pandy69 (pandy69)

Race #2916

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Official speed 116.46 wpm (89.03 seconds elapsed during race)
Without ending ping 116.83 wpm (280 ms delay sending score to TypeRacer’s server)
Timerless 117.12 wpm (225 ms elapsed before first character typed; 88.52 seconds elapsed during race)
Timerless minus one 116.99 wpm, ignoring the first character typed
Race Start April 7, 2024 9:41:01am UTC
Race Finish April 7, 2024 9:42:30am UTC
Outcome Win (1 of 3)
Opponents 2. hh_chng (89.31 wpm)
Accuracy 99.3%
Points 314.44
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 quantitiy 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 barerel change as a function of the amount of liquid poured into it? We see change occuriring in nreearly 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 chanppter, 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 calculcuus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 225 213 329 365 108 124 199 196 85 95 133 17 117 90 133 44 125 198 83 153 84 170 58 97 53
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 127 91 43 159 95 111 53 133 94 44 78 111 88 124 71 99 114 84 102 98 58 116 18 140 97
Character c h a n g e i n o n e q u a n t i t i -i y
Milliseconds 135 38 78 66 97 215 154 118 66 30 98 56 66 69 99 35 152 48 151 127 120 165 379 170 217
Character i s r e l a t e d t o a c h a n g e i n
Milliseconds 191 125 105 116 61 57 111 79 60 151 91 89 28 102 54 109 166 58 106 70 121 95 101 113 18
Character a n o t h e r . H o w d o e s t h e s p
Milliseconds 105 146 51 59 77 37 86 39 87 50 230 115 94 86 109 70 69 41 125 59 75 73 68 77 60
Character e e d o f a f a l l i n g o b j e c t c
Milliseconds 179 143 160 56 128 44 89 66 123 78 100 90 131 49 76 87 66 49 122 148 50 144 86 74 124
Character h a n g e a s a f u n c t i o n o f t i
Milliseconds 116 155 53 125 88 122 125 46 113 91 150 69 130 200 110 113 18 67 46 48 136 101 68 113 97
Character m e ? H o w d o e s t h e l e v e l o f
Milliseconds 149 69 163 69 191 125 135 68 113 68 42 56 83 123 45 93 72 66 69 119 72 68 90 84 33
Character w a t e r i n a b a r e -e r e l c h a n
Milliseconds 115 56 88 92 124 57 78 81 75 23 76 89 88 58 117 116 315 74 60 72 87 75 37 64 74
Character g e a s a f u n c t i o n o f t h e a
Milliseconds 100 68 93 180 58 78 122 120 125 86 134 107 95 25 40 19 80 122 33 91 92 55 88 68 69
Character m o u n t o f l i q u i d p o u r e d i n
Milliseconds 96 40 112 104 211 131 103 112 67 101 81 134 110 74 193 90 93 181 58 125 210 168 99 99 26
Character t o i t ? W e s e e c h a n g e o c c u
Milliseconds 144 16 81 70 102 244 35 169 156 124 50 53 121 98 147 62 60 67 94 61 112 79 44 110 122
Character r i -i r i n g i n n r e -e -r e a r l y e v e
Milliseconds 59 147 544 122 88 66 80 79 76 30 79 98 108 45 314 133 52 49 40 93 82 66 105 97 125
Character r y t h i n g w e o b s e r v e i n t h e
Milliseconds 108 51 431 121 114 25 139 139 100 76 135 223 97 106 81 266 230 42 150 82 29 64 81 88 78
Character w o r l d a n d u n i v e r s e , a n d
Milliseconds 73 81 120 107 63 83 124 93 72 102 65 89 152 94 46 168 82 95 79 77 61 84 91 66 64
Character p o w e r f u l m o d e r n i n s t r u m e n
Milliseconds 94 90 320 101 61 153 102 63 119 154 108 62 143 49 51 124 124 61 105 81 146 81 164 78 72
Character t s h e l p u s s e e m o r e a n d m
Milliseconds 118 79 97 78 113 102 15 125 111 88 115 93 83 113 112 74 81 13 63 106 96 92 76 77 103
