Erick (strosekd)

Race #3048

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Official speed 89.16 wpm (116.29 seconds elapsed during race)
Without ending ping 89.26 wpm (134 ms delay sending score to TypeRacer’s server)
Timerless 89.73 wpm (607 ms elapsed before first character typed; 115.54 seconds elapsed during race)
Timerless minus one 89.63 wpm, ignoring the first character typed
Race Start December 2, 2024 7:29:37pm UTC
Race Finish December 2, 2024 7:31:33pm UTC
Outcome No win (3 of 3)
Opponents 2. 5andos (93.61 wpm)
Accuracy 97.0%
Points 240.73
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 undrestaerstand how a change in one oquantity 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? W e e see change accocurrcurring in rnearly evryerything we boserobserve in the world and universe, and powerful moderr nins instruments help us see more and more. In this section we introduce the ideas of average and instantianeous rates of change, and show that they are closely related to the slope of a curve at a pontiint P on th ucre curve. We give pecisrecise development sof ts of these pimportant concepts in the next chapter, but for nowwe we use an informal approach oso so you will see how they load ed nad naturally to the main ideoa of this chapter ,the l, the limit. Theidea idea of a limit plays a foundational role throughout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 607 130 27 156 85 96 135 83 187 49 53 124 32 139 34 61 125 57 167 66 54 68 51 170 0
Character e l p s u s u n d r e s t a -a -t -s -e -r e r s t
Milliseconds 101 116 127 71 155 157 82 159 95 52 118 129 100 100 64 105 302 114 118 168 116 152 44 156 61
Character a n d h o w a c h a n g e i n o n e o
Milliseconds 135 48 67 135 65 87 80 183 0 202 344 53 40 80 49 68 160 21 70 133 153 76 105 152 64
Character -o q u a n t i t y i s r e l a t e d t o a
Milliseconds 375 42 97 88 102 57 52 121 79 174 331 129 176 36 84 73 62 71 72 72 589 140 93 116 80
Character c h a n g e i n a n o t h e r . H o w d
Milliseconds 101 67 53 61 71 53 749 218 84 59 161 92 84 80 68 48 38 79 120 117 117 134 53 163 10
Character o e s t h e s p e e d o f a f a l l i n
Milliseconds 71 114 72 171 60 41 29 169 0 85 167 132 28 133 15 47 149 30 140 87 87 98 114 139 90
Character g o b j e c t c h a n g e a s a f u n c
Milliseconds 41 135 136 94 252 163 0 151 168 50 21 76 54 48 62 122 31 57 143 35 129 41 94 71 114
Character t i o n o f t i m e ? H o w d o e s t h
Milliseconds 149 53 80 18 168 14 90 154 90 101 78 104 331 89 111 137 63 173 39 61 113 81 177 93 35
Character e l e v e l o f w a t e r i n a b a r
Milliseconds 63 132 47 89 100 74 59 154 65 66 135 181 100 50 115 50 160 49 74 155 535 164 80 134 74
Character r e l c h a n g e a s a f u n c t i o n
Milliseconds 111 86 78 133 84 17 66 122 34 84 118 29 59 112 62 115 31 87 83 106 179 49 83 44 171
Character o f t h e a m o u n t o f l i q u i d p
Milliseconds 35 60 141 80 23 45 150 44 68 109 79 32 41 138 19 81 142 13 222 200 117 179 55 150 78
Character o u r e d i n t o i t ? W e - -e - e s
Milliseconds 154 80 74 77 43 173 0 50 36 90 138 35 63 420 96 125 205 42 277 279 77 144 292 224 608
Character e e c h a n g e a c c -c -c -a o c u r r -r -r -u c
Milliseconds 113 118 158 90 35 63 59 62 46 121 134 131 116 353 82 146 95 90 121 160 124 360 88 117 121
Character u r r i n g i n r -r n e a r l y e v r y -y -r
Milliseconds 107 104 115 88 76 53 185 15 87 209 71 355 62 84 101 16 146 150 118 101 71 148 47 671 301
Character e r y t h i n g w e b o s e r -r -e -s -o -b o b s
Milliseconds 100 259 151 172 61 87 48 64 140 70 97 130 72 57 89 99 62 374 288 95 136 137 159 64 141
Character e r v e i n t h e w o r l d a n d u n i
Milliseconds 115 79 176 59 150 187 145 263 73 32 65 140 39 174 37 113 87 153 25 78 72 154 265 129 118
Character v e r s e , a n d p o w e r f u l m o d e r
Milliseconds 91 125 47 109 124 121 132 74 49 62 147 73 119 81 79 66 100 136 43 157 80 101 106 127 40
Character r - -r n i n s -s -n -i i n s t r u m e n t s h
Milliseconds 170 143 301 80 149 297 121 74 386 59 135 233 270 92 133 193 64 134 75 108 50 90 115 119 30
Character e l p u s s e e m o r e a n d m o r e .
