J (pjonathan)

Race #1830

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Official speed 110.60 wpm (93.74 seconds elapsed during race)
Without ending ping 110.68 wpm (67 ms delay sending score to TypeRacer’s server)
Timerless 111.13 wpm (376 ms elapsed before first character typed; 93.30 seconds elapsed during race)
Timerless minus one 111.00 wpm, ignoring the first character typed
Race Start January 19, 2024 11:05:22pm UTC
Race Finish January 19, 2024 11:06:56pm UTC
Outcome Win (1 of 3)
Accuracy 97.8%
Points 298.61
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 the speed of a falling object change as a function of time? How does thtee level of water in a barrel change as a function of the amount of liquid pouried into it? We se cha ecah e change occurring in nearly everything we sobserve in teh worhe world and universe, and powerful modern instruments help us see more and more. I n this section we introduce the ieadeas of average and instanteaneous rates of changes, and show that they are closely related to the slope of a curve at a point P on the curve. We give precise edevelopments of these important concepts in th ee next chapter, but for now wse use use an informal approach so you will see how hthey lead naturally to the main aidea of this chapter, the limit. The diidea of a limti pit plays a foundational frole 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 376 468 101 138 94 310 77 111 102 137 80 20 170 30 182 48 149 153 210 87 63 38 82 52 97
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 81 78 144 68 60 100 58 72 81 108 53 399 71 116 61 81 90 110 100 100 73 70 35 81 90
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 123 78 122 78 88 82 18 72 111 26 81 81 71 60 149 62 106 73 130 60 108 151 68 91 50
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 82 101 57 71 71 80 88 150 50 122 9 80 80 91 90 71 79 98 53 67 40 82 69 60 50
Character n o t h e r . H o w d o e s t h e s p e e
Milliseconds 74 77 59 53 77 53 46 72 122 60 86 61 131 50 89 70 29 109 9 93 59 71 90 88 132
Character d o f a f a l l i n g o b j e c t c h a
Milliseconds 121 78 82 60 70 80 110 139 71 47 143 68 64 37 90 73 78 170 61 69 151 57 153 28 110
Character n g e a s a f u n c t i o n o f t i m e
Milliseconds 61 30 109 52 73 77 60 107 100 83 79 81 49 149 61 18 70 81 88 82 61 86 52 82 40
Character ? H o w d o e s t h t e -e -t e l e v e l
Milliseconds 130 93 147 170 88 142 68 80 110 82 80 99 71 108 231 249 261 138 74 148 40 99 82 71 88
Character o f w a t e r i n a b a r r e l c h a n
Milliseconds 82 97 123 72 87 50 109 82 140 79 80 70 48 90 113 88 82 189 108 123 359 219 70 29 109
Character g e a s a f u n c t i o n o f t h e a
Milliseconds 45 56 88 81 81 40 109 73 39 90 71 71 148 54 27 41 60 87 78 43 71 49 41 100 59
Character m o u n t o f l i q u i d p o u r i -i e d
Milliseconds 60 111 49 30 70 132 81 67 74 208 180 130 80 150 250 73 235 141 98 89 200 222 50 118 73
Character i n t o i t ? W e s e c h a -a -h -c - e c
Milliseconds 99 73 138 71 79 118 124 98 108 81 183 105 64 107 203 169 71 109 201 128 142 131 99 0 219
Character a h -h -a -c -e - - e c h a n g e o c c u r r i
Milliseconds 88 11 282 109 141 140 129 120 321 138 99 90 90 54 126 63 58 81 99 99 121 100 88 111 62
Character n g i n n e a r l y e v e r y t h i n g w
Milliseconds 81 38 121 8 100 81 109 92 69 61 88 81 73 108 89 100 81 0 130 29 62 107 12 140 29
Character e s -s o b s e r v e i n t e h w o r -r -o -w
Milliseconds 120 52 149 251 170 48 82 150 80 199 68 43 89 69 81 8 99 9 142 4 108 53 227 130 140
Character - -h -e h e w o r l d a n d u n i v e r s e ,
Milliseconds 140 139 128 173 69 82 80 70 96 64 98 49 82 71 61 27 140 82 108 62 89 71 97 91 220
Character a n d p o w e r f u l m o d e r n i n s t
Milliseconds 235 147 70 69 89 119 162 8 73 47 141 72 69 110 121 51 56 151 50 89 110 82 80 70 49
