Cloud (cloudrazer)

Race #16

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Official speed 98.48 wpm (105.28 seconds elapsed during race)
Without ending ping 98.60 wpm (133 ms delay sending score to TypeRacer’s server)
Timerless 98.81 wpm (223 ms elapsed before first character typed; 104.92 seconds elapsed during race)
Timerless minus one 98.70 wpm, ignoring the first character typed
Race Start May 30, 2024 1:12:49am UTC
Race Finish May 30, 2024 1:14:35am UTC
Outcome Win (1 of 2)
Accuracy 97.0%
Points 265.89
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 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 falling objobject fachange as a funciton otion of time? HOw ow does the level of water in a barrel change as a function of the amount lfoof liquied d poured into it? We see change occurring in nearly everythingf w we observe in the world and universe, and powerful modern instruments hlep=elp us see more and more. In this section we introduce the ideas of average and instantaneiouous rates of change, and show that they are closed relly related ot to the slolppe of a curve at a apoint P on the curve. We give precise developments oc f these inimportant concepts in the next chaprter, but for now sewe use an informal approach so you will see how they lead naturally to the main idea of this chapter, the limit. The idea oof a limit plyasays a foundational role throughout claalculus/.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 223 184 75 124 206 215 168 101 35 97 95 33 119 38 109 52 120 135 39 139 96 57 52 55 102
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 66 69 95 104 27 121 89 44 89 159 6 145 66 66 93 60 73 100 20 84 59 29 81 55 83
Character c h a n g e i n o n e q u a n i t -t -i t i t
Milliseconds 112 78 77 68 67 54 18 51 56 63 60 85 31 103 135 68 101 81 102 31 362 99 130 75 105
Character y i s r e l a t e d t o a c h a n g e
Milliseconds 69 63 93 85 45 198 55 116 75 43 62 140 49 113 5 87 52 99 87 62 77 76 62 52 29
Character i n a n o t h e r , -, . H o w d o e s t h
Milliseconds 62 65 81 29 88 37 85 46 90 48 98 244 213 84 179 112 110 93 112 64 106 46 58 96 44
Character e s p e e d o f a f a l l i n g o b j -j
Milliseconds 80 52 95 69 85 138 128 81 88 46 85 61 80 72 53 52 133 65 60 76 36 62 117 26 257
Character -b o -o b j e c t f a -a -f c h a n g e a s a
Milliseconds 185 422 281 140 94 129 122 170 69 116 58 243 117 127 77 49 91 55 50 66 80 44 28 313 189
Character f u n c i t o n o -o - -n -o -t -i t i o n o f t
Milliseconds 121 54 155 64 161 3 41 34 91 79 256 111 126 124 124 378 140 114 48 76 98 102 107 54 129
Character i m e ? H O w - -w -O o w d o e s t h e l
Milliseconds 41 56 59 175 158 241 58 153 89 226 113 127 205 43 93 56 74 91 55 41 120 36 95 36 74
Character e v e l o f w a t e r i n a b a r r e l
Milliseconds 83 63 83 66 98 138 127 81 95 59 69 104 63 23 82 46 102 99 78 119 71 104 142 62 58
Character c h a n g e a s a f u n c t i o n o f
Milliseconds 56 96 72 60 80 53 42 76 80 35 54 176 218 149 95 143 64 146 8 49 32 71 75 68 64
Character t h e a m o u n t l f -f o -o -l o f l i q u i
Milliseconds 85 38 86 56 85 65 29 124 140 66 108 73 171 264 411 265 116 182 90 75 64 87 97 132 83
Character e d - -d -e d p o u r e d i n t o i t ? W
Milliseconds 60 0 124 270 118 133 89 87 114 82 152 134 73 159 110 79 50 120 55 65 116 94 190 156 197
Character e s e e c h a n g e o c c u r r i n g i n
Milliseconds 233 185 67 58 117 103 90 75 63 79 67 66 64 58 107 178 337 83 219 197 47 77 43 67 43
Character n e a r l y e v e r y t h i n g f w -w - -f
Milliseconds 99 119 52 332 90 100 124 91 73 147 121 75 71 115 75 72 105 77 4 59 90 251 118 139 192
Character w e o b s e r v e i n t h e w o r l d a
Milliseconds 61 88 238 151 91 127 60 63 207 93 88 84 68 75 27 96 42 94 48 98 74 79 87 55 95
Character n d u n i v e r s e , a n d p o w e r f u l
Milliseconds 44 114 16 97 131 94 4 147 73 55 65 117 107 140 120 96 113 190 72 55 46 44 136 135 123
Character m o d e r n i n s t r u m e n t s h l e p =
