Ciseak (ciseak)

Race #44

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Official speed 105.28 wpm (98.48 seconds elapsed during race)
Without ending ping 105.58 wpm (278 ms delay sending score to TypeRacer’s server)
Timerless 105.94 wpm (336 ms elapsed before first character typed; 97.87 seconds elapsed during race)
Timerless minus one 105.82 wpm, ignoring the first character typed
Race Start May 14, 2024 4:32:31pm UTC
Race Finish May 14, 2024 4:34:09pm UTC
Outcome Win (1 of 2)
Accuracy 97.9%
Points 284.25
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 rlaelated to a change in another. How does the speed of a falling object change as a fucntnnction of time? How does the level of water in a brarrel change as a function of the amount of liquid poured into it? We chssee change occurring in nearly everything we observe in twhhe world and universe, and powerrrful modern isntrnstruments help us see more and more. UIn this section we introduce the ideas of average and instraantaneous rates of change, and show that they are closely related to the slope of a curve ast a point P on the curve. We give precise developments aof these important concepts in the next chapter, fbut for now we use an informal approach to so you will see how they lead naturally ot theto the main idea of this chapter, sthe limit. The idea of a limit plays a foundational role throughout caculculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 336 160 63 110 48 167 139 53 40 61 108 78 109 48 123 18 153 154 76 64 107 62 156 15 77
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 76 448 154 78 77 92 138 124 93 137 46 141 108 155 44 92 78 77 44 78 153 45 79 77 63
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 108 31 114 26 151 31 68 53 140 62 107 128 42 47 107 46 122 47 124 46 79 92 93 63 79
Character r l a -a -l e l a t e d t o a c h a n g e
Milliseconds 63 78 184 110 200 153 93 92 94 170 46 123 46 78 47 78 108 62 122 45 124 33 135 63 75
Character i n a n o t h e r . H o w d o e s t h e
Milliseconds 48 153 47 92 76 153 46 93 48 104 77 156 137 145 57 93 109 64 91 139 76 77 48 77 62
Character s p e e d o f a f a l l i n g o b j e c t
Milliseconds 88 68 106 139 123 46 63 76 65 91 61 78 155 62 125 142 108 78 44 77 61 140 93 171 94
Character c h a n g e a s a f u c n t -t -n n -n -c n c
Milliseconds 278 278 63 108 47 155 58 65 77 156 76 62 76 93 62 124 62 141 264 138 342 218 103 157 46
Character t i o n o f t i m e ? H o w d o e s t h
Milliseconds 152 30 79 122 75 93 63 32 76 32 124 60 158 228 123 200 61 77 111 47 93 137 60 94 30
Character e l e v e l o f w a t e r i n a b r -r
Milliseconds 124 47 106 93 156 124 16 77 92 76 45 110 151 79 94 124 76 46 163 101 109 31 139 60 329
Character a r r e l c h a n g e a s a f u n c t i o
Milliseconds 79 154 109 153 45 64 92 75 95 71 162 77 70 85 139 78 62 94 92 62 139 76 141 31 92
Character n o f t h e a m o u n t o f l i q u i d
Milliseconds 108 93 94 93 31 290 46 129 55 125 94 153 138 138 77 31 94 62 61 92 169 94 60 116 91
Character p o u r e d i n t o i t ? W e c h -h s -s
Milliseconds 28 125 232 247 95 154 128 72 31 123 78 77 47 92 63 171 186 215 201 62 93 78 277 64 62
Character -c s e e c h a n g e o c c u r r i n g i n
Milliseconds 299 149 157 93 76 76 65 108 30 167 78 45 93 76 109 108 78 108 109 107 77 32 76 153 63
Character n e a r l y e v e r y t h i n g w e o b s e
Milliseconds 261 92 146 163 48 111 108 92 93 61 152 49 138 64 94 137 46 47 107 132 86 61 108 200 107
Character r v e i n t w h -h -w h e w o r l d a n d
Milliseconds 155 76 124 123 77 122 78 14 247 123 250 122 217 48 108 79 93 78 106 78 95 63 92 78 47
Character u n i v e r s e , a n d p o w e r r -r r -r f u
Milliseconds 61 122 154 30 187 137 171 123 61 111 109 76 92 46 93 123 48 151 18 140 340 201 324 63 104
Character l m o d e r n i s n t r -r -t -n -s n s t r u m e
