Ramble (ramble)

Race #3374

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Official speed 111.61 wpm (92.89 seconds elapsed during race)
Without ending ping 112.49 wpm (727 ms delay sending score to TypeRacer’s server)
Timerless 112.81 wpm (264 ms elapsed before first character typed; 91.90 seconds elapsed during race)
Timerless minus one 112.68 wpm, ignoring the first character typed
Race Start December 27, 2023 11:12:35am UTC
Race Finish December 27, 2023 11:14:07am UTC
Outcome Win (1 of 5)
Opponents 2. kamikamigod (110.42 wpm)
3. 28promises (107.98 wpm)
Accuracy 97.3%
Points 301.36
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 Claalculus is a tool that helps us understand how a change in one quantityu is related to a change in another.l H How sddoes the speed of a falling object change as a function of time? HOwow does the level of water in a barrel change as a function of the amount of liquid poured into it? We see change cooccurring in nearly everything we observe in the world and universe, and powerful modern instruments help us see more and more. In this section we intorroduce the ideas of average and instantaneous reaates of change, and show tahhat they are closely related to the slope of a curve at a poin t Pt P on the curve. WEe give precise delevelopments of theese se imporattant concepts in the necxt chapter, but for noeww we use an informal apapporroach so you will see how they lead naturally otto the main idea odf htthis chapter, the limit. The idea of limia limit play ss a foundational role throughout clacalculus.
Timing
Character C l a -a -l a l c u l u s i s a t o o l t h
Milliseconds 264 153 0 401 116 110 84 101 166 148 128 42 36 102 31 81 40 83 80 119 115 91 69 74 61
Character a t h e l p s u s u n d e r s t a n d h o
Milliseconds 72 46 69 85 61 107 95 77 29 118 33 98 135 95 61 145 67 85 102 62 57 100 50 55 109
Character w a c h a n g e i n o n e q u a n t i t
Milliseconds 19 71 90 99 92 124 67 113 27 90 53 48 89 62 83 95 49 37 188 285 72 70 82 81 69
Character y u - -u i s r e l a t e d t o a c h a
Milliseconds 124 18 74 425 116 61 83 79 78 110 56 82 105 73 82 155 44 83 52 65 85 94 164 104 73
Character n g e i n a n o t h e r . l H -H - -l H o w
Milliseconds 91 39 89 29 61 82 50 58 54 102 47 72 71 54 51 13 71 152 240 116 126 55 113 147 70
Character s d -d -s d o e s t h e s p e e d o f a
Milliseconds 103 211 69 195 108 35 128 54 43 84 122 43 100 72 122 74 50 133 113 54 37 89 79 113 38
Character f a l l i n g o b j e c t c h a n g e a s
Milliseconds 157 71 96 560 190 60 80 47 158 156 88 79 188 111 39 161 92 76 56 26 73 95 79 68 116
Character a f u n c t i o n o f t i m e ? H O w -w -O
Milliseconds 73 90 85 110 113 53 122 39 131 69 22 106 40 68 90 50 77 59 143 77 204 123 151 204 126
Character o w d o e s t h e l e v e l o f w a t e
Milliseconds 105 58 65 161 104 41 68 62 69 67 70 58 67 57 92 50 228 104 110 31 83 78 69 118 73
Character r i n a b a r r e l c h a n g e a s a
Milliseconds 79 50 46 72 67 90 72 114 50 90 134 59 54 54 165 68 94 43 97 47 75 76 76 128 42
Character f u n c t i o n o f t h e a m o u n t o
Milliseconds 103 51 94 82 54 120 68 143 52 42 87 39 71 82 64 59 57 83 57 101 74 120 24 45 59
Character f l i q u i d p o u r e d i n t o i t ?