Milliseconds 110 100 75 40 143 50 63 76 145 163 132 39 152 93 155 41 116 41 83 29 70 118 6 85 334
Character -= -p -e -l e l p u s s e e m o r e a n d m
Milliseconds 4 119 130 121 101 105 105 413 163 93 73 121 52 160 53 45 62 41 42 70 78 61 90 45 33
Character o r e . I n t h i s s e c t i o n w e i
Milliseconds 64 54 46 98 104 201 133 68 125 60 72 66 82 92 38 180 179 8 44 13 103 113 73 98 150
Character n t r o d u c e t h e i d e a s o f a v e
Milliseconds 53 67 131 56 91 62 108 49 68 107 62 54 85 50 88 168 76 62 103 76 84 102 36 114 113
Character r a g e a n d i n s t a n t a n e i o u -u -o -i
Milliseconds 80 102 69 57 66 83 71 92 67 78 77 23 60 83 97 109 173 207 277 117 95 116 278 127 585
Character o u s r a t e s o f c h a n g e , a n d
Milliseconds 257 75 87 59 128 79 113 70 47 49 86 84 57 124 61 73 87 88 41 112 61 121 91 110 96
Character s h o w t h a t t h e y a r e c l o s e d
Milliseconds 174 102 67 66 94 87 83 39 47 82 75 86 69 107 69 102 193 85 168 138 65 119 53 33 145
Character r e l -l -e -r - -d l y r e l a t e d o t - -t
Milliseconds 75 113 43 98 224 122 139 134 246 230 201 86 138 54 131 74 40 67 133 92 125 24 130 314 115
Character -o t o t h e s l o l p -p -l p e o f a c u
Milliseconds 136 173 61 49 89 115 64 131 83 108 235 10 46 359 126 329 138 83 112 99 133 55 102 80 150
Character r v e a t a a -a p o i n t P o n t h e
Milliseconds 75 202 71 116 305 88 109 118 108 90 463 276 65 125 62 114 84 210 132 144 55 86 88 80 60
Character c u r v e . W e g i v e p r e c i s e d
Milliseconds 76 161 71 103 181 53 92 64 174 203 144 119 90 75 54 85 112 104 69 171 182 83 57 159 549
Character e v e l o p m e n t s o c - -c f t h e s e
Milliseconds 163 108 70 64 143 86 2763 77 102 88 58 44 88 122 38 331 124 206 312 133 90 78 80 84 80
Character i n -n -i i m p o r t a n t c o n c e p t s i n
Milliseconds 102 52 284 121 350 84 114 79 134 177 68 91 106 65 116 48 64 132 59 105 142 91 122 90 64
Character t h e n e x t c h a p r -r t e r , b u t
Milliseconds 85 47 108 43 152 144 118 165 165 97 118 137 89 105 113 292 111 131 51 99 82 140 94 93 102
Character f o r n o w s e -e -s w e u s e a n i n f
Milliseconds 171 61 132 63 55 59 41 110 102 91 248 143 110 76 49 232 76 52 72 122 93 81 164 94 107
Character o r m a l a p p r o a c h s o y o u w i l
Milliseconds 99 105 72 91 83 68 110 109 153 131 79 104 63 122 83 93 145 26 339 90 76 74 76 102 124
Character l s e e h o w t h e y l e a d n a t u r
Milliseconds 147 41 76 59 167 167 109 66 47 110 108 44 116 33 44 121 68 58 118 135 124 101 85 478 92
Character a l l y t o t h e m a i n i d e a o f
Milliseconds 68 63 125 151 47 149 27 70 82 66 66 74 74 138 74 56 83 79 111 145 80 23 76 94 69
Character t h i s c h a p t e r , t h e l i m i t .
Milliseconds 111 40 116 58 103 116 178 74 109 91 118 61 101 57 167 40 110 42 71 112 135 117 163 141 85
Character T h e i d e a o -o o f a l i m i t p l y
Milliseconds 214 97 104 111 69 60 124 64 43 280 249 546 113 63 83 80 88 81 95 106 112 74 200 159 176
Character a s -s -a -y a y s a f o u n d a t i o n a l r
Milliseconds 11 209 232 121 135 120 100 88 92 107 72 98 48 74 123 58 88 101 70 56 39 90 85 56 110
Character o l e t h r o u g h o u t c l a -a -l a l c u l
Milliseconds 61 142 53 85 66 86 91 8 85 94 58 36 116 69 87 124 99 28 292 125 110 121 112 132 135
Character u s / -/ .
Milliseconds 132 133 609 482 258
WPM Timing
Seconds WPM
2.11 96.88
4.21 125.38
6.32 129.18
8.42 129.65
10.53 127.66
12.63 132.98
14.74 119.68
16.84 116.12
18.95 107.02
21.06 103.72
23.16 108.28
25.27 110.18
27.37 110.47
29.48 105.84
31.58 105.62
33.69 105.43
35.8 105.6
37.9 103.85
40.01 106.48
42.11 107.14
44.22 106.93
46.32 105.95
48.43 107.79
50.53 109.23
52.64 110.11
54.75 106.97
56.85 108.28
58.96 108.49
61.06 106.51
63.17 105.24
65.27 104.05
67.38 102.94
69.48 103.1
71.59 102.58
73.7 100.63
75.8 98.94
77.91 97.5
80.01 98.23
82.12 97.76
84.22 97.74
86.33 98.27
88.44 98.65
90.54 98.87
92.65 99.73
94.75 100.43
96.86 99.98
98.96 99.43
101.07 99.62
103.17 99.79
105.28 98.48