FFX^5 (ffxxxxx5)

Race #77

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Official speed 75.30 wpm (137.69 seconds elapsed during race)
Without ending ping 75.44 wpm (252 ms delay sending score to TypeRacer’s server)
Timerless 75.61 wpm (313 ms elapsed before first character typed; 137.12 seconds elapsed during race)
Timerless minus one 75.52 wpm, ignoring the first character typed
Race Start October 31, 2023 5:04:31pm UTC
Race Finish October 31, 2023 5:06:49pm UTC
Outcome No win (5 of 5)
Opponents 1. quitlessfus (114.50 wpm)
2. alifeee (97.58 wpm)
3. ivious (82.96 wpm)
4. ngurfour (78.36 wpm)
Accuracy 97.5%
Points 203.31
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 Calculus is a tool that helps us understand how a change in one quantity is related to a change in another. How does htthe speed of a falling object change as a function of time? How does the level o fwf whaater in a barrel change sas a function of the amount of liquid poured into it? We see change occuring occurring in nearly eveythrything we observe in the world an dud universe, and poewrwefrful modern instruments help us see more and more. IN thiiIn this section we introduce the ideas of average and instantaneious ous reaates of change, and show that hethey are closely realtelated to the slope of a curve at a point P on the curve. We give precise developments of these important concveepts in the next chapter, but for noeww we use an informal approach so wyou will see how they lead naturally to the main idea of this chapter, the limit. The idaea of a limit plays 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 313 135 481 183 129 232 528 129 79 120 120 48 137 95 176 72 136 152 121 72 102 72 81 48 137
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 88 55 153 127 96 121 127 104 121 152 38 154 79 137 95 120 152 137 48 136 79 80 72 113 87
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 193 80 103 81 56 63 56 72 137 47 112 120 97 71 161 95 120 88 152 160 224 88 145 64 112
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 80 87 96 64 321 136 80 199 64 137 31 105 448 87 129 111 88 97 135 97 112 71 121 63 161
Character n o t h e r . H o w d o e s h t -t -h t h e
Milliseconds 79 90 126 32 169 88 39 201 111 89 119 281 360 152 95 120 16 201 15 523 118 103 97 103 64
Character s p e e d o f a f a l l i n g o b j e c t
Milliseconds 344 96 225 152 168 47 113 112 96 72 128 280 119 289 151 136 121 72 87 153 520 112 104 168 136
Character c h a n g e a s a f u n c t i o n o f
Milliseconds 88 111 81 87 97 31 88 112 89 168 63 153 200 71 161 152 80 144 7 88 57 160 80 111 64
Character t i m e ? H o w d o e s t h e l e v e l
Milliseconds 137 48 136 104 176 152 201 111 112 176 344 79 106 134 33 167 80 56 113 216 97 135 96 128 240
Character o f w -w -f - f w h a -a -h a t e r i n a b
Milliseconds 216 151 57 264 288 152 136 264 145 296 136 63 241 135 112 111 105 104 55 225 120 80 128 104 143
Character a r r e l c h a n g e s -s a s a f u n c t
Milliseconds 136 169 104 152 120 103 129 64 120 65 46 56 194 6 330 520 168 86 145 111 177 87 161 56 144
Character i o n o f t h e a m o u n t o f l i q u
Milliseconds 16 113 22 98 135 112 80 176 80 72 95 121 96 127 89 176 80 56 112 144 47 97 72 177 111
Character i d p o u r e d i n t o i t ? W e s e e
Milliseconds 80 176 128 456 240 153 159 289 191 73 87 103 138 88 400 151 104 304 112 480 184 97 144 215 137
Character c h a n g e o c c u r i n g - -g -o -c -c -u -r -i
Milliseconds 95 224 47 170 64 71 64 64 113 159 169 199 160 104 128 112 40 305 135 289 0 0 0 0 0
Character -n o c c u r r i n g i n n e a r l y e v e y
Milliseconds 0 570 46 167 560 161 199 129 103 105 47 97 119 80 209 104 455 104 104 144 112 97 159 72 320
Character t h -h -t -y r y t h i n g w e o b s e r v e i
Milliseconds 224 88 241 126 137 232 488 136 64 96 104 72 88 129 95 96 425 143 409 103 129 184 55 112 96
Character n t h e w o r l d a n d u -u -d - d u n i
Milliseconds 72 96 177 104 87 96 73 111 177 7 384 112 257 79 105 15 200 337 152 136 88 95 137 184 87
Character v e r s e , a n d p o e w r -r -w -e w e f -f r f
Milliseconds 32 728 409 175 233 128 120 160 95 104 32 145 119 129 23 121 376 136 151 64 32 672 336 97 183
