Greg J (gregjay3)

Race #653

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Official speed 102.95 wpm (100.71 seconds elapsed during race)
Without ending ping 103.19 wpm (230 ms delay sending score to TypeRacer’s server)
Timerless 103.51 wpm (316 ms elapsed before first character typed; 100.16 seconds elapsed during race)
Timerless minus one 103.39 wpm, ignoring the first character typed
Race Start July 25, 2024 7:16:06pm UTC
Race Finish July 25, 2024 7:17:47pm UTC
Outcome Win (1 of 4)
Accuracy 96.7%
Points 277.97
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 ACalculus is a tool that helps us sundndertsrstand how a change in on que quantity is related to a change in another. How does the speed of a falling objects chobveject change as a function of time? How does the level of water in a barrel change sas a function of the amount of liquid poured into it? We see change occuring ioccurring in earnearly everything we observe in the world and universe, and powerufful modern instruments help us see more and more. In this secitontion we introdfuuce the ideas of average and instantaneous ratees oftrates of change, and show that hey they are closeslyly related to the slope of a curve at a point P on the mnecurve. WE giEe we WE g e give prrecise devlopelopments of thse ese important concepts in the next chapter ,, but for now we use an informal approach so you will se how see how they lead lnmatuaturally to hte the maiun n idea of this chapter, the limit. The odeidea of a limit plays a founatddndational role thgroughout claalculus.
Timing
Character A -A C a l c u l u s i s a t o o l t h a t
Milliseconds 316 249 90 94 72 91 89 158 228 204 50 131 74 53 88 64 96 36 105 124 44 56 97 16 64
Character h e l p s u s s u n d -d -s -n n d e r t s -s -t
Milliseconds 34 61 64 118 109 161 58 138 88 70 126 76 136 38 158 236 0 144 32 91 80 4 97 190 89
Character -r r s t a n d h o w a c h a n g e i n o
Milliseconds 93 420 113 111 86 76 55 53 150 69 84 40 99 48 117 82 80 55 65 53 50 37 140 34 137
Character n q u -u -q - e q u a n t i t y i s r e l a
Milliseconds 143 143 100 98 182 98 96 53 40 67 96 111 96 83 133 82 132 50 87 54 56 192 132 74 116
Character t e d t o a c h a n g e i n a n o t h e
Milliseconds 120 43 106 45 126 10 68 81 66 80 66 91 55 69 52 28 69 145 22 87 70 137 55 104 59
Character r . H o w d o e s t h e s p e e d o f
Milliseconds 44 76 24 176 59 107 54 88 59 72 58 18 127 56 69 25 134 29 121 123 54 85 56 65 72
Character a f a l l i n g o b j e c t s c h -c -h -o -b -j
Milliseconds 59 80 81 104 80 106 124 144 38 45 106 27 203 52 59 147 83 42 123 70 226 0 121 0 0
Character -e -c -t -s - o b v e -e -v j e c t c h a n g e a s
Milliseconds 0 0 0 0 0 153 171 6 220 184 84 157 75 33 175 104 156 104 75 59 73 43 78 115 217
Character a f u n c t i o n o f t i m e ? H o w
Milliseconds 38 107 73 106 52 149 49 138 82 123 50 65 111 85 47 99 48 141 29 155 77 134 76 97 29
Character d o e s t h e l e v e l o f w a t e r i
