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Race #588

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Official speed 90.43 wpm (114.65 seconds elapsed during race)
Without ending ping 90.54 wpm (142 ms delay sending score to TypeRacer’s server)
Timerless 90.84 wpm (381 ms elapsed before first character typed; 114.13 seconds elapsed during race)
Timerless minus one 90.74 wpm, ignoring the first character typed
Race Start January 28, 2024 9:11:59am UTC
Race Finish January 28, 2024 9:13:54am UTC
Outcome Win (1 of 3)
Opponents 2. olijoao (69.81 wpm)
Accuracy 97.3%
Points 244.17
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 Calculesus is a tool that helpes us understand how a changie in one quarntity is related to a chancege in another. How does the speed of a falling object change as a function of time? How does the level of water in a barred cl chanegge as a funcrtiontion oft he of the amount of liquid poured into it? We see change occurring in nearly everything we observe it nin the world and universe, and powerful modern instruments help us tsee tomoerre and more. In this section we introduce the idea ss ss of average and instantaneous raettes of change, and show that they are closedly related to the slope of a curve at a point P on the curve. We ive pgive precise developments of these mipoimportant concepts in the next chapter, but for now we use an informal approach yso you will see how they lead natunallrally to the main idea of this schapter, the limit. The idea of a dillimit plays a foundartional role throughout calculus.
Timing
Character C a l c u l e s -s -e u s i s a t o o l t h
Milliseconds 381 126 73 110 183 251 140 266 229 107 191 82 35 132 132 124 119 100 178 179 128 54 105 111 61
Character a t h e l p e -e s u s u n d e r s t a n d
Milliseconds 35 56 72 145 71 88 100 98 345 84 66 147 112 91 223 60 33 87 65 100 90 39 144 27 77
Character h o w a c h a n g i -i e i n o n e q u a
Milliseconds 164 38 56 87 106 93 68 79 51 53 255 345 317 161 56 84 69 81 111 72 60 103 574 155 48
Character r -r n t i t y i s r e l a t e d t o a c
Milliseconds 109 385 52 41 141 114 159 100 102 75 73 169 67 129 120 95 79 93 90 126 128 82 539 59 159
Character h a n c e -e -c g e i n a n o t h e r . H o w
Milliseconds 67 49 72 101 31 305 109 86 146 59 131 65 109 328 163 86 113 37 88 42 177 98 128 105 127
Character d o e s t h e s p e e d o f a f a l l
Milliseconds 117 93 125 48 18 113 81 99 37 79 75 109 51 143 56 67 107 47 77 136 98 169 173 78 99
Character i n g o b j e c t c h a n g e a s a f u
Milliseconds 88 65 80 36 153 248 250 179 58 32 99 151 55 55 99 80 38 104 71 129 45 134 104 145 58
Character n c t i o n o f t i m e ? H o w d o e s
Milliseconds 83 101 54 127 69 56 103 92 38 76 77 107 96 86 246 206 183 168 97 83 96 66 66 52 60
Character t h e l e v e l o f w a t e r i n a b
Milliseconds 126 49 64 87 29 120 83 73 455 144 123 42 67 183 61 108 64 111 81 166 60 81 86 116 125
Character a r r e d c -c - -d l c h a n e g -g -e g e a s
Milliseconds 127 73 130 86 106 99 146 324 116 147 100 89 141 71 152 86 133 116 344 101 95 128 150 159 89
Character a f u n c r t i o n -n -o -i -t -r t i o n o f t
Milliseconds 57 106 119 170 44 73 114 82 14 52 33 170 219 110 147 149 175 110 122 53 128 123 165 38 153
Character h e -o -f -t - -h -e - o f t h e a m o u n t
Milliseconds 54 100 50 134 272 0 0 0 0 0 0 354 36 61 173 16 54 80 123 136 222 38 55 45 145
Character o f l i q u i d p o u r e d i n t o i t ?
