Alexander (torphon)

Race #35925

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Official speed 94.50 wpm (109.71 seconds elapsed during race)
Without ending ping 94.55 wpm (53 ms delay sending score to TypeRacer’s server)
Timerless 95.77 wpm (1,398 ms elapsed before first character typed; 108.26 seconds elapsed during race)
Timerless minus one 95.66 wpm, ignoring the first character typed
Race Start January 24, 2024 7:47:12am UTC
Race Finish January 24, 2024 7:49:02am UTC
Outcome Win (1 of 3)
Accuracy 98.2%
Points 255.14
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 calCalculus is a tool that helps us understand how a change in one quantity is related to a change in another. How does the speed ofa a f a falling object change as a function of time? How does that e level of water in a barrel change as a function of the amount of liquid poured into it? We see change occuriring in nearly everyhtthing we observe in teh worhehe world and auniverse, and powerful modern instruments help us see more and more. In this cesection we introduce the ideas of average adn innd instanteaneous 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 concenpts in teh he next chapter, but for now we use an informal approach so you will see how they lead naturally to the main diidea of this chapter, the limit. The idea of a limit plays a foundational role throughout calculus.
Timing
Character c a l -l -a -c C a l c u l u s i s a t o o l
Milliseconds 1398 103 88 328 169 167 721 520 216 648 17 190 193 95 113 112 88 63 73 112 104 47 153 184 87
Character t h a t h e l p s u s u n d e r s t a n d
Milliseconds 96 73 31 97 31 161 72 87 201 144 39 121 95 81 144 192 15 153 72 119 121 23 80 120 56
Character h o w a c h a n g e i n o n e q u a n t
Milliseconds 72 56 72 89 135 96 120 48 89 96 64 88 39 64 88 65 136 64 63 105 151 64 232 128 128
Character i t y i s r e l a t e d t o a c h a n g
Milliseconds 89 143 73 119 153 95 121 208 47 161 55 120 80 168 89 103 64 97 96 103 193 39 73 119 65
Character e i n a n o t h e r . H o w d o e s t h
Milliseconds 71 80 105 55 65 215 81 47 96 66 54 88 88 56 225 135 81 87 120 80 88 97 40 79 41
Character e s p e e d o f a - -a a f -f - -a a f a
Milliseconds 55 65 120 79 128 136 160 88 32 104 121 79 377 167 144 128 193 224 159 168 73 80 119 217 31
Character l l i n g o b j e c t c h a n g e a s a
Milliseconds 136 112 104 65 55 72 89 152 112 71 152 136 88 128 40 81 127 57 71 192 265 120 112 63 112
Character f u n c t i o n o f t i m e ? H o w d o e
Milliseconds 88 48 193 80 135 56 64 64 96 112 457 87 144 105 95 80 248 120 208 152 104 464 136 72 88
Character s t h a t - -t -a e l e v e l o f w a t e
Milliseconds 56 72 104 65 23 104 64 345 151 168 80 72 96 40 160 64 128 96 232 416 97 96 54 121 96
Character r i n a b a r r e l c h a n g e a s a
Milliseconds 104 63 81 96 71 17 128 153 55 184 136 193 183 72 184 40 80 104 40 104 56 96 104 104 105
Character f u n c t i o n o f t h e a m o u n t o
Milliseconds 71 112 55 201 80 136 48 72 80 80 144 80 57 87 64 32 72 120 64 64 136 200 360 144 168
Character f l i q u i d p o u r e d i n t o i t ?
