𝐓𝐇𝐏 (dontgototoilet)

Race #2394

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Official speed 105.33 wpm (98.43 seconds elapsed during race)
Without ending ping 105.75 wpm (392 ms delay sending score to TypeRacer’s server)
Timerless 106.00 wpm (234 ms elapsed before first character typed; 97.81 seconds elapsed during race)
Timerless minus one 105.88 wpm, ignoring the first character typed
Race Start December 3, 2023 3:30:41pm UTC
Race Finish December 3, 2023 3:32:20pm UTC
Outcome Win (1 of 3)
Accuracy 99.0%
Points 284.39
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 heplps us understand how a change in one quantity is related to a change in another. How does the speded of a falling object change as a fucnnction of time? How does the level of water in a barrel change as a fucnction of the amount of liquid poured into it? We see change occuring ring in nearly everything we observe in the world and universe, and powerful modern instruments help us see more amnd 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 developemments 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 foundateionional 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 234 232 147 129 321 399 154 131 47 82 105 43 130 77 41 153 139 112 172 113 90 67 73 39 111
Character e p -p l p s u s u n d e r s t a n d h o w
Milliseconds 99 98 477 189 166 141 51 263 304 145 172 162 54 166 65 166 141 439 104 83 57 112 47 50 79
Character a c h a n g e i n o n e q u a n t i t y
Milliseconds 102 99 52 78 116 63 119 61 47 89 73 65 110 98 66 98 123 112 142 83 204 88 104 380 114
Character i s r e l a t e d t o a c h a n g e i n
Milliseconds 139 98 79 105 84 101 146 73 65 175 39 178 0 45 86 112 109 88 119 44 134 71 35 98 79
Character a n o t h e r . H o w d o e s t h e s p
Milliseconds 78 142 82 86 108 55 111 48 53 74 179 260 94 85 120 83 123 84 55 70 86 61 91 92 54
Character e d -d e d o f a f a l l i n g o b j e c t
Milliseconds 102 241 366 84 178 73 76 71 108 32 152 142 87 96 181 82 71 85 46 91 320 239 95 109 221
Character c h a n g e a s a f u c n -n -c n c t i o n
Milliseconds 110 159 76 87 79 90 53 75 78 107 56 119 71 77 86 204 98 263 96 175 65 179 23 86 25
Character o f t i m e ? H o w d o e s t h e l e
Milliseconds 117 163 123 65 113 100 35 116 275 89 171 196 84 110 83 81 140 61 44 54 93 70 86 62 69
Character v e l o f w a t e r i n a b a r r e l
Milliseconds 205 221 156 105 153 234 103 119 104 80 162 55 57 99 74 66 61 102 92 119 100 184 55 90 85
Character c h a n g e a s a f u c -c n c t i o n o f
Milliseconds 152 68 139 53 103 41 68 103 94 45 146 79 142 123 200 372 156 69 179 53 70 65 78 104 90
Character t h e a m o u n t o f l i q u i d p o u
Milliseconds 55 119 59 58 115 121 96 153 54 160 65 91 49 113 64 106 73 175 101 80 120 112 404 200 89
Character r e d i n t o i t ? W e s e e c h a n g
Milliseconds 85 77 166 53 79 117 0 228 190 120 87 299 83 233 231 85 191 86 162 76 129 89 131 65 111
Character e o c c u r i n g - -g -n -i r i n g i n n e
Milliseconds 59 49 294 164 172 91 91 107 76 86 72 261 113 139 142 170 114 70 105 100 84 75 60 177 94
Character a r l y e v e r y t h i n g w e o b s e r v
Milliseconds 89 79 52 128 61 65 210 151 100 92 153 100 88 109 66 129 91 49 112 104 124 146 42 93 150
Character e i n t h e w o r l d a n d u n i v e r
Milliseconds 101 66 97 73 71 37 92 71 83 82 71 84 79 100 70 86 80 86 91 131 161 90 69 170 82
Character s e , a n d p o w e r f u l m o d e r n i
Milliseconds 183 95 41 89 78 91 59 101 47 160 22 47 51 161 68 85 116 107 120 107 144 59 73 71 93
Character n s t r u m e n t s h e l p u s s e e m o
