m (mpb10)

Race #418

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Official speed 102.92 wpm (100.74 seconds elapsed during race)
Without ending ping 104.75 wpm (1,763 ms delay sending score to TypeRacer’s server)
Timerless 106.98 wpm (2,057 ms elapsed before first character typed; 96.92 seconds elapsed during race)
Timerless minus one 106.85 wpm, ignoring the first character typed
Race Start February 21, 2025 5:17:04pm UTC
Race Finish February 21, 2025 5:18:45pm UTC
Outcome No win (2 of 4)
Opponents 1. anthonywspt (116.60 wpm)
3. steffin02 (98.77 wpm)
4. qu63y (92.13 wpm)
Accuracy 97.9%
Points 277.89
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 isa a toolt hat hool 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 ow does the level of water in a barrell change as a function of the amount of liquid poruured into it? We see change occurring in nearly everything we observe int he wn the world and universe, and powerful modern instrument hels 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 ont he c the curve. We give precise cdevelopments of these imiporportant concepts in the enxnext chapter, but for now ewe use an informal approach so you will se e how they lead naturally toth the main idea of this chapter, th e 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 - -a a t o o l t h
Milliseconds 2057 161 72 103 74 187 118 87 62 66 70 176 52 304 117 231 161 176 176 73 112 161 108 0 87
Character a t h -o -o -l -t - -h -a -t - -h o o l t h a t h e
Milliseconds 49 33 86 111 701 0 0 0 0 0 0 0 0 0 86 138 127 64 48 68 83 38 54 51 125
Character l p s u s u n d e r s t a n d h o w a c
Milliseconds 94 74 78 244 134 117 59 98 138 51 144 58 129 67 107 73 70 78 98 91 120 68 67 94 77
Character h a n g e i n o n e q u a n t i t y i s
Milliseconds 76 87 46 65 100 23 90 114 40 65 117 33 90 141 25 176 18 337 44 101 97 84 100 86 53
Character r e l a t e d t o a c h a n g e i n a n
Milliseconds 44 96 119 153 32 133 189 33 110 33 74 64 87 96 50 82 68 48 86 35 84 68 60 85 65
Character o t h e r . H o w d o e s t h e s p e e d
Milliseconds 69 115 54 77 70 85 49 164 87 110 154 101 81 66 131 52 84 65 64 41 96 83 83 103 183
Character o f a f a l l i n g o b j e c t c h a n
Milliseconds 32 60 91 103 48 119 82 127 57 151 67 75 40 96 38 112 66 86 153 153 62 146 71 67 84
Character g e a s a f u n c t i o n o f t i m e ?
Milliseconds 51 113 87 28 65 109 75 84 102 82 138 48 166 64 82 55 46 86 55 55 114 25 131 87 603
Character H O w - -w -O o w d o e s t h e l e v e l
Milliseconds 164 179 59 125 139 320 129 116 174 99 41 127 70 54 116 55 108 89 35 96 100 41 155 120 53
Character o f w a t e r i n a b a r r e l l -l c
Milliseconds 92 87 117 121 97 181 35 163 39 51 103 79 41 60 116 70 96 104 121 88 99 141 310 62 159
Character h a n g e a s a f u n c t i o n o f t h
Milliseconds 49 69 80 50 104 115 34 45 103 99 48 75 89 125 71 177 48 68 60 41 98 54 87 63 67
Character e a m o u n t o f l i q u i d p o r u -u -r
Milliseconds 76 41 113 38 133 129 132 38 91 62 100 68 41 115 103 89 110 168 68 173 118 91 51 391 127
Character u r e d i n t o i t ? W e s e e c h a n
Milliseconds 188 17 87 190 41 99 55 53 120 44 105 82 302 124 202 253 86 94 72 164 111 140 46 106 49
Character g e o c c u r r i n g i n n e a r l y e v
Milliseconds 47 118 102 120 52 139 73 132 86 84 47 96 71 49 69 85 157 55 101 37 78 161 58 69 152
Character e r y t h i n g w e o b s e r v e i n t h
Milliseconds 131 54 46 136 76 102 83 61 87 32 63 75 81 282 137 97 85 180 99 54 40 76 87 0 147
Character e w -w -n -t - -h -e - n t h e w o r l d a n d
Milliseconds 0 133 0 285 487 0 0 0 0 0 44 120 259 73 67 63 102 114 60 94 105 41 122 46 100
Character u n i v e r s e , a n d p o w e r f u l m
Milliseconds 49 101 174 61 141 88 115 87 69 82 35 116 44 85 38 82 84 118 31 89 170 41 185 89 90
Character o d e r n i n s t r u m e n t h e l -l -e -h - s
