☄ (strongly_typed_comet)

Race #1584

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Official speed 91.08 wpm (113.83 seconds elapsed during race)
Without ending ping 91.27 wpm (233 ms delay sending score to TypeRacer’s server)
Timerless 91.60 wpm (413 ms elapsed before first character typed; 113.19 seconds elapsed during race)
Timerless minus one 91.49 wpm, ignoring the first character typed
Race Start September 22, 2024 5:21:54am UTC
Race Finish September 22, 2024 5:23:48am UTC
Outcome No win (3 of 4)
Opponents 2. typervain (96.10 wpm)
Accuracy 97.4%
Points 245.92
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 usunderstand how a change in one quantity is related to a change ain another. Ho ww does the speed of a fialling object change as a fiunction 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 nealrly everything we observe in the world and universe, and powervfful modoern instrumenst ts help us see more and more. In this section we introduce the ideeaideacs of average and instantaneous ritesrateso s of change, and show that they are closerylyoy related to the slope of a curve at a point P on thoe curve. We give precise developments of these important concepts in the next chapte,r r, but for now we use an informal approach so you will see how they lead naturally to the main ideaof thiidea of this chapter, the limit. Thi The ideaof a idea of a limit plays a foundational role throught t out calcululi.ss.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 413 167 116 66 111 100 100 244 132 136 68 129 97 93 111 120 127 14 115 105 49 70 47 60 98
Character e l p s u s u s -s -u u n d e r s t a n d h o
Milliseconds 97 49 448 438 384 163 198 176 179 0 447 115 224 51 75 105 87 36 156 30 252 135 174 115 37
Character w a c h a n g e i n o n e q u a n t i t
Milliseconds 36 83 86 103 63 45 57 35 82 84 173 124 84 60 181 87 104 117 83 93 28 119 94 105 95
Character y i s r e l a t e d t o a c h a n g e
Milliseconds 100 124 85 53 104 77 79 90 64 112 82 44 88 113 31 111 69 111 124 54 53 47 87 13 96
Character a -a i n a n o t h e r . H o w -w - w d o e
Milliseconds 239 331 206 36 93 70 64 102 98 44 53 69 92 88 93 197 155 86 223 90 75 82 107 39 161
Character s t h e s p e e d o f a f i -i a l l i n
Milliseconds 59 96 43 59 32 113 4 120 37 139 170 128 68 65 77 71 98 201 65 282 186 58 130 87 70
Character g o b j e c t c h a n g e a s a f i -i u
Milliseconds 61 2 327 47 138 212 34 58 42 128 47 53 61 53 49 220 118 99 101 111 125 129 65 529 214
Character n c t i o n o f t i m e ? H o w d o e s
Milliseconds 40 63 12 71 39 51 125 84 49 81 66 93 83 83 241 115 142 143 104 63 127 53 173 68 99
Character t h e l e v e l o f w a t e r i n a b
Milliseconds 58 63 33 118 10 114 84 95 62 105 104 57 78 124 98 84 153 132 186 152 83 107 59 111 145
Character a r r e l c h a n g e a s a f u n c t i o
Milliseconds 140 140 150 161 142 117 104 62 59 54 65 78 120 56 101 77 113 126 159 71 39 466 59 125 27
Character n o f t h e a m o u n t o f l i q u i d
Milliseconds 48 91 64 57 67 95 74 21 115 124 91 102 48 41 130 138 70 70 75 101 93 188 121 155 113
Character p o u r e d i n t o i t ? W e s e e c
Milliseconds 124 159 55 49 360 171 61 90 106 46 79 49 114 108 65 216 101 121 180 76 103 69 128 79 126
Character h a n g e o c c u r r i n g i n n e a l -l r
Milliseconds 51 59 56 54 36 139 91 95 131 116 85 167 106 50 77 21 112 68 122 156 77 52 63 327 71
Character l y e v e r y t h i n g w e o b s e r v e
Milliseconds 141 72 119 93 75 83 40 147 81 507 70 69 56 95 108 78 90 234 68 111 150 97 67 322 159
Character i n t h e w o r l d a n d u n i v e r s e
Milliseconds 53 67 112 48 84 27 119 52 75 84 178 98 125 134 22 136 90 129 42 124 126 89 83 46 32
Character , a n d p o w e r v f -f -v f u l m o d o -o e
Milliseconds 85 85 121 53 67 110 123 45 66 140 49 116 74 292 101 173 52 42 121 127 83 141 105 332 197
Character r n i n s t r u m e n s t - -t -s t s h e l p
Milliseconds 53 43 98 126 21 375 37 197 192 353 187 47 82 32 205 317 122 122 544 37 205 369 49 40 87
Character u s s e e m o r e a n d m o r e . I n