Milliseconds 168 291 169 144 97 49 145 96 110 118 162 77 68 57 85 136 55 52 59 119 95 53 73 90 208
Character I n t h i s s e c t i o n w e i n t r o
Milliseconds 382 396 253 205 61 35 161 61 160 70 97 63 152 66 64 40 153 63 115 153 67 60 176 51 64
Character d u c e t h e i d e a s o f a v e r a g e
Milliseconds 77 85 83 81 136 64 24 65 137 54 39 151 85 80 121 62 39 154 229 130 113 87 85 64 82
Character a n d i n s t a n t i -i a n e o u s r a t e
Milliseconds 147 31 73 51 136 35 349 86 246 139 111 132 133 512 70 113 234 180 74 85 185 76 70 79 77
Character s o f c h a n g e , a n d s h o w t h a
Milliseconds 76 195 175 116 165 81 56 44 83 65 22 138 125 76 62 45 159 77 48 115 68 207 0 48 105
Character t t h e y a r e c l o s e l y r e l a t e
Milliseconds 47 196 46 44 107 124 118 27 82 75 140 0 93 78 114 55 109 112 127 16 63 83 78 89 69
Character d t o t h e s l o p e o f a c u r v e
Milliseconds 71 189 26 79 154 0 30 109 132 8 189 84 135 142 139 70 45 155 43 117 138 182 116 139 97
Character a t a p o n t i -i -t -n i n t P o n t h
Milliseconds 144 72 33 164 18 166 33 157 114 45 19 666 101 139 93 99 33 226 211 186 83 47 151 38 45
Character u c r -r -c -u - e c u r v e . W e g i v e
Milliseconds 145 0 115 129 329 65 135 132 100 199 94 147 71 173 84 167 146 114 134 149 55 82 99 72 144
Character p e c i s -s -i -c -e r e c i s e d e v e l o p m e
Milliseconds 102 164 57 140 87 309 90 165 146 139 98 106 116 93 101 247 109 131 47 99 51 102 84 115 75
Character n t s o f t -t - -f -o -s - s o f t h e s e
Milliseconds 60 48 224 0 49 46 151 104 276 69 167 153 165 116 168 198 102 69 141 88 30 75 77 87 110
Character p -p i m p o r t a n t c o n c e p t s i n t
Milliseconds 127 331 67 114 86 66 31 61 108 49 37 181 33 112 39 69 95 151 46 65 191 0 92 146 44
Character h e n e x t c h a p t e r , b u t f o r
Milliseconds 51 78 132 0 121 133 73 155 40 50 76 121 164 50 77 87 134 57 79 58 156 107 102 61 145
Character n o w w e - -e -w w e u s e a n i n f o r
Milliseconds 75 47 147 224 102 123 318 86 133 260 276 97 145 57 46 101 120 115 83 156 183 82 52 139 62
Character m a l a p p r o a c h o s o - -o -s -o s o y
Milliseconds 135 124 86 184 109 151 158 120 49 83 68 43 151 23 40 131 78 366 83 152 153 124 64 193 35
Character o u w i l l s e e h o w t h e y l o a d
Milliseconds 120 74 113 63 57 86 106 429 124 85 115 154 60 121 89 142 60 48 74 67 154 20 77 107 83
Character - -d -a -o e d n -n - -d a d n a t u r a l l y
Milliseconds 171 509 83 354 260 232 109 204 110 289 95 136 77 89 198 161 75 94 99 106 75 100 131 85 153
Character t o t h e m a i n i d e o -o a o f t h i
Milliseconds 63 75 174 0 43 76 140 38 91 135 95 133 51 60 127 162 425 67 149 109 85 163 226 37 230
Character s c h a p t e r , t h e l -l - -e -h -t -, - ,
Milliseconds 200 249 202 42 68 101 63 105 57 210 0 68 53 91 76 60 343 75 155 142 137 156 160 129 185
Character t h e l i m i t . T h e i d e a -a -e -d -i i d
Milliseconds 121 27 58 172 25 84 81 74 50 141 138 116 101 97 185 48 154 88 365 80 154 114 256 209 89
Character e a o f a l i m i t p l a y s a f o u
Milliseconds 104 89 204 145 124 161 122 130 80 134 70 93 34 156 65 61 107 92 68 145 23 139 68 158 105
Character n d a t i o n a l r o l e t h r o u g h o u t
Milliseconds 102 81 148 159 124 105 147 117 51 167 47 19 128 82 192 260 42 108 152 296 524 185 152 96 99
Character c a l c u l u s .
Milliseconds 170 92 100 77 223 139 82 177 107 115
WPM Timing
Seconds WPM
2.33 92.88
4.65 92.88
6.98 86
9.3 92.88
11.63 90.81
13.95 92.02
16.28 98.03
18.61 101.9
20.93 103.19
23.26 105.26
25.58 106.01
27.91 109.21
30.23 109.54
32.56 103.56
34.89 101.13
37.21 98.36
39.54 95.61
41.86 93.45
44.19 92.88
46.51 93.91
48.84 93.37
51.17 91.47
53.49 92.2
55.82 91.8
58.14 93.29
60.47 94.26
62.79 93.07
65.12 94.35
67.45 96.08
69.77 96.83
72.1 95.7
74.42 94.65
76.75 94.44
79.07 93.63
81.4 91.99
83.73 92.88
86.05 93.99
88.38 93.01
90.7 93.27
93.03 92.62
95.35 93
97.68 90.91
100.01 91.08
102.33 90.88
104.66 90.01
106.98 89.85
109.31 88.81
111.63 89.44
113.96 89.4
116.29 89.16