Milliseconds 191 36 143 123 62 107 140 15 77 75 127 0 139 124 295 139 155 232 185 62 166 155 63 138 94
Character n t s h e l p u s s e e m o r e a n d
Milliseconds 62 61 185 31 124 109 78 63 136 93 108 78 92 184 125 61 77 140 62 123 108 77 94 69 24
Character m o r e . U -U I n t h i s s e c t i o n w
Milliseconds 93 134 68 92 76 169 153 356 137 156 78 92 62 153 62 107 278 138 169 139 46 62 136 91 91
Character e i n t r o d u c e t h e i d e a s o f
Milliseconds 124 92 61 124 61 125 79 122 62 124 137 55 99 15 107 31 62 107 94 160 151 106 93 83 103
Character a v e r a g e a n d i n s t r a -a -r a n t a n
Milliseconds 261 187 154 154 170 31 108 92 77 91 78 32 77 138 61 141 0 157 346 119 91 109 93 248 138
Character e o u s r a t e s o f c h a n g e , a n d
Milliseconds 137 186 156 74 114 302 184 140 61 139 47 79 75 30 112 67 114 46 156 78 123 91 140 78 93
Character s h o w t h a t t h e y a r e c l o s e
Milliseconds 61 108 31 170 77 81 77 77 108 168 31 94 47 109 44 63 93 141 105 63 107 76 137 47 91
Character l y r e l a t e d t o t h e s l o p e o
Milliseconds 77 110 93 123 141 108 94 171 139 124 93 94 30 62 62 77 94 60 94 77 139 122 77 77 31
Character f a c u r v e a s -s t a p o i n t P
Milliseconds 93 48 124 46 123 80 91 199 155 72 268 154 401 63 94 92 63 77 171 170 141 60 95 109 76
Character o n t h e c u r v e . W e g i v e p r e
Milliseconds 83 151 113 35 84 93 64 92 46 109 155 141 62 215 386 173 77 93 61 139 122 47 91 77 124
Character c i s e d e v e l o p m e n t s a -a o f t h
Milliseconds 155 77 92 140 108 79 138 157 172 62 123 139 157 41 96 46 201 124 185 224 100 78 77 92 47
Character e s e i m p o r t a n t c o n c e p t s i n
Milliseconds 107 172 122 48 46 123 185 141 77 92 219 92 78 63 123 47 125 62 139 78 109 200 108 75 123
Character t h e n e x t c h a p t e r , f -f b u t
Milliseconds 63 15 92 46 63 66 73 168 32 78 107 64 110 108 92 140 110 47 79 311 207 107 69 62 49
Character f o r n o w w e u s e a n i n f o r m a
Milliseconds 135 32 94 63 312 149 60 38 125 170 139 140 79 108 125 124 93 141 92 125 109 49 76 61 93
Character l a p p r o a c h t o - -o -t s o y o u w
Milliseconds 76 107 31 79 125 60 92 76 139 77 124 160 105 79 279 129 149 139 30 78 92 63 140 62 46
Character i l l s e e h o w t h e y l e a d n a t
Milliseconds 67 166 124 45 63 109 137 78 94 154 61 33 94 31 111 44 64 125 74 144 141 84 63 78 156
Character u r a l l y o t t h e -t -h -e -o -t - t o t h e
Milliseconds 61 95 185 52 102 61 46 124 16 76 138 63 170 233 0 0 334 0 0 255 105 61 77 79 77
Character m a i n i d e a o f t h i s c h a p t e
Milliseconds 32 77 93 81 120 63 90 63 107 171 105 65 91 30 96 28 137 47 46 91 46 109 92 109 139
Character r , s -s t h e l i m i t . T h e i d e a
Milliseconds 108 31 62 110 277 76 76 80 31 80 167 138 111 59 107 107 93 140 60 93 61 78 120 166 129
Character o f a l i m i t p l a y s a f o u n d a
Milliseconds 80 75 48 170 62 107 155 124 153 31 123 76 139 76 118 99 109 155 93 139 45 125 127 44 170
Character t i o n a l r o l e t h r o u g h o u t c a
Milliseconds 155 0 78 109 152 34 107 93 30 139 80 61 249 106 107 79 115 100 46 172 116 69 55 100 138
Character c u -u -c l c u l u s .
Milliseconds 212 50 403 108 78 139 92 184 188 77 108
WPM Timing
Seconds WPM
1.97 109.67
3.94 103.57
5.91 117.79
7.88 117.28
9.85 118.2
11.82 120.84
13.79 123.59
15.76 120.33
17.73 111.7
19.7 112.71
21.67 114.1
23.64 113.22
25.6 113.88
27.57 114.45
29.54 113.32
31.51 110.05
33.48 110.38
35.45 111.36
37.42 109.03
39.39 109.67
41.36 107.93
43.33 105.79
45.3 105.43
47.27 106.37
49.24 104.79
51.21 105.68
53.18 105.38
55.15 104.66
57.12 104.2
59.09 105
61.06 105.74
63.03 106.62
65 105.79
66.97 106.08
68.94 105.84
70.91 105.6
72.88 105.22
74.84 105.98
76.81 105.76
78.78 105.71
80.75 105.95
82.72 105.6
84.69 106.12
86.66 104.82
88.63 105.88
90.6 105.83
92.57 106.04
94.54 106.11
96.51 106.43
98.48 105.28