Milliseconds 108 47 72 172 577 131 263 6 130 250 237 82 31 237 130 89 92 171 63 24 89 86 107 57 181
Character W e s e e c h a n g e o c c u r r i n g
Milliseconds 99 114 143 79 224 98 117 93 427 101 45 65 52 71 152 181 68 141 134 97 142 76 80 45 66
Character i n n e a r l y e v e r y t h i n g w e o
Milliseconds 84 104 206 6 231 32 96 193 70 95 134 62 84 103 128 86 120 50 29 48 87 270 80 84 219
Character b s e r v e i t - -t -i n -n i n t h e w o r
Milliseconds 119 57 147 82 92 65 155 106 123 91 473 103 120 132 379 230 91 73 128 50 28 123 11 130 46
Character l d a n d u n i v e r s e , a n d p o w e
Milliseconds 181 57 109 54 79 43 68 538 126 481 237 149 34 57 65 96 68 88 10 51 417 151 53 59 104
Character r f u l m o d e r n i n s t r u m e n t s h
Milliseconds 59 124 63 55 97 126 107 133 200 36 112 74 151 46 114 53 34 104 104 129 43 62 55 104 127
Character e l p u s t -t s e e t o -o -t m o e r -r -e r e
Milliseconds 75 99 139 200 60 106 95 195 341 156 76 118 69 186 41 328 108 132 196 160 99 262 102 73 111
Character a n d m o r e . I n t h i s s e c t i o
Milliseconds 67 90 20 26 105 132 83 84 86 109 112 142 157 59 87 82 41 61 67 215 111 112 48 82 37
Character n w e i n t r o d u c e t h e i d e a s
Milliseconds 58 77 157 40 97 170 63 64 89 150 135 138 282 118 154 103 66 25 77 97 94 150 40 82 37
Character -s s - -s s -s - s o f a v e r a g e a n d
Milliseconds 354 143 117 215 125 163 216 112 110 125 145 37 68 303 91 79 216 380 248 137 195 117 70 38 67
Character i n s t a n t a n e o u s r a e t -t -e t e s o
Milliseconds 293 150 41 15 178 157 184 228 246 196 202 23 89 231 152 66 156 77 310 96 91 128 45 113 88
Character f c h a n g e , a n d s h o w t h a t t
Milliseconds 44 94 115 72 46 81 86 43 161 63 100 18 36 130 173 127 32 169 128 142 67 46 70 64 125
Character h e y a r e c l o s e d -d l y r e l a t e d
Milliseconds 72 37 128 69 121 68 81 94 477 108 103 138 193 122 376 90 73 66 131 99 157 213 143 63 98
Character t o t h e s l o p e o f a c u r v e
Milliseconds 85 152 106 120 111 67 50 60 76 52 77 68 109 119 122 61 70 132 87 568 347 65 65 140 117
Character a t a p o i n t P o n t h e c u r v e
Milliseconds 117 63 112 204 114 148 75 53 34 65 77 136 118 75 93 44 165 32 36 72 142 251 184 159 125
Character . W e i v e p -p - -e -v -i g i v e p r e c i
Milliseconds 291 114 233 126 83 238 84 82 65 156 210 125 140 141 127 117 103 97 49 158 583 65 73 138 139
Character s e d e v e l o p m e n t s o f t h e s e
Milliseconds 131 89 86 112 76 82 98 57 153 76 251 141 42 54 67 64 111 47 74 124 66 33 72 99 86
Character m i p o -o -p -i -m i m p o r t a n t c o n c e p t
Milliseconds 124 25 180 81 268 120 138 143 213 66 103 104 56 54 147 113 46 133 118 113 58 137 157 135 113
Character s i n t h e n e x t c h a p t e r , b u
Milliseconds 95 103 151 67 71 128 43 40 72 127 102 179 147 151 150 106 59 275 526 141 123 229 132 226 52
Character t f o r n o w w e u s e a n i n f o r
Milliseconds 81 11 235 44 57 59 154 51 100 33 189 59 120 120 68 73 83 120 50 141 173 114 129 118 67
Character m a l a p p r o a c h y -y s o y o u w i l
Milliseconds 173 112 146 105 102 149 123 178 159 141 99 200 129 122 307 78 67 80 77 59 37 89 17 156 120
Character l s e e h o w t h e y l e a d n a t u n
Milliseconds 416 159 198 92 128 112 187 62 101 72 132 62 41 172 84 242 139 45 62 107 146 80 57 122 73
Character a l l -l -l -a -n r a l l y t o t h e m a i n
Milliseconds 85 115 122 264 116 150 119 85 78 81 123 34 100 83 68 76 72 87 34 74 88 110 48 70 72
Character i d e a o f t h i s s -s c h a p t e r , t
Milliseconds 143 129 82 37 69 125 30 83 81 91 31 88 46 155 560 124 347 38 103 94 104 172 80 102 81
Character h e l i m i t . T h e i d e a o f a d
Milliseconds 84 33 97 44 92 117 94 125 131 98 84 108 48 83 141 112 100 49 71 186 53 70 136 100 151
Character i l -l -i -d l i m i t p l a y s a f o u n d a
Milliseconds 80 34 266 111 141 126 107 65 96 100 126 158 93 90 48 110 166 99 122 156 33 46 87 55 93
Character r -r t i o n a l r o l e t h r o u g h o u t
Milliseconds 85 372 65 218 71 91 374 167 114 131 95 90 104 112 121 97 84 97 20 165 74 285 42 93 123
Character c a l c u l u s .
Milliseconds 111 90 99 99 106 106 134 396 124
WPM Timing
Seconds WPM
2.29 47.1
4.59 73.27
6.88 94.2
9.17 85.04
11.47 86.87
13.76 83.73
16.05 88.22
18.34 92.24
20.64 95.36
22.93 97.86
25.22 98.96
27.52 96.38
29.81 93.8
32.1 88.96
34.4 89.31
36.69 89.29
38.98 89.58
41.27 91
43.57 91.99
45.86 89.75
48.15 89.46
50.45 90.63
52.74 91.24
55.03 88.96
57.33 90.85
59.62 91.58
61.91 89.55
64.21 88.96
66.5 88.42
68.79 89.31
71.08 89.81
73.38 89.46
75.67 89.76
77.96 90.66
80.26 89.41
82.55 88.67
84.84 89.53
87.14 89.1
89.43 89.5
91.72 89.36
94.01 89.86
96.31 89.84
98.6 89.82
100.89 89.2
103.19 90.48
105.48 90.33
107.77 90.41
110.07 90.71
112.36 90.46
114.65 90.43