cu63y (qu63y)

Race #18366

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Official speed 92.13 wpm (112.54 seconds elapsed during race)
Without ending ping 93.13 wpm (1,206 ms delay sending score to TypeRacer’s server)
Timