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Race #347

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Official speed 101.51 wpm (102.14 seconds elapsed during race)
Without ending ping 101.79 wpm (282 ms delay sending score to TypeRacer’s server)
Timerless 102.13 wpm (343 ms elapsed before first character typed; 101.51 seconds elapsed during race)
Timerless minus one 102.02 wpm, ignoring the first character typed
Race Start January 19, 2024 3:23:10pm UTC
Race Finish January 19, 2024 3:24:52pm UTC
Outcome Win (1 of 4)
Accuracy 96.3%
Points 274.09
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 uncerderstand how a change in one quantity id s arelated to a change in anotehr. her. How dos es the speed of a falling object change as a function fo of time?> How does the level of water in a brrearrel change as a function f of the amount of liquid poured into it? We see change occuring in occurring in nearly evertything we observe in the world and universe, anx d powerful modern instruments hekl lp us see more and more. In this section we introduce the ideas of acerverage and instantaneous rate s of chagne, nnge, and show that they are closelty ry related to the slop oe of a curve at a point P on the ciururve. We give precide s ee sedevelopments of these important conceoptspts in the next chapter, but for now we juuse an inform apprinformal appraooach so you will see how they lead naturally tio o the main idea of thic s chapter, the limit. The idea of a limit plays a foundation ak l role thourrought out calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 343 126 16 503 78 251 157 124 63 77 78 47 248 30 267 30 247 0 500 78 94 0 63 48 63
Character e l p s u s u n c e r -r -e -c d e r s t a n d
Milliseconds 62 126 31 94 16 93 77 63 93 108 63 62 92 238 128 125 76 78 96 92 78 95 31 109 31
Character h o w a c h a n g e i n o n e q u a n t
Milliseconds 62 31 79 62 46 95 108 49 45 141 124 78 47 63 46 63 78 62 47 62 171 64 109 96 123
Character i t y i d - -d s a -a r e l a t e d t o a
Milliseconds 77 79 109 79 45 64 125 347 95 45 63 46 452 47 31 95 47 62 62 94 48 92 32 77 61
Character c h a n g e i n a n o t e h r . - -. -r -h -e
Milliseconds 78 125 79 16 125 47 48 61 47 48 63 122 79 31 123 63 15 62 125 77 188 141 124 123 111
Character h e r . H o w d o s - -s e s t h e s p e
Milliseconds 139 30 46 80 78 171 80 184 78 93 47 187 93 310 111 77 94 94 78 64 63 62 107 78 77
Character e d o f a f a l l i n g o b j e c t c h
Milliseconds 108 61 93 78 63 48 61 78 154 94 125 110 141 76 63 125 78 139 92 93 62 110 95 282 78
Character a n g e a s a f u n c t i o n f o - -o -f
Milliseconds 15 110 0 63 109 78 93 64 45 108 95 78 124 92 126 31 31 124 62 31 109 220 169 127 124
Character o f t i m e ? > - -> H o w d o e s t h e
Milliseconds 97 110 32 95 62 125 65 220 0 63 296 124 93 140 61 110 94 77 65 93 108 31 109 47 138
Character l e v e l o f w a t e r i n a b r r e
Milliseconds 93 279 46 78 78 47 63 94 48 46 139 93 48 94 62 46 79 30 78 62 63 78 110 140 62
Character -e -r -r a r r e l c h a n g e a s a f u n c
Milliseconds 236 138 126 17 355 157 141 93 63 153 93 32 107 32 46 92 109 32 47 94 453 171 94 109 63
Character t i o n f - -f o f t h e a m o u n t o f
Milliseconds 125 46 48 124 46 47 156 283 124 125 94 47 46 77 31 94 0 154 124 64 125 32 78 47 62
Character l i q u i d p o u r e d i n t o i t ? W
Milliseconds 77 93 156 141 142 30 62 93 78 79 202 47 31 92 62 108 47 62 62 94 111 46 156 77 144
Character e s e e c h a n g e o c c u r i n g i n
Milliseconds 109 60 109 171 124 47 124 46 62 77 47 47 46 47 94 111 63 94 47 47 46 62 94 16 95
Character - -i -n -o -c -c -u -r -i -n -g - o c c u r r i n g i n
Milliseconds 169 126 0 125 0 0 0 0 0 0 0 0 576 98 108 110 312 109 61 32 45 64 61 32 94
Character n e a r l y e v e r t -t y t h i n g w e o b
Milliseconds 294 93 79 79 78 47 77 63 62 79 94 247 468 31 139 48 47 47 77 93 63 47 62 46 109
Character s e r v e i n t h e w o r l d a n d u n
Milliseconds 108 111 45 156 62 80 62 46 62 111 76 80 46 77 79 62 31 107 16 107 0 124 16 79 111
Character i v e r s e , a n x - -x d p o w e r f u l
Milliseconds 61 79 62 92 111 126 77 78 62 94 109 62 311 108 47 61 78 62 47 94 47 156 47 140 93
Character m o d e r n i n s t r u m e n t s h e k l -