Milliseconds 100 21 63 168 67 185 89 89 79 102 147 149 103 79 149 85 94 80 118 301 63 185 65 96 88
Character r e a m -m n d m o r e . I n t h i s s e
Milliseconds 51 45 88 113 83 304 175 89 69 76 93 72 49 97 100 115 146 71 54 83 56 75 77 116 56
Character c t i o n w e i n t r o d u c e t h e i d
Milliseconds 204 179 65 73 25 97 99 58 77 129 63 65 167 71 169 93 114 66 100 90 56 71 88 86 39
Character e a s o f a v e r a g e a n d i n s t a n
Milliseconds 188 95 143 94 72 109 75 113 121 68 169 94 123 67 86 87 75 76 88 103 78 35 95 103 113
Character t a n e o u s r a t e s o f c h a n g e ,
Milliseconds 138 368 202 324 237 106 125 93 197 92 94 84 103 40 85 174 135 210 105 22 177 79 38 136 40
Character a n d s h o w t h a t t h e y a r e c l
Milliseconds 96 105 85 130 100 80 92 57 119 34 121 82 80 122 45 154 51 137 56 60 96 83 24 217 24
Character o s e l y r e l a t e d t o t h e s l o p
Milliseconds 129 59 55 140 161 55 167 98 89 160 47 78 172 62 62 87 78 42 73 93 103 96 89 140 151
Character e o f a c u r v e a t a p o i n t P
Milliseconds 122 78 150 398 136 97 113 96 121 88 200 57 71 106 71 78 87 98 115 173 52 89 42 112 158
Character o n t h e c u r v e . W e g i v e p r
Milliseconds 177 138 80 53 84 83 54 68 126 90 79 225 39 125 73 351 213 100 92 99 125 52 64 239 152
Character e c i s e d e v e l o p e m -m -e m e n t s o f
Milliseconds 80 190 66 129 38 79 135 136 173 34 86 152 117 142 89 385 101 205 134 101 99 101 46 105 83
Character t h e s e i m p o r t a n t c o n c e p t s
Milliseconds 117 62 105 87 180 103 128 117 118 61 201 73 177 107 114 103 140 168 96 42 205 29 503 127 165
Character i n t h e n e x t c h a p t e r , b u t
Milliseconds 116 67 88 61 20 134 44 108 105 28 200 211 68 210 93 104 78 80 146 55 51 65 113 165 56
Character f o r n o w w e u s e a n i n f o r m
Milliseconds 107 106 74 82 92 71 98 171 114 274 97 69 149 71 60 69 124 167 139 127 71 95 108 86 101
Character a l a p p r o a c h s o y o u w i l l s
Milliseconds 109 97 89 142 113 143 110 105 145 154 85 63 89 84 56 123 106 66 49 49 92 167 117 42 101
Character e e h o w t h e y l e a d n a t u r a l l
Milliseconds 51 156 67 93 75 72 76 117 81 90 91 61 88 92 93 137 90 69 60 67 153 93 117 80 133
Character y t o t h e m a i n i d e a o f t h i
Milliseconds 105 53 69 80 74 66 78 113 62 101 120 111 63 78 98 82 153 80 56 89 81 81 103 67 53
Character s c h a p t e r , t h e l i m i t . T h e
Milliseconds 56 76 117 317 101 68 108 145 52 49 81 75 52 106 40 71 47 153 101 126 144 94 273 129 68
Character i d e a o f a l i m i t p l a y s a
Milliseconds 86 83 73 161 66 81 65 94 64 88 89 153 66 149 85 106 98 40 151 105 69 140 67 105 86
Character f o u n d a t e i o n -n -o -i -e i o n a l r o l e
Milliseconds 84 108 73 225 120 72 117 18 46 76 75 265 111 128 93 232 79 97 138 54 87 96 49 157 125
Character t h r o u g h o u t c l a -a -l a l c u l u s .
Milliseconds 118 90 63 114 46 41 124 90 379 81 144 89 216 115 68 344 114 93 109 142 96 159 106 120 104
WPM Timing
Seconds WPM
1.97 60.95
3.94 79.24
5.91 77.21
7.87 85.34
9.84 87.77
11.81 94.48
13.78 98.4
15.75 98.29
17.72 98.21
19.69 98.14
21.66 98.08
23.62 99.05
25.59 99.87
27.56 100.58
29.53 101.19
31.5 100.58
33.47 100.04
35.44 99.9
37.4 97.85
39.37 98.44
41.34 100.14
43.31 101.41
45.28 102.56
47.25 102.35
49.22 102.65
51.19 103.86
53.15 104.53
55.12 104.71
57.09 104.04
59.06 104.64
61.03 105.39
63 105.91
64.97 105.66
66.93 105.95
68.9 105.54
70.87 104.64
72.84 104.78
74.81 104.1
76.78 104.4
78.75 104.54
80.72 104.81
82.68 105.22
84.65 105.89
86.62 106.53
88.59 107.15
90.56 107.33
92.53 107.51
94.5 106.54
96.46 106.36
98.43 105.33