Character o r e . I n t h i s s e c t i o n w e i
Milliseconds 60 64 72 97 35 190 171 62 135 103 46 127 72 212 105 176 115 23 37 21 54 155 45 107 89
Character n t r o d u c e t h e i d e a s o f a v e
Milliseconds 55 110 152 111 159 442 121 64 129 111 58 70 73 54 51 122 52 93 100 74 117 175 169 114 184
Character r a g e a n d i n s t a n t a n e o u s r a
Milliseconds 102 100 116 100 100 98 49 105 48 92 59 67 69 162 167 139 259 323 446 118 100 115 80 56 85
Character t e s o f c h a n g e , a n d s h o w t
Milliseconds 104 105 84 129 120 90 95 115 55 62 83 70 139 119 75 102 217 116 112 227 105 29 174 101 66
Character h a t t h e y a r e c l o s e l y r e l a
Milliseconds 57 52 52 55 85 57 84 48 59 85 32 71 82 146 85 122 43 67 119 99 36 113 65 104 86
Character t e d t o t h e s l o p e o f a c u r
Milliseconds 76 71 290 161 123 57 65 148 36 140 95 92 118 142 78 118 118 98 69 80 34 134 57 109 68
Character v e a t a p o i n t P o n t h e c u
Milliseconds 217 67 133 53 70 124 42 119 175 143 91 6 50 144 151 190 117 108 17 101 64 74 60 134 67
Character r v e . W e g i v e p r e c i s e d e v e
Milliseconds 70 199 31 132 37 194 200 84 100 51 100 31 68 88 56 57 174 76 101 87 151 76 203 125 73
Character l o p m e n t s o f t h e s e i m p o r t a
Milliseconds 95 154 51 182 129 76 74 68 90 69 81 65 93 90 102 88 61 64 60 180 20 190 59 135 64
Character n t c o n c e p t s i n t h e n e x t c
Milliseconds 63 69 129 203 79 51 66 188 109 119 137 88 91 54 49 70 79 50 84 54 62 139 54 92 96
Character h a n p -p -n p t e r , b u t f o r n o w w
Milliseconds 70 80 67 173 370 125 153 38 138 41 65 42 152 87 91 81 93 56 82 49 73 41 54 78 137
Character e u s e a n i n f o r m a l a p p r o a c
Milliseconds 13 185 397 51 54 131 37 230 84 153 61 72 117 47 105 102 61 98 62 76 143 66 119 120 97
Character h s o y o u w i l l s e e h o w t h e
Milliseconds 65 56 127 60 63 45 100 67 26 106 51 30 152 26 45 84 123 98 73 43 64 65 103 49 111
Character y l e a d n a t u r a l l y t o t h e m
Milliseconds 20 66 62 85 98 70 104 142 58 74 86 68 99 38 121 76 50 90 79 71 84 73 95 61 78
Character a i n i d e a o f t h i s c h a p t e r ,
Milliseconds 68 107 27 68 178 147 129 67 84 47 78 83 67 69 40 64 79 53 110 57 160 169 181 66 84
Character t h e l i m i t . T h e i d e a o f a
Milliseconds 58 96 90 141 108 60 40 175 132 82 93 70 209 140 127 132 99 189 211 93 106 101 70 86 47
Character l i m i t p l a y s a f o u n d a t i o n
Milliseconds 103 61 115 164 139 39 162 83 33 84 88 130 76 94 46 158 88 51 139 74 119 68 98 55 63
Character a l r o l e t h r o u g h o u t c a l c u l
Milliseconds 122 64 79 74 83 147 14 173 170 123 200 89 62 103 63 103 345 191 132 94 100 33 189 110 68
Character c u -u -c u s .
Milliseconds 183 306 262 98 148 100 41
WPM Timing
Seconds WPM
1.78 53.92
3.56 84.24
5.34 98.85
7.12 106.15
8.9 98.4
10.68 103.34
12.46 107.83
14.24 111.2
16.02 112.33
17.81 113.22
19.59 113.96
21.37 117.38
23.15 116.65
24.93 118.91
26.71 118.17
28.49 117.1
30.27 117.74
32.05 114.57
33.83 114.22
35.61 113.22
37.39 113.93
39.17 114.27
40.95 114.57
42.73 115.42
44.51 115.65
46.29 115.35
48.07 115.32
49.85 115.54
51.64 113.88
53.42 113.9
55.2 114.79
56.98 114.99
58.76 115.39
60.54 115.17
62.32 115.34
64.1 115.7
65.88 115.85
67.66 116.17
69.44 115.26
71.22 115.92
73 116.05
74.78 116.82
76.56 117.71
78.34 118.25
80.12 118.47
81.9 117.94
83.68 118.16
85.47 118.5
87.25 118.01
89.03 116.46