Milliseconds 142 0 144 29 52 105 99 67 127 69 154 57 166 69 87 33 83 101 204 62 244 122 121 145 124
Character h e l p u s s e e m o r e a n d m o r
Milliseconds 35 151 160 53 95 68 84 112 89 150 0 446 190 83 153 0 46 113 115 54 96 45 95 98 31
Character e - . I n t h i s s e c t i o n w e i
Milliseconds 42 193 314 217 113 100 89 78 39 131 342 86 57 116 155 185 213 37 45 64 49 88 59 118 140
Character n t r o d u c e t h e i d e a s o f a v e
Milliseconds 47 121 145 51 133 96 92 145 86 87 72 58 52 46 83 114 116 50 67 116 64 72 32 170 145
Character r a g e a n d i n s t a n t a n e o u s r a
Milliseconds 52 132 85 80 111 57 90 71 69 92 67 50 78 120 99 68 168 411 121 159 84 147 0 208 127
Character t e s o f c h a n g e , a n d s h o w t
Milliseconds 91 87 144 74 60 87 80 202 124 68 134 0 105 59 31 82 73 66 46 117 41 48 126 85 21
Character h a t t h e y a r e c l o s e l y r e l a
Milliseconds 104 27 79 45 85 0 149 34 84 56 40 83 30 170 19 141 23 69 102 160 98 84 97 93 111
Character t e d t o t h e s l o p e o f a c u r
Milliseconds 45 128 156 56 107 58 44 97 44 104 30 135 74 136 60 114 88 71 74 170 0 129 116 161 60
Character v e a t a p o i n t P o n t h e c -c
Milliseconds 193 106 98 69 291 102 92 81 150 111 88 82 53 130 136 215 117 52 146 0 86 28 73 116 161
Character - -e -h - -t t h e c u r v e . W e g i v e
Milliseconds 149 122 138 127 214 127 75 70 93 45 169 88 118 165 139 0 73 160 82 151 100 75 152 110 40
Character p r e c i s e c -c d e v e l o p m e n t s o f
Milliseconds 87 34 87 215 52 114 84 165 249 283 71 133 127 126 20 149 45 159 88 84 36 133 33 65 74
Character t h e s e i m i p o r -r -o -p -i p o r t a n t
Milliseconds 101 59 65 100 104 77 56 111 138 45 36 70 126 266 119 132 119 201 140 76 106 140 38 117 51
Character c o n c e p t s i n t h e e n x -x -n -e n e x
Milliseconds 215 102 36 111 255 62 97 137 25 371 59 97 44 101 17 66 104 0 247 249 119 150 199 54 154
Character t c h a p t e r , b u t f o r n o w e -e
Milliseconds 191 28 172 32 116 90 131 133 52 82 22 113 63 133 37 132 31 116 65 121 95 56 103 61 438
Character w e u s e a n i n f o r m a l a p p r o a
Milliseconds 142 46 84 175 83 70 62 115 70 119 97 84 317 71 95 70 80 99 81 101 83 135 64 104 166
Character c h s o y o u w i l l s e - e h o w
Milliseconds 368 84 97 216 20 78 126 110 89 44 12 101 138 133 63 68 80 123 341 157 41 172 93 56 91
Character t h e y l e a d n a t u r a l l y t o t h -h
Milliseconds 47 67 84 65 52 136 30 104 89 73 98 68 122 82 87 110 24 130 134 111 37 100 116 50 385
Character -t t h e m a i n i d e a o f t h i s c
Milliseconds 137 177 432 51 84 36 82 99 81 69 80 81 56 147 69 148 93 107 67 97 67 90 67 82 134
Character h a p t e r , t h - e l i m i t . T h e
Milliseconds 101 94 38 119 107 68 43 31 99 38 99 459 169 79 123 84 166 148 59 121 69 113 75 44 88
Character i d e a o f a l i m i t p l a y s a f
Milliseconds 87 60 116 84 85 79 70 90 60 85 79 85 153 120 51 94 165 174 44 111 83 85 184 78 105
Character o u n d a t i o n a l r o l e t h r o u g h o
Milliseconds 74 74 143 73 108 79 79 804 67 347 85 46 754 47 139 33 100 52 44 146 0 58 100 51 64
Character u t c a l c u l u s .
Milliseconds 88 54 76 119 99 50 140 139 171 145 93 116
WPM Timing
Seconds WPM
2.01 0
4.03 35.74
6.04 29.78
8.06 53.6
10.07 72.66
12.09 81.4
14.1 91.89
16.12 97.53
18.13 101.25
20.15 104.23
22.16 98.55
24.18 100.76
26.19 101.71
28.21 105.51
30.22 104.83
32.24 103.86
34.25 104.76
36.27 106.55
38.28 105.01
40.3 104.53
42.31 105.79
44.32 105.85
46.34 104.36
48.35 103.73
50.37 104.11
52.38 105.15
54.4 106.11
56.41 105.72
58.43 108.03
60.44 109
62.46 109.32
64.47 108.51
66.49 106.85
68.5 107.03
70.52 107.04
72.53 105.72
74.55 105.76
76.56 104.7
78.58 104.61
80.59 104.97
82.61 105.03
84.62 105.08
86.64 104.58
88.65 104.77
90.66 104.69
92.68 105.4
94.69 105.56
96.71 104.11
98.72 104.66
100.74 102.92