80 91 175 22 49 57 75 229 76 120 92
Character t e r , t h i -i e l i m i t . T h e i d e
Milliseconds 182 104 72 73 57 116 27 69 388 106 93 124 67 173 54 89 130 35 89 51 89 84 110 75 133
Character a o f a l i m i t p l a y s a f o u n
Milliseconds 62 91 64 84 64 57 98 107 59 168 63 83 68 122 124 72 65 98 108 74 134 72 67 45 168
Character d a t i o n a l r o l e t h r o u g h o u t
Milliseconds 36 75 82 33 13 87 103 31 80 115 95 146 82 89 328 89 96 107 82 75 120 87 77 44 103
Character c a l c u l u s .
Milliseconds 109 46 63 125 86 122 171 146 58
WPM Timing
Seconds WPM
1.76 95.59
3.51 105.84
5.27 113.8
7.03 116.08
8.79 120.17
10.54 124.04
12.3 122.91
14.06 122.91
15.82 121.39
17.57 120.86
19.33 117.94
21.09 119.49
22.85 117.65
24.6 119.49
26.36 119.26
28.12 118.21
29.88 118.09
31.63 116.08
33.39 117.16
35.15 118.47
36.91 120.3
38.66 120.73
40.42 121.42
42.18 122.62
43.94 121.27
45.69 119.49
47.45 119.62
49.21 117.79
50.97 117.73
52.72 119.26
54.48 120.48
56.24 120.56
58 120.84
59.75 120.09
61.51 119.78
63.27 120.25
65.03 119.58
66.78 118.95
68.54 119.23
70.3 118.81
72.05 117.58
73.81 116.57
75.57 117.03
77.33 116.85
79.08 117.6
80.84 117.12
82.6 117.39
84.36 117.64
86.11 117.89
87.87 117.99