Milliseconds 112 47 71 56 26 95 60 51 28 124 54 83 75 56 57 115 15 79 68 109 78 66 81 45 47
Character n a b a r r e l c h a n g e s -s a s a
Milliseconds 146 37 40 85 90 142 44 114 93 77 70 115 75 50 88 37 84 45 119 261 146 31 88 59 72
Character f u n c t i o n o f t h e a m o u n t o f
Milliseconds 77 75 141 26 171 20 113 41 54 81 66 59 86 37 69 48 100 56 132 154 150 36 57 80 74
Character l i q u i d p o u r e d i n t o i t ? W
Milliseconds 45 144 118 62 118 119 53 45 101 13 416 101 103 106 42 52 150 47 102 44 99 99 143 65 103
Character e s e e c h a n g e o c c u r i n g i -o -c
Milliseconds 75 49 182 49 109 74 97 88 35 111 66 76 61 79 106 119 88 83 60 142 24 55 83 204 0
Character -c -u -r -i -n -g - -i o c c u r r i n g i n e a r -r
Milliseconds 0 0 0 0 0 0 0 0 231 92 131 112 71 100 81 127 43 43 80 130 32 364 89 105 179
Character -a -e n e a r l y e v e r y t h i n g w e o b
Milliseconds 106 93 174 38 93 61 96 63 67 108 115 58 68 136 100 35 118 156 19 56 119 49 46 145 56
Character s e r v e i n t h e w o r l d a n d u n
Milliseconds 186 59 121 143 90 55 61 146 34 69 97 11 71 107 84 50 99 47 45 42 82 69 49 73 135
Character i v e r s e , a n d p o w e r u f -f -u f u l
Milliseconds 137 60 95 51 164 74 72 100 73 55 73 44 162 125 84 22 119 61 81 131 100 72 79 135 71
Character m o d e r n i n s t r u m e n t s h e l p u
Milliseconds 112 124 54 109 48 60 77 71 154 102 194 105 27 208 109 64 75 107 58 29 111 69 119 64 142
Character s s e e m o r e a n d m o r e . I n t
Milliseconds 49 40 123 128 121 35 62 132 13 38 48 96 61 71 28 58 123 37 18 130 92 92 130 24 73
Character h i s s e c i t o n -n -o -t -i t i o n w e i n
Milliseconds 80 115 39 53 97 29 146 134 0 110 146 146 101 93 303 285 40 117 146 29 92 47 67 74 129
Character t r o d f u -u -f u c e t h e i d e a s o f
Milliseconds 48 97 108 53 13 172 153 114 402 74 106 15 116 19 113 78 73 83 123 42 61 68 81 62 66
Character a v e r a g e a n d i n s t a n t a n e o u s
Milliseconds 130 149 326 93 107 109 64 39 113 63 58 40 114 134 24 126 56 336 56 370 135 264 93 158 83
Character r a t e e s o f -r -a -t -e -e -s - -o -f t -t r a t e
Milliseconds 33 73 107 119 54 205 31 67 84 67 257 0 0 0 0 0 0 0 0 167 196 92 117 101 123
Character s o f c h a n g e , a n d s h o w t h a
Milliseconds 10 277 114 47 63 108 76 73 78 54 61 129 104 91 114 40 52 184 70 163 39 46 174 79 42
Character t h e y - -h -e -y t h e y a r e c l o s e s
Milliseconds 99 12 150 50 120 70 167 104 0 0 154 64 63 78 73 68 54 103 59 95 58 117 48 44 106
Character l y -y -l -s l y r e l a t e d t o t h e s l
Milliseconds 80 82 118 90 100 90 59 84 100 149 104 115 62 85 103 42 141 10 100 65 96 30 54 104 48
Character o p e o f a c u r v e a t a p o i n t
Milliseconds 120 124 13 51 91 60 31 107 61 63 95 66 126 40 83 108 144 68 58 85 349 154 129 158 39
Character P o n t h e m n e -e -n -m c u r v e . W E
Milliseconds 47 106 51 132 148 34 58 94 38 41 319 27 32 195 107 88 271 94 77 139 88 110 335 93 50
Character g i -E - -g -i E -E -W e - -e w e - -e -w W E g -g
Milliseconds 73 113 72 349 0 0 0 55 325 131 85 53 183 98 107 73 113 168 108 103 156 53 143 236 192
Character - - -E e g i v e p r -r r e c i s e d e v l
Milliseconds 104 138 113 109 116 47 151 82 63 76 20 186 44 193 256 133 109 72 85 54 47 109 102 81 116
Character o p -p -o -l e l o p m e n t s o f t h s e - -e
Milliseconds 126 131 108 98 155 102 65 118 117 195 101 49 62 122 50 43 90 26 112 40 111 13 82 237 81
Character -s e s e i m p o r t a n t c o n c e p t s i
Milliseconds 94 325 92 56 49 48 137 145 95 41 123 78 70 47 70 98 31 161 29 82 120 16 145 61 78
Character n t h e n e x t c h a p t e r , -, - , b
Milliseconds 135 42 53 86 38 38 95 43 146 173 43 115 79 71 156 66 78 37 77 224 172 99 125 94 48
Character u t f o r n o w w e u s e a n i n f o
Milliseconds 83 73 49 96 44 90 33 63 136 44 25 116 52 38 110 61 38 37 148 94 71 97 138 72 89
Character r m a l a p p r o a c h s o y o u w i l l
Milliseconds 63 79 80 67 40 91 97 107 64 88 70 57 104 31 92 65 69 150 54 134 34 94 34 155 89
Character s e h o w -s -e - -h -o -w - s e e h o w t h
Milliseconds 78 81 35 96 69 144 38 64 227 0 0 0 0 0 0 309 40 142 85 97 157 56 25 103 66
Character e y l e a d l -l n m a t u -u -m -a -t a t u r a l
Milliseconds 46 84 38 223 68 101 83 57 114 159 129 12 60 79 84 154 249 0 0 51 86 86 40 92 73
Character l y t o h t e - -h -t -e t h e m a i u n -
Milliseconds 102 37 47 204 88 81 148 18 187 43 129 106 0 0 102 274 50 50 84 87 71 13 122 48 135
Character -n -u n i d e a o f t h i s c h a p t e r ,
Milliseconds 100 88 262 81 80 93 130 91 39 92 44 47 94 68 120 47 10 81 108 98 119 56 111 61 71
Character t h e l i m i t . T h e o d e -e -d -o i d e
Milliseconds 70 63 66 126 29 58 125 146 125 55 153 133 144 91 90 64 80 61 138 69 104 92 194 19 123
Character a o f a l i m i t p l a y s a f o u n
Milliseconds 75 32 98 45 60 67 81 25 115 143 131 23 53 108 116 22 109 125 53 94 69 142 57 139 154
Character a t -t -a -n d -d d -d n d a t i o n a l r o l e t
Milliseconds 104 134 205 95 92 204 141 165 255 159 55 77 103 47 108 81 137 47 64 101 24 134 45 36 97
Character h g -g r o u g h o u t c l a -a -l a l c u l u s .
Milliseconds 148 19 255 383 67 162 67 85 149 116 61 58 276 136 29 177 115 68 83 65 119 136 148 112 90
WPM Timing
Seconds WPM
2.01 77.45
4.03 101.28
6.04 85.39
8.06 92.35
10.07 96.52
12.09 107.24
14.1 114.9
16.11 105.75
18.13 103.93
20.14 106.64
22.16 113.2
24.17 113.69
26.18 116.86
28.2 116.6
30.21 115.98
32.23 113.57
34.24 111.8
36.26 113.53
38.27 115.08
40.28 114.39
42.3 115.75
44.31 116.72
46.33 115.27
48.34 114.44
50.35 114.15
52.37 111.82
54.38 110.55
56.4 110.43
58.41 109.91
60.43 111.21
62.44 111.47
64.45 110.4
66.47 107.42
68.48 104.44
70.5 104.35
72.51 103.93
74.52 103.38
76.54 104.57
78.55 104.8
80.57 105.9
82.58 105.35
84.6 105.4
86.61 104.75
88.62 103.85
90.64 104.99
92.65 104.52
94.67 105.08
96.68 103.76
98.69 103.59
100.71 102.95