Milliseconds 95 46 93 62 77 31 62 63 61 31 92 126 61 141 95 47 77 140 17 77 109 78 0 92 248
Character -l -k l p u s s e e m o r e a n d m o r e
Milliseconds 123 126 252 93 62 124 48 91 173 140 124 78 46 47 30 33 46 61 63 64 47 48 46 62 31
Character . I n t h i s s e c t i o n w e i n t r
Milliseconds 78 76 141 110 64 94 46 16 109 32 157 139 79 140 48 32 125 46 47 48 78 95 63 32 110
Character o d u c e t h e i d e a s o f a c e r -r -e
Milliseconds 47 139 110 124 62 95 245 62 78 62 47 62 78 31 111 78 31 79 63 250 107 96 109 141 125
Character -c v e r a g e a n d i n s t a n t a n e o u s
Milliseconds 125 47 92 79 45 125 63 93 32 109 107 62 170 125 93 250 93 139 155 92 267 219 95 31 94
Character r a t e - s o f c h a g n e , - -, -e -n n
Milliseconds 77 77 62 92 63 358 295 31 62 62 63 62 205 109 32 94 15 63 95 63 217 124 141 171 377
Character -n -g n g e , a n d s h o w t h a t t h e y
Milliseconds 188 108 141 78 61 63 62 47 107 15 219 358 47 48 79 77 93 63 31 79 63 61 92 234 94
Character a r e c l o s e l t y r -r - -y -t y r e l a
Milliseconds 64 75 94 32 31 124 128 110 47 92 64 78 0 47 78 251 124 139 94 31 94 79 31 62 78
Character t e d t o t h e s l o p o -o - e o f a
Milliseconds 93 78 92 31 124 16 63 94 46 30 96 63 109 170 127 157 247 203 109 62 46 95 46 80 62
Character c u r v e a t a p o i n t P o n t h
Milliseconds 48 345 126 49 153 93 32 310 62 62 94 62 80 93 234 46 47 46 141 157 157 62 61 17 107
Character e c i u r -r -u -i u r v e . W e g i v e p r
Milliseconds 33 46 156 215 0 204 189 111 109 106 47 125 63 77 65 111 124 48 217 94 468 47 32 78 79
Character e c i d e - -e -d s e -e - e s e -e -s d e v e l
Milliseconds 46 296 76 78 33 122 264 142 95 60 96 16 405 109 186 63 76 109 252 108 62 79 76 63 79
Character o p m e n t s o f t h e s e i m p o r t a n
Milliseconds 139 0 234 78 94 121 142 45 62 156 63 142 47 47 142 109 63 108 139 95 77 46 126 46 77
Character t c o n c e o p t s -s -t -p -o p t s i n t h e
Milliseconds 94 78 112 45 64 94 46 80 0 31 188 205 125 126 126 141 63 169 61 126 47 62 31 63 78
Character n e x t c h a p t e r , b u t f o r n o
Milliseconds 47 48 45 125 422 110 77 78 46 110 110 221 92 0 62 123 17 46 95 79 125 77 77 47 46
Character w w e j u -u -j u s e a n i n f o r m a p
Milliseconds 77 79 112 61 45 81 249 204 126 127 32 125 63 94 16 62 94 78 63 94 47 108 79 31 108
Character p r -r -a -p -p -i -n -f -o -r -m - i n f o r m a l a p p
Milliseconds 94 78 175 125 0 0 141 0 0 0 0 0 0 528 60 141 78 63 78 93 548 63 123 94 113
Character r a o -o -a o a c h s o y o u w i l l s e e
Milliseconds 61 61 47 561 93 343 79 92 31 45 95 62 62 111 47 47 76 108 63 141 108 64 48 124 110
Character h o w t h e y l e a d n a t u r a l l y
Milliseconds 63 412 77 30 111 16 78 62 46 47 31 142 94 15 47 62 110 390 78 95 95 125 111 46 77
Character t i o - -o -i o t h e m a i n i d e a o f
Milliseconds 93 33 0 92 234 141 107 111 92 15 94 47 79 46 92 79 32 62 62 92 31 78 31 62 93
Character t h i c - -c s c h a p t e r , t h e l i
Milliseconds 48 77 63 31 126 128 313 109 32 46 125 0 172 78 127 77 79 0 62 94 47 63 46 108 153
Character m i t . T h e i d e a o f a l i m i t
Milliseconds 285 62 112 76 77 93 77 46 78 46 31 77 16 62 343 62 48 47 123 62 186 125 47 80 94
Character p l a y s a f o u n d a t i o n - a k - -k
Milliseconds 47 78 16 110 202 112 94 77 159 31 32 108 48 79 78 63 31 111 64 329 63 93 78 328 96
Character l r o l e t h o u r -r -u -o r o u g h t - -t o
Milliseconds 123 79 63 93 94 63 61 156 77 95 63 157 203 142 93 94 93 31 94 61 77 78 328 109 142
Character u t c a l c u l u s .
Milliseconds 46 46 79 79 63 144 220 172 171 125 46 125
WPM Timing
Seconds WPM
2.04 70.49
4.09 93.99
6.13 97.91
8.17 108.68
10.21 104.56
12.26 100.84
14.3 99.87
16.34 103.54
18.38 107.05
20.43 103.39
22.47 104.14
24.51 103.78
26.56 103.48
28.6 103.22
30.64 105.35
32.68 107.21
34.73 102.28
36.77 103.13
38.81 104.19
40.86 106.62
42.9 107.7
44.94 106.27
46.98 108.8
49.03 109.9
51.07 109.5
53.11 109.13
55.15 108.79
57.2 105.74
59.24 106.35
61.28 106.13
63.33 105.93
65.37 106.11
67.41 105.21
69.45 105.05
71.5 102.55
73.54 102.97
75.58 102.88
77.62 103.11
79.67 103.63
81.71 102.07
83.75 101.3
85.8 100.84
87.84 101.64
89.88 101.07
91.92 101.82
93.97 102.55
96.01 103.11
98.05 102.56
100.09 102.02
102.14 101.51