Milliseconds 80 57 67 116 73 127 134 33 64 190 133 147 248 57 174 44 82 97 39 58 113 105 48 236 65
Character W e s e e c h a n g e c o -o -c o c c u r r i
Milliseconds 129 202 81 100 61 106 44 156 27 105 35 86 51 65 141 12 318 110 69 66 122 130 91 124 107
Character n g i n n e a r l y e v e r y t h i n g w
Milliseconds 90 65 41 81 64 64 159 52 48 53 102 91 19 115 96 44 118 60 102 72 59 95 28 61 90
Character e o b s e r v e i n t h e w o r l d a n
Milliseconds 80 53 116 157 89 48 248 156 56 76 35 74 84 52 54 78 54 137 38 60 357 159 83 113 78
Character d u n i v e r s e , a n d p o w e r f u l
Milliseconds 91 65 111 96 105 72 51 146 62 44 104 59 50 80 102 90 131 149 34 79 35 184 68 164 42
Character m o d e r n i n s t r u m e n t s h e l p u
Milliseconds 76 92 95 172 60 51 195 90 94 65 68 140 73 119 29 383 87 58 82 146 86 92 99 76 108
Character s s e e m o r e a n d m o r e . I n t
Milliseconds 56 98 66 73 117 51 87 61 17 58 53 42 106 52 25 82 77 55 34 114 37 269 123 435 63
Character h i s s e c t i o n w e i n t o r -r -o r o d
Milliseconds 30 119 45 65 90 58 163 136 31 138 55 46 45 65 70 146 75 82 125 37 228 112 53 29 151
Character u c e t h e i d e a s o f a v e r a g e
Milliseconds 89 107 152 71 110 57 73 62 78 67 139 66 74 116 56 102 102 63 138 59 139 69 108 54 53
Character a n d i n s t a n t a n e o u s r e a -a -e a t
Milliseconds 123 101 80 42 161 67 68 121 32 319 92 340 106 113 193 97 355 92 159 84 21 343 110 40 52
Character e s o f c h a n g e , a n d s h o w t a
Milliseconds 102 128 83 67 77 71 177 64 65 80 53 41 93 48 198 133 82 114 230 61 96 35 64 107 91
Character h -h -a h a t t h e y a r e c l o s e l y r
Milliseconds 19 274 119 109 8 72 140 21 615 103 96 66 26 75 56 88 143 58 124 33 49 80 79 33 154
Character e l a t e d t o t h e s l o p e o f a
Milliseconds 51 107 86 78 108 155 36 102 42 77 77 107 63 45 89 73 124 85 54 63 100 47 83 28 99
Character c u r v e a t a p o i n t P -P - -t - t
Milliseconds 283 119 116 189 38 83 129 78 76 63 81 64 176 106 102 14 29 21 184 236 114 137 115 57 49
Character P o n t h e c u r v e . W E -E e g i v e
Milliseconds 132 127 191 128 22 78 55 82 63 142 59 73 177 47 65 72 173 25 323 162 78 206 82 85 47
Character p r e c i s e d e l e -e -l v e l o p m e n t s
Milliseconds 62 91 82 62 178 97 90 68 66 168 111 76 153 170 112 63 53 105 149 93 202 56 97 45 79
Character o f t h e e s e - -e -s -e s e i m p o r a t
Milliseconds 225 109 48 67 92 63 73 98 14 102 67 314 106 140 128 68 62 70 140 81 86 114 94 112 76
Character -t -a t a n t c o n c e p t s i n t h e n e
Milliseconds 256 107 57 59 84 48 73 236 51 79 115 167 81 110 50 253 89 48 42 61 38 98 72 39 68
Character c -c x t c h a p t e r , b u t f o r n o e
Milliseconds 182 334 36 113 59 203 264 51 88 95 63 105 73 68 117 109 56 54 109 33 104 59 58 102 46
Character w -w -e w w e u s e a n i n f o r m a l a
Milliseconds 61 169 116 53 44 131 53 105 151 60 44 77 83 85 148 78 89 71 94 84 68 89 74 66 142
Character p a -a -p p p o r -r -o r o a c h s o y o u w i
Milliseconds 115 4 240 99 170 128 169 25 222 106 63 94 38 162 130 43 84 82 92 57 42 77 43 38 83
Character l l s e e h o w t h e y l e a d n a t u
Milliseconds 154 105 32 34 65 112 64 10 126 37 70 167 49 103 28 82 98 40 60 112 58 34 98 54 105
Character r a l l y o t -t -o t o t h e m a i n i d e
Milliseconds 48 62 87 131 34 30 129 0 394 105 54 34 86 46 88 63 61 74 79 43 77 35 106 57 149
Character a o d -d f h t -t -h t h i s c h a p t e r ,
Milliseconds 36 81 119 84 221 69 44 208 0 260 103 42 83 88 32 48 175 74 51 102 57 88 93 82 59
Character t h e l i m i t . T h e i d e a o f l i
Milliseconds 86 119 39 53 89 143 78 102 40 133 23 169 205 57 79 95 98 135 44 94 91 69 66 90 136
Character m i -i -m -i -l a l i m i t p l a y s -s - s a
Milliseconds 84 80 235 145 135 140 417 75 149 131 88 78 66 36 61 123 31 67 43 91 170 94 64 74 42
Character f o u n d a t i o n a l r o l e t h r o u g
Milliseconds 129 228 82 105 123 0 104 60 83 130 69 59 170 58 97 83 98 13 79 65 91 87 381 97 73
Character h o u t c l a c -c -a -l a l c u l u s .
Milliseconds 76 178 48 61 47 169 91 0 164 239 118 116 57 126 59 92 187 101 83 43
WPM Timing
Seconds WPM
1.86 64.59
3.72 106.57
5.57 122.72
7.43 116.26
9.29 117.55
11.15 116.26
13.01 113.49
14.86 111.42
16.72 113.39
18.58 114.97
20.44 113.91
22.29 116.8
24.15 120.24
26.01 121.8
27.87 120.57
29.73 119.49
31.58 121.2
33.44 122.36
35.3 122.04
37.16 122.4
39.02 121.8
40.87 123.31
42.73 123.28
44.59 122.45
46.45 122.72
48.31 120.73
50.16 119.85
52.02 118.8
53.88 118.71
55.74 119.49
57.59 119.59
59.45 117.67
61.31 117.04
63.17 116.45
65.03 116.26
66.88 114.47
68.74 114.69
70.6 114.05
72.46 113.94
74.32 113.84
76.17 113.58
78.03 114.72
79.89 114.91
81.75 114.21
83.61 114.68
85.46 113.73
87.32 112.96
89.18 113.17
91.04 112.83
92.89 111.61