Character u l m o d e r n i n s t r u m e n t s h e l
Milliseconds 97 159 128 144 81 200 183 89 135 105 135 120 121 168 168 112 784 104 112 56 152 368 360 103 88
Character p u s s e e m o r e a n d m o r e . I
Milliseconds 137 176 424 95 73 208 152 151 97 152 64 112 80 48 120 95 73 79 129 32 143 72 321 112 184
Character N t h i -t -h -i -I -N - i -i I n t h i s s e c t
Milliseconds 88 96 72 128 47 521 0 0 376 0 0 328 280 169 118 89 105 110 33 96 135 185 160 192 160
Character i o n w e i n t r o d u c e t h e i d e a
Milliseconds 16 96 56 88 208 128 104 160 120 296 233 94 569 152 104 152 48 152 64 119 96 138 103 105 449
Character s o f a v e r a g e a n d i n s t a n t a
Milliseconds 126 216 192 112 64 329 320 54 154 183 96 72 80 137 111 72 63 122 119 120 169 71 144 216 144
Character n e i o u s - -s -u -o -i o u s r e a -a -e a t e s
Milliseconds 143 569 177 79 24 113 103 248 153 152 152 311 336 73 71 113 207 64 209 343 136 88 80 89 271
Character o f c h a n g e , a n d s h o w t h a t
Milliseconds 96 112 111 89 160 47 154 64 152 55 88 129 103 96 135 97 130 102 65 63 121 143 96 88 80
Character h e -e -h t h e y a r e c l o s e l y r e a
Milliseconds 81 255 129 312 167 72 105 104 95 129 503 136 79 114 279 72 169 400 119 136 144 129 159 57 79
Character l t e -e -t -l -a l a t e d t o t h e s l o p e
Milliseconds 88 112 81 280 229 74 136 409 7 168 72 185 112 119 57 104 160 79 105 71 97 103 168 168 145
Character o f a c u r v e a t a p o i n t P
Milliseconds 79 137 135 81 80 160 240 96 120 391 105 127 96 128 104 113 111 233 15 153 129 111 104 176 120
Character o n t h e c u r v e . W e g i v e p r e
Milliseconds 96 128 95 113 103 73 96 111 88 112 305 95 144 281 345 143 111 193 128 112 79 80 136 121 87
Character c i s e d e v e l o p m e n t s o f t h e s
Milliseconds 320 353 144 151 120 178 182 56 137 7 168 113 192 87 144 193 208 296 168 128 39 153 56 376 408
Character e i m p o r t a n t c o n c v e -e -v e p t s
Milliseconds 96 112 128 136 79 137 200 216 119 120 97 95 153 80 120 104 167 89 400 128 201 175 119 128 144
Character i n t h e n e x t c h a p t e r , b u t
Milliseconds 105 120 128 39 152 65 79 137 72 183 120 160 368 113 120 129 119 88 111 113 104 256 95 105 80
Character f o r n o e w -w -e w w e u s e a n i n f
Milliseconds 233 118 82 78 120 129 7 65 384 136 401 111 240 111 64 185 64 112 143 97 96 120 104 183 89
Character o r m a l a p p r o a c h s o w -w y o u w
Milliseconds 160 48 144 104 208 144 111 121 136 89 128 22 633 128 152 240 104 112 104 344 161 79 120 104 136
Character i l l s e e h o w t h e y l e a d n a t
Milliseconds 96 160 136 112 193 136 127 144 160 88 120 88 192 95 145 64 128 111 82 72 231 127 210 103 215
Character u r a l l y t o t h e m a i n i d e a o
Milliseconds 169 120 120 104 120 191 81 121 87 80 120 104 88 96 168 136 64 88 81 336 111 184 72 144 136
Character f t h i s c h a p t e r , t h e l i m i t
Milliseconds 112 63 131 46 72 80 80 208 96 120 121 144 119 81 104 127 193 111 104 64 73 55 184 56 88
Character . T h e i d a -a e a o f a l i m i t p
Milliseconds 208 209 344 168 86 105 168 128 288 480 96 88 280 144 128 64 128 88 169 87 185 63 81 143 200
Character l a y s a f o u n d a t i o n a l r o l e
Milliseconds 153 80 111 137 78 121 80 161 88 71 185 223 137 135 80 80 88 103 105 121 160 103 169 78 50
Character t h r o u g h o u t c l a -a -l a l c u l u s .
Milliseconds 168 47 177 224 88 151 104 489 63 112 96 224 88 112 312 137 63 137 440 88 136 407 192 121
WPM Timing
Seconds WPM
2.75 61.01
5.51 84.97
8.26 97.32
11.02 94.78
13.77 96.74
16.52 90.06
19.28 88.4
22.03 90.97
24.78 91.51
27.54 86.72
30.29 85.57
33.05 85.34
35.8 87.49
38.55 85.91
41.31 84.83
44.06 80.34
46.81 80.49
49.57 78.92
52.32 79.13
55.08 77.35
57.83 76.15
60.58 75.07
63.34 74.46
66.09 75.17
68.84 73.21
71.6 73.91
74.35 73.76
77.11 74.24
79.86 72.73
82.61 72.19
85.37 72.96
88.12 72.58
90.87 72.1
93.63 72.54
96.38 73.46
99.14 73.47
101.89 73.49
104.64 73.62
107.4 73.63
110.15 73.86
112.91 73.76
115.66 73.98
118.41 73.98
121.17 74.38
123.92 74.95
126.67 75.6
129.43 75.19
132.18 75.62
134.94 75.95
137.69 75.3