Darien (devonent)

Race #516

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Official speed 89.57 wpm (115.75 seconds elapsed during race)
Without ending ping 89.69 wpm (155 ms delay sending score to TypeRacer’s server)
Timerless 90.03 wpm (442 ms elapsed before first character typed; 115.16 seconds elapsed during race)
Timerless minus one 89.93 wpm, ignoring the first character typed
Race Start September 13, 2023 3:09:20am UTC
Race Finish September 13, 2023 3:11:15am UTC
Outcome Win (1 of 4)
Accuracy 98.8%
Points 241.83
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 a nother. How does the speed of a falling ojbbject 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 ocucurring in nearly everything we observe in the world and universe, and powerful modern instruments help us se moe 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 the curve. We give precise developments of these important concetppts in the next chapter, but for now we ose use ainn informal apporroach so you will see how they lead naturally to the main idea of this chapter, the limit. The idea of a limit plays a offoundational role throughout calcuulus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 442 200 169 98 73 145 188 111 95 149 91 94 88 89 114 82 145 160 84 124 101 67 76 74 160
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 91 95 167 365 122 131 121 95 169 174 40 154 25 255 177 70 114 72 93 141 41 106 70 121 96
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 117 136 98 84 79 34 77 110 78 73 183 97 150 230 262 90 148 64 94 78 101 252 306 194 79
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 82 196 55 132 84 117 65 250 147 104 102 81 355 110 244 88 101 83 77 54 78 101 102 47 141
Character - n o t h e r . H o w d o e s t h e s p
Milliseconds 368 319 194 73 109 130 87 96 136 77 163 90 188 134 206 56 99 57 74 326 60 136 93 144 130
Character e e d o f a f a l l i n g o j b -b -j b j e
Milliseconds 73 169 161 95 360 122 66 121 82 120 104 121 150 122 64 103 86 92 211 22 460 172 139 425 78
Character c t c h a n g e a s a f u n c t i o n o
Milliseconds 202 159 70 284 151 82 100 45 47 107 100 137 143 233 74 174 99 172 83 156 146 82 103 95 159
Character f t i m e ? H o w d o e s t h e l e v e
Milliseconds 104 66 121 67 68 82 228 107 331 274 114 92 140 91 107 91 58 169 82 100 73 145 57 102 88
Character l o f w a t e r i n a b a r r e l c h
Milliseconds 220 113 154 123 105 302 96 152 61 115 88 100 69 98 74 139 108 87 137 154 177 156 122 279 84
Character a n g e a s a f u n c t i o n o f t h e
Milliseconds 61 106 112 57 119 103 126 123 144 81 181 130 201 91 267 218 46 94 174 264 152 133 90 102 100
Character a m o u n t o f l i q u i d p o u r e d
Milliseconds 108 112 85 309 86 191 64 96 135 116 58 115 91 183 67 82 222 122 241 352 363 203 196 183 74
Character i n t o i t ? W e s e e c h a n g e o c
Milliseconds 108 79 62 95 87 126 106 336 106 288 181 149 125 148 150 97 155 86 74 94 59 38 113 103 153
Character u -u c u r r i n g i n n e a r l y e v e r y
Milliseconds 216 311 147 110 160 161 129 148 107 86 132 45 53 136 101 119 132 143 154 44 87 174 49 175 155
Character t h i n g w e o b s e r v e i n t h e w
Milliseconds 235 133 94 118 100 109 145 86 142 156 127 161 60 84 192 72 119 128 402 188 108 86 90 86 105
Character o r l d a n d u n i v e r s e , a n d p o
Milliseconds 106 115 111 122 179 145 142 166 171 190 186 101 77 58 173 117 72 151 57 131 111 95 127 128 91
Character w e r f u l m o d e r n i n s t r u m e n t s
Milliseconds 110 41 82 164 114 148 105 232 117 131 157 82 68 88 111 72 110 97 178 95 193 102 80 86 147
Character h e l p u s s e m o -o -m - e m o r e a
