🤔 (akixuu)

Race #792

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Official speed 100.86 wpm (102.80 seconds elapsed during race)
Without ending ping 100.90 wpm (36 ms delay sending score to TypeRacer’s server)
Timerless 101.18 wpm (288 ms elapsed before first character typed; 102.47 seconds elapsed during race)
Timerless minus one 101.06 wpm, ignoring the first character typed
Race Start March 17, 2024 8:13:01pm UTC
Race Finish March 17, 2024 8:14:44pm UTC
Outcome Win (1 of 3)
Accuracy 96.6%
Points 272.31
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 Cslcalculus is a tool that helps us understand how a change in one quanittity is related to a change in another . How does the speed of a wafalling object change as a funtionction of tiemme? hoHow des oes the level of water in a barrel change as a function of the amount of liquird poured into it? We see change occuring iring in nearly everything we observe in the world and univdrserse, and powerful modersn n instruments help us see more and more. In this section we insttrocudece thuce the ideas of average and instanteanoeeous rates of change, and sho ww that they are cllosely relalteated to teh he slope of a cuve rve at a point P on the curve. We give precised devleopelopments of tehsehese important concepts in the next chapter, but for now we use an informal appraocoach so you will see how they lead naturally to the main dieidea of this chapter, the limit. The idea of a limit plays a foundational role thorughhtthroughout calculus.
Timing
Character C s l c -c -l -s a l c u l u s i s a t o o l
Milliseconds 288 170 60 115 227 125 104 72 98 121 150 152 132 105 60 116 72 61 120 74 145 36 122 144 103
Character t h a t h e l p s u s u n d e r s t a n d
Milliseconds 99 67 35 79 30 73 103 68 88 32 126 86 157 103 188 31 66 135 63 82 108 73 49 73 59
Character h o w a c h a n g e i n o n e q u a n i
Milliseconds 80 42 54 91 141 143 140 43 74 85 116 35 101 201 59 97 151 62 84 75 253 62 157 44 187
Character t -t -i t i t y i s r e l a t e d t o a c
Milliseconds 7 321 133 101 74 297 114 182 163 52 66 118 44 80 88 75 71 189 23 116 50 58 152 230 130
Character h a n g e i n a n o t h e r - . H o w d
Milliseconds 60 84 68 59 44 49 52 56 79 17 116 49 78 53 62 74 167 202 149 69 162 103 57 60 114
Character o e s t h e s p e e d o f a w a -a -w f a
Milliseconds 78 82 24 42 120 86 46 50 122 84 79 149 171 26 73 204 141 259 116 249 74 167 116 152 37
Character l l i n g o b j e c t c h a n g e a s a
Milliseconds 102 134 122 60 52 34 108 107 74 97 175 122 85 146 49 29 122 85 36 42 65 90 88 90 103
Character f u n t i o n -n -o -i -t c t i o n o f t i e m -m
Milliseconds 81 113 29 123 121 56 30 185 124 127 126 83 135 25 61 30 66 108 33 66 114 39 40 12 475
Character -e m e ? h o -o -h H o w d e s - -s -e o e s t
Milliseconds 115 166 69 218 73 289 208 188 113 142 107 13 189 96 158 47 85 169 136 131 128 74 18 53 113
Character h e l e v e l o f w a t e r i n a b a
Milliseconds 52 36 54 110 84 116 61 53 111 137 115 50 145 73 145 67 100 46 74 54 91 61 108 92 131
Character r r e l c h a n g e a s a f u n c t i o n
Milliseconds 98 159 114 103 96 135 65 6 121 74 42 31 48 120 70 83 103 114 93 41 67 133 25 36 11
Character o f t h e a m o u n t o f l i q u i r -r
Milliseconds 98 109 48 61 156 43 43 54 145 86 75 77 128 47 54 79 109 44 120 73 122 109 29 80 279
Character d p o u r e d i n t o i t ? W e s e e
Milliseconds 71 43 230 68 362 98 60 189 42 144 39 84 97 86 217 92 186 110 131 178 66 265 124 150 63
Character c h a n g e o c c u r i n g i -i - -g -n -i r i n
Milliseconds 137 56 7 137 78 32 48 65 87 132 97 74 91 60 60 55 74 228 123 138 129 121 97 55 42
Character g i n n e a r l y e v e r y t h i n g w e
Milliseconds 77 37 92 36 73 163 67 57 71 84 109 73 59 140 86 67 41 140 50 66 109 55 46 86 103
Character o b s e r v e i n t h e w o r l d a n d
Milliseconds 80 158 107 146 74 54 176 43 59 80 47 67 73 73 6 91 85 43 108 79 80 54 72 120 92
Character u n i v d r s -s -r -d e r s e , a n d p o w e
Milliseconds 50 227 25 207 97 68 113 74 157 133 135 85 54 83 110 85 68 88 93 56 64 84 26 97 48
Character r f u l m o d e r s n - -n -s n i n s t r u m
Milliseconds 44 161 32 49 85 134 52 68 140 48 80 112 148 91 133 138 170 79 86 54 84 104 150 67 164