Character r u m e n t s h e l p u s s e e m o r e
Milliseconds 111 78 133 99 70 81 80 68 71 100 150 171 98 161 121 58 101 62 115 75 98 71 9 92 37
Character a n d m o r e . I - n t h i s s e c t i
Milliseconds 112 28 88 42 80 82 28 59 110 92 141 80 230 181 101 75 63 79 50 89 72 80 129 150 88
Character o n w e i n t r o d u c e t h e i e a -a -e
Milliseconds 71 60 62 149 78 112 130 61 69 132 106 91 98 103 69 72 98 40 61 80 161 677 81 199 130
Character d e a s o f a v e r a g e a n d i n s t a
Milliseconds 62 150 71 59 124 97 90 86 101 99 111 53 89 99 82 47 43 107 111 80 92 88 0 89 100
Character n t e -e a n e o u s r a t e s o f c h a n g
Milliseconds 110 132 188 303 79 80 128 110 83 188 93 318 211 88 80 90 81 110 480 71 199 50 30 120 39
Character e s -s , a n d s h o w t h a t t h e y a
Milliseconds 50 62 350 199 82 29 128 30 113 106 72 70 39 119 51 74 37 73 26 120 21 108 53 108 99
Character r e c l o s e l y r e l a t e d t o t h e
Milliseconds 91 79 101 132 88 151 29 121 100 150 128 200 73 67 73 79 81 130 69 141 8 90 51 81 49
Character s l o p e o f a c u r v e a t a p o
Milliseconds 91 71 100 106 143 109 80 98 83 59 52 126 182 71 96 194 90 58 61 141 98 20 151 99 131
Character i n t P o n t h e c u r v e . W e g i
Milliseconds 81 58 13 146 133 119 211 79 79 63 88 29 82 138 82 109 221 88 123 45 213 139 92 460 70
Character v e p r e c i s e e -e d e v e l o p m e n t s
Milliseconds 109 80 59 129 101 90 123 106 83 109 91 118 320 39 152 100 70 60 151 128 91 71 88 63 97
Character o f t h e s e i m p o r t a n t c o n c e
Milliseconds 82 97 103 50 97 50 31 110 80 132 78 81 98 153 50 140 70 118 89 100 152 49 39 112 81
Character p t s i n t h e -e - e n e x t c h a p t
Milliseconds 79 130 99 80 161 71 77 40 71 162 28 281 131 70 72 128 48 172 200 97 163 159 129 90 191
Character e r , b u t f o r n o w w s e u s -s -u -
Milliseconds 109 81 88 83 107 71 72 70 230 50 79 71 79 80 53 87 89 51 71 47 210 80 203 149 140
Character -e -s e u s e a n i n f o r m a l a p p r o
Milliseconds 140 150 117 93 143 106 62 70 129 106 55 102 77 69 142 140 106 111 112 99 111 81 118 83 96
Character a c h s o y o u w i l l s e e h o w h
Milliseconds 101 72 98 132 120 97 91 171 120 40 98 91 50 49 125 78 27 93 117 90 82 70 58 90 120
Character -h t h e y l e a d n a t u r a l l y t o t
Milliseconds 210 83 91 79 67 81 120 42 58 114 77 158 111 82 117 80 83 47 122 81 80 109 52 70 60
Character h e m a i n a -a i d e a o f t h i s c h
Milliseconds 78 68 140 114 79 130 88 162 146 213 152 47 175 0 96 99 62 78 72 58 80 61 80 81 67
Character a p t e r , t h e l i m i t . T h e d i -i
Milliseconds 75 78 143 84 83 80 48 92 48 61 79 110 72 80 99 19 182 101 98 89 109 81 109 41 251
Character -d i d e a o f a l i m t i p -p - -i -t i t
Milliseconds 118 152 49 132 99 70 150 161 79 99 110 72 78 89 94 0 159 87 292 128 162 118 153 88 82
Character p l a y s a f o u n d a t i o n a l f -f r o
Milliseconds 81 148 51 107 82 75 76 109 120 59 50 62 26 94 80 69 51 48 81 120 153 147 220 99 72
Character l e t h r o u g h o u t c a l c u l u s .
Milliseconds 161 87 50 173 46 80 72 71 48 50 91 80 51 149 171 100 60 130 89 101 139 118 112
WPM Timing
Seconds WPM
1.87 57.6
3.75 92.81
5.62 102.41
7.5 112.01
9.37 119.05
11.25 128.01
13.12 129.84
15 131.21
16.87 131.57
18.75 126.09
20.62 125.68
22.5 126.41
24.37 127.52
26.25 123.89
28.12 120.76
30 113.21
31.87 113.33
33.75 115.21
35.62 113.86
37.5 111.37
39.37 111.55
41.25 112.88
43.12 113.54
45 113.87
46.87 114.18
48.75 112.01
50.62 113.31
52.5 111.78
54.37 111.01
56.25 111.58
58.12 111.9
60 112.41
61.87 112.69
63.75 112.57
65.62 111.73
67.5 112.19
69.37 112.61
71.24 111.67
73.12 111.76
74.99 110.09
76.87 110.21
78.74 110.79
80.62 110.74
82.49 111.28
84.37 111.37
86.24 111.59
88.12 110.99
89.99 110.14
91.87 110.24
93.74 110.6