Milliseconds 73 162 127 85 218 185 129 78 112 200 84 122 190 84 202 156 173 178 82 149 49 73 26 134 149
Character n d m o r e . I n t h i s s e c t i o n
Milliseconds 77 103 115 87 45 106 11 165 122 198 212 218 166 91 36 117 101 87 61 228 142 74 53 129 70
Character w e i n t r o d u c e t h e i d e a s o f
Milliseconds 110 21 146 279 73 86 162 88 115 91 116 138 88 103 79 95 70 118 45 124 72 127 166 168 114
Character a v e r a g e a n d i n s t a n t a n e o u
Milliseconds 99 90 182 78 253 90 196 123 125 312 139 127 118 191 39 113 143 62 121 145 67 199 170 192 64
Character s r a t e s o f c h a n g e , a n d s h
Milliseconds 109 95 149 74 152 46 102 62 130 124 110 151 100 93 79 63 38 137 56 87 101 125 126 396 112
Character o w t h a t t h e y a r e c l o s e l y
Milliseconds 50 93 91 256 112 81 75 117 142 289 228 100 192 167 185 318 141 335 101 135 27 52 169 180 50
Character r e l a t e d t o t h e s l o p e o f a
Milliseconds 136 52 146 138 129 49 168 113 128 91 100 39 260 168 83 150 100 136 117 92 75 169 91 85 87
Character c u r v e a t a p o i n t P o n t -
Milliseconds 131 86 147 68 224 75 127 124 183 121 110 82 157 123 297 80 151 132 209 107 192 110 203 35 288
Character -t t h e c u r v e . W e g i v e p r e c
Milliseconds 177 109 145 132 96 91 127 90 98 393 80 155 140 289 211 160 287 143 73 62 87 112 333 183 247
Character i s e d e v e l o p m e n t s o f t h e s e
Milliseconds 96 102 65 108 371 140 156 43 81 164 127 222 92 98 71 101 86 140 92 105 137 127 92 130 96
Character i m p o r t a n t c o n c e t p -p -t p t s i
Milliseconds 125 123 100 61 84 13 173 65 115 84 149 146 75 135 99 135 188 43 218 144 188 65 52 95 125
Character n t h e n e x t c h a p t e r , b u t f
Milliseconds 60 63 126 77 90 89 121 84 206 186 151 311 94 75 111 122 93 111 113 62 167 142 126 98 140
Character o r n o w w e o s e - -e -s -o u s e a i n
Milliseconds 77 106 76 153 51 94 88 125 183 163 246 97 44 99 237 161 149 130 130 85 15 94 219 117 135
Character -n -i n i n f o r m a l a p p o r -r -o r o a c h
Milliseconds 167 180 133 71 127 76 115 73 107 95 102 127 195 230 82 186 171 227 200 150 85 82 92 168 86
Character s o y o u w i l l s e e h o w t h e y
Milliseconds 71 170 62 85 148 112 70 97 202 77 158 201 114 159 81 189 145 162 70 215 102 150 80 98 89
Character l e a d n a t u r a l l y t o t h e m a
Milliseconds 87 274 100 48 189 100 134 74 101 139 99 31 71 164 193 77 130 40 80 98 101 101 78 162 146
Character i n i d e a o f t h i s c h a p t e r ,
Milliseconds 120 39 87 147 54 142 57 134 136 110 82 276 89 57 104 97 161 112 137 117 127 164 38 118 81
Character t h e l i m i t . T h e i d e a o f a
Milliseconds 114 68 115 80 146 93 105 96 121 250 185 229 113 89 97 96 67 136 82 120 144 90 92 90 101
Character l i m i t p l a y s a o f -f -o f o u n d a t
Milliseconds 127 90 100 103 143 88 145 79 77 157 122 82 74 93 226 51 181 151 139 67 64 168 50 82 162
Character i o n a l r o l e t h r o u g h o u t c a l
Milliseconds 87 89 48 114 108 125 110 125 176 101 130 128 152 129 112 77 162 122 172 75 135 110 150 96 103
Character c u u -u l u s .
Milliseconds 151 86 516 297 184 122 121 72
WPM Timing
Seconds WPM
2.32 82.94
4.63 88.12
6.95 96.76
9.26 93.3
11.58 92.27
13.89 90.71
16.21 91.82
18.52 91.36
20.84 86.39
23.15 88.12
25.47 88.59
27.78 89.85
30.1 90.51
32.41 89.6
34.73 90.19
37.04 89.09
39.36 89.03
41.67 88.41
43.99 88.94
46.3 88.9
48.62 89.11
50.93 89.77
53.25 90.15
55.56 89.2
57.88 89.57
60.19 90.51
62.51 90.23
64.82 90.53
67.14 91.16
69.45 90.88
71.77 90.79
74.08 91.2
76.4 90.95
78.71 90.1
81.03 89.6
83.34 89.56
85.66 90.08
87.97 90.16
90.29 90.11
92.6 89.16
94.92 89
97.23 88.49
99.55 88.48
101.86 88.94
104.18 89.39
106.49 89.7
108.81 89.99
111.12 89.95
113.44 90.13
115.75 89.57