Character e n t s h e l p u s s e e m o r e a n d
Milliseconds 86 84 87 47 66 199 79 56 66 79 78 85 96 118 89 153 89 99 59 103 37 42 67 67 84
Character m o r e . I n t h i s s e c t i o n w e
Milliseconds 55 43 54 83 44 79 71 153 145 122 91 58 58 43 53 122 246 182 133 23 69 7 84 67 80
Character i n s t -t -s t r o c u -u -c d e -e c e t h -h -t -
Milliseconds 78 143 51 140 108 291 133 55 139 42 190 94 219 127 43 164 235 62 156 62 98 54 200 127 139
Character -e -c u c e t h e i d e a s o f a v e r a g
Milliseconds 146 103 145 37 163 56 90 60 37 66 114 56 123 28 134 61 125 62 72 177 103 120 87 66 121
Character e a n d i n s t a n t e -e a n o e -e -o e o u s
Milliseconds 30 57 57 110 50 65 59 52 415 111 59 124 65 91 315 68 109 127 181 104 125 104 66 110 56
Character r a t e s o f c h a n g e , a n d s h o
Milliseconds 126 120 68 121 37 78 79 163 91 73 156 58 35 129 59 36 74 53 55 103 60 61 97 68 12
Character w -w - w t h a t t h e y a r e c l -l l o
Milliseconds 339 23 254 111 66 36 92 66 25 96 25 143 14 60 117 55 76 66 63 37 223 48 272 564 153
Character s e l y r e l a l -l -a t e -e -t a t e d t o t
Milliseconds 73 54 143 128 73 134 49 18 377 72 308 117 169 78 225 117 101 91 66 169 66 117 29 74 110
Character e h - -h -e h e s l o p e o f a c u v e
Milliseconds 115 0 193 217 129 122 131 43 50 78 96 153 109 120 67 84 79 78 62 132 87 85 134 114 91
Character - -e -v r v e a t a p o i n t P o n t h
Milliseconds 205 128 139 90 190 61 72 91 357 73 79 115 93 46 56 29 54 38 254 121 109 48 79 101 38
Character e c u r v e . W e g i v e p r e c i s e d
Milliseconds 31 78 134 90 98 159 40 86 61 229 159 66 159 81 106 35 42 146 109 61 183 65 105 113 184
Character - -d d e v l e o p -p -o -e -l e l o p m e n t s
Milliseconds 33 348 108 24 103 158 110 61 17 127 50 296 123 137 122 91 102 600 67 205 75 84 62 71 61
Character o f t e h s e -e -s -h -e h e s e i m p o r t a n
Milliseconds 73 67 66 98 37 0 151 89 206 133 129 315 149 57 134 89 73 120 76 41 66 67 162 37 68
Character t c o n c e p t s i n t h e n e x t c h
Milliseconds 67 54 153 46 32 115 168 62 99 71 55 126 50 66 120 48 24 80 198 38 182 140 47 178 42
Character a p t e r , b u t f o r n o w w e u s e
Milliseconds 55 132 103 73 80 77 91 140 54 110 55 128 65 78 57 72 41 60 92 250 115 78 187 74 91
Character a n i n f o r m a l a p p r a o c -c -o -a o a
Milliseconds 54 295 112 102 114 45 78 119 68 119 63 345 138 281 179 131 48 90 7 199 162 119 129 142 35
Character c h s o y o u w i l l s e e h o w t h
Milliseconds 153 74 84 108 104 68 166 61 61 84 105 31 60 133 41 87 67 164 52 87 40 183 128 213 9
Character e y l e a d n a t u r a l l y t o t h e
Milliseconds 69 84 62 85 82 39 130 33 68 60 114 79 95 21 43 131 73 48 110 42 67 122 55 53 61
Character m a i n d i e -e -i -d i d e a o f t h i s c
Milliseconds 109 60 109 54 49 96 37 138 164 140 118 138 68 136 51 90 134 61 55 121 36 42 62 59 139
Character h a p t e r , t h e l i m i t . T h e i d
Milliseconds 66 61 121 85 86 91 358 102 98 61 55 63 51 97 53 98 83 117 74 175 90 49 61 137 52
Character e a o f a l i m i t p l a y s a f o u
Milliseconds 173 15 96 120 60 90 50 110 74 96 60 115 147 114 115 169 317 40 100 145 59 218 0 49 48
Character n d a t i o n a l r o l e t h o r u g h -h -t -h
Milliseconds 150 43 51 102 53 50 24 96 116 296 202 114 169 98 35 147 36 115 24 47 105 67 186 184 0
Character -o -r -u -g h t -t -h t h r o u g h o u t c a l c u l
Milliseconds 0 0 0 0 443 52 224 103 87 60 97 61 84 375 118 126 91 98 48 239 64 53 122 95 130
Character u s .
Milliseconds 128 138 126
WPM Timing
Seconds WPM
2.06 52.53
4.11 93.39
6.17 108.95
8.22 100.68
10.28 102.73
12.34 106.04
14.39 108.4
16.45 105.06
18.5 105.06
20.56 102.14
22.62 96.57
24.67 99.71
26.73 102.37
28.78 106.31
30.84 105.06
32.89 104.33
34.95 103
37.01 105.39
39.06 107.83
41.12 106.52
43.17 106.17
45.23 106.92
47.29 108.87
49.34 107.98
51.4 103.9
53.45 104.61
55.51 104.41
57.57 104.23
59.62 104.86
61.68 103.9
63.73 102.05
65.79 101.23
67.85 100.64
69.9 101.29
71.96 101.73
74.01 99.55
76.07 99.07
78.12 98.76
80.18 99.67
82.24 100.39
84.29 100.22
86.35 99.5
88.4 100.31
90.46 101.48
92.52 101.56
94.57 102.02
96.63 102.21
98.68 102.51
100.74 101.01
102.8 100.86