Milliseconds 64 80 192 56 152 104 64 232 112 136 40 368 128 80 168 88 71 81 48 137 79 152 64 256 96
Character W e s e e c h a n g e o c c u r i -i r i n g
Milliseconds 176 144 128 112 192 136 88 120 40 89 119 48 80 104 152 136 152 72 96 88 400 120 55 115 32
Character i n n e a r l y e v e r y h t -t -h t h i n g
Milliseconds 134 80 73 95 288 88 41 62 121 121 103 104 160 72 88 89 0 167 312 144 200 47 73 112 56
Character w e o b s e r v e i n t e h w o r -r -o -w
Milliseconds 96 121 79 112 384 128 160 80 81 183 80 120 64 55 73 80 121 0 71 112 17 95 240 136 160
Character - -h h e -e -h -e h e w o r l d a n d a -a u n i
Milliseconds 136 152 185 168 95 168 168 184 80 88 96 80 96 80 128 63 65 96 47 89 73 432 160 191 40
Character v e r s e , a n d p o w e r f u l m o d e r
Milliseconds 80 175 97 128 88 144 128 112 80 72 112 184 72 104 40 55 193 40 136 104 120 64 96 136 88
Character n i n s t r u m e n t s h e l p u s s e e
Milliseconds 128 152 136 88 143 137 161 31 200 80 128 80 127 105 88 240 64 200 88 144 96 104 104 176 136
Character m o r e a n d m o r e . I n t h i s c
Milliseconds 144 48 88 112 48 80 103 89 72 64 88 39 89 47 97 55 185 176 80 80 88 24 88 81 143
Character e -e -c s e c t i o n w e i n t r o d u c e t
Milliseconds 160 279 162 47 64 200 120 32 72 72 104 104 80 120 224 120 88 168 48 160 72 136 136 80 88
Character h e i d e a s o f a v e r a g e a d n i
Milliseconds 80 48 72 136 88 128 80 136 232 129 71 48 112 193 119 112 80 168 88 88 104 153 0 79 129
Character n -n -i - -n -d n d i n s t a n t e -e a n e o u s
Milliseconds 87 208 128 152 120 168 136 80 72 144 425 86 145 56 184 465 46 346 238 169 192 601 87 88 128
Character r a t e s o f c h a n g e , a n d s h o w
Milliseconds 216 55 137 72 145 111 112 88 56 152 48 48 137 54 113 72 88 80 96 25 103 112 80 32 104
Character t h a t t h e y a r e c l o s e l y r e
Milliseconds 88 128 80 32 88 89 79 56 64 120 47 89 88 56 88 192 80 176 55 33 136 160 72 168 55
Character l a t e d t o t h e s l o p e o f a c
Milliseconds 105 80 112 80 160 88 112 63 97 49 111 40 56 240 48 144 137 127 120 128 56 80 88 97 119
Character u r v e a t a p o i n t P o n t h e
Milliseconds 112 72 176 80 72 80 152 88 48 112 88 48 104 136 72 136 232 256 144 72 56 88 112 23 105
Character c u r v e . W e g i v e p r e c i s e d e
Milliseconds 256 120 104 192 96 104 64 176 112 120 120 80 88 72 88 120 384 64 208 152 112 144 136 136 151
Character v e l o p m e n t s o f t h e s e i m p o r
Milliseconds 257 160 104 160 160 184 104 112 75 165 64 112 72 64 96 64 137 39 136 112 128 104 80 56 112
Character t a n t c o n c e n -n p t s i n t e h - -h
Milliseconds 184 40 120 56 112 168 40 96 96 168 136 344 199 65 96 104 80 104 47 81 104 0 80 353 143
Character -e h e n e x t c h a p t e r , b u t f o r
Milliseconds 176 152 112 88 112 56 168 128 113 167 56 80 96 160 136 80 144 72 120 72 120 72 120 72 88
Character n o w w e u s e a n i n f o r m a l a
Milliseconds 56 96 64 57 104 119 96 104 192 56 120 104 191 153 120 48 88 128 112 88 152 72 96 72 152
Character p p r o a c h s o y o u w i l l s e e h
Milliseconds 96 136 72 112 136 232 88 72 264 144 128 120 64 120 48 80 104 160 136 48 96 192 136 136 240
Character o w t h e y l e a d n a t u r a l l y t o
Milliseconds 80 72 200 64 88 81 111 56 184 96 39 153 104 216 105 215 80 136 56 80 152 136 64 120 72
Character t h e m a i n d i -i -d i d e a o f t h i
Milliseconds 96 57 79 80 72 96 80 136 64 47 321 0 336 159 113 112 136 55 217 120 80 72 88 25 47
Character s c h a p t e r , t h e l i m i t . T h e
Milliseconds 112 55 201 72 64 112 128 104 96 96 88 192 96 80 64 200 72 208 48 96 136 88 184 112 88
Character i d e a o f a l i m i t p l a y s a
Milliseconds 151 121 80 128 32 144 152 64 80 23 121 192 81 183 80 128 120 136 168 72 128 88 72 104 96
Character f o u n d a t i o n a l r o l e t h r o u g h
Milliseconds 129 55 55 177 39 57 152 80 55 137 304 200 104 248 40 192 47 89 208 56 160 80 40 160 88
Character o u t c a l c u l u s .
Milliseconds 88 112 48 112 184 120 112 208 48 168 152 144 96
WPM Timing
Seconds WPM
2.19 0
4.39 13.67
6.58 47.4
8.78 65.62
10.97 76.56
13.17 82.03
15.36 89.06
17.55 88.18
19.75 86.28
21.94 88.05
24.14 88.49
26.33 85.68
28.53 87.08
30.72 89.06
32.91 91.15
35.11 90.58
37.3 91.04
39.5 91.45
41.69 91.24
43.89 91.05
46.08 88.02
48.27 87.75
50.47 88.93
52.66 89.55
54.86 90.12
57.05 90.44
59.25 91.15
61.44 91.8
63.63 89.76
65.83 88.23
68.02 88.73
70.22 90.41
72.41 91.31
74.61 92
76.8 92.34
78.99 92.21
81.19 92.08
83.38 92.97
85.58 91.99
87.77 92.01
89.97 92.7
92.16 92.84
94.35 93.1
96.55 93.34
98.74 93.21
100.94 93.68
103.13 93.9
105.33 94.34
107.52 94.31
109.71 94.5