Milliseconds 104 59 51 119 54 80 139 112 11 73 56 80 102 43 62 64 95 96 46 88 85 43 127 76 202
Character t h i s s e c t i o n w e i n t r o d u c
Milliseconds 123 88 40 63 71 96 85 97 107 97 119 45 69 133 83 70 125 348 85 70 377 217 130 128 68
Character e t h e i d e e a -a -i -d -e -e i d e a c -c s o
Milliseconds 147 218 48 72 27 119 111 122 129 229 41 400 134 0 0 0 317 212 74 102 100 282 56 86 67
Character f a v e r a g e a n d i n s t a n t a n e o
Milliseconds 69 88 119 139 26 105 133 176 86 92 150 109 83 128 147 83 90 49 131 112 136 128 153 221 201
Character u s r i t e s -s -r -i -t -e r a t e s o - -o -s s
Milliseconds 55 53 128 113 73 95 83 118 231 117 0 0 0 189 75 88 56 83 137 95 291 109 127 490 156
Character o f c h a n g e , a n d s h o w t h a t
Milliseconds 95 49 94 330 54 38 54 82 62 162 363 77 73 88 128 41 72 34 52 114 164 97 30 58 85
Character t h e y a r e c l o s e r y -y -r l y o -o -y y
Milliseconds 95 30 37 173 125 37 102 79 135 95 88 10 157 45 96 82 357 125 174 226 0 419 94 443 254
Character r e l a t e d t o t h e s l o p e o f a
Milliseconds 90 53 340 103 108 79 104 135 87 31 125 92 48 27 115 56 50 73 72 97 124 75 27 100 57
Character c u r v e a t a p o i n t P o n t h
Milliseconds 106 302 167 153 83 79 120 103 93 259 87 104 59 63 34 57 49 106 126 109 90 85 85 135 97
Character o -o e c u r v e . W e g i v e p r e c i s
Milliseconds 67 385 386 130 662 156 63 82 73 204 128 93 303 87 188 93 79 63 114 389 78 155 98 138 109
Character e d e v e l o p m e n t s o f t h e s e i
Milliseconds 62 116 109 63 81 127 95 106 432 145 144 46 82 62 70 81 59 80 105 77 71 51 133 109 78
Character m p o r t a n t c o n c e p t s i n t h e
Milliseconds 85 72 105 214 37 445 100 24 128 94 82 590 30 93 65 214 122 149 132 79 157 57 46 36 118
Character n e x t c h a p t e , r - -r -, r , b u t f
Milliseconds 183 238 33 80 91 149 83 39 124 98 94 99 4 216 260 125 139 128 53 148 80 72 74 64 124
Character o r n o w w e u s e a n i n f o r m a l
Milliseconds 37 58 128 82 90 76 101 95 75 177 98 76 68 112 83 25 138 135 73 103 87 93 174 105 178
Character a p p r o a c h s o y o u w i l l s e e
Milliseconds 322 112 153 153 81 82 119 74 116 167 65 67 114 103 49 62 155 103 90 129 147 59 121 81 163
Character h o w t h e y l e a d n a t u r a l l y
Milliseconds 109 117 25 79 107 157 70 39 132 122 102 49 47 130 109 107 28 108 70 72 93 91 114 44 111
Character t o t h e m a i n i d e a o f t h i -i -d -e
Milliseconds 73 33 97 51 71 36 102 81 65 54 74 130 90 140 72 69 202 68 62 141 83 47 412 0 0
Character -a -o -f - -t -h -i i d e a o f t h i s c h a p t
Milliseconds 0 0 0 0 0 0 0 458 92 104 61 176 49 81 73 127 78 47 65 70 157 55 58 111 123
Character e r , t h e l i m i t . T h i - -T -h -i T h
Milliseconds 185 90 52 120 12 75 44 102 7 89 121 70 112 178 173 37 142 112 300 266 129 0 0 311 397
Character e i d e a o f a -i -d -e -a -o -f - -a - i d e a
Milliseconds 42 116 108 87 113 54 172 52 83 97 135 400 0 0 0 0 0 0 0 0 687 125 94 72 191
Character o f a l i m i t p l a y s a f o u n d a
Milliseconds 29 69 94 73 159 580 108 75 51 99 108 132 140 103 75 109 177 50 129 64 62 27 54 94 125
Character t i o n a l r o l e t h r o u g h t - -t -
Milliseconds 119 138 30 26 259 210 20 662 99 82 88 145 75 40 102 85 27 99 93 140 283 340 121 815 577
Character t - -t o u t c a l c u l u l i . -. -i s -s -l s .
Milliseconds 110 147 501 127 261 16 50 153 154 98 75 113 77 81 105 145 95 0 439 139 316 190 124 133 118
WPM Timing
Seconds WPM
2.28 84.33
4.55 81.7
6.83 75.55
9.11 90.92
11.38 101.2
13.66 96.63
15.94 100.15
18.21 101.46
20.49 101.32
22.77 103.31
25.04 103.02
27.32 104.54
29.6 106.23
31.87 105.79
34.15 107.52
36.43 106.73
38.7 106.97
40.98 108.34
43.26 106.25
45.53 102.78
47.81 102.66
50.09 104.22
52.36 103.58
54.64 100.37
56.92 100.99
59.19 99.33
61.47 97.41
63.75 98.45
66.02 97.06
68.3 96.63
70.58 97.09
72.85 96.85
75.13 96.15
77.41 95.81
79.68 96.38
81.96 96.34
84.24 95.73
86.51 96.54
88.79 96.63
91.07 97.12
93.34 98.35
95.62 96.76
97.9 97.69
100.17 96.07
102.45 94.64
104.73 94.53
107 94.54
109.28 93.45
111.56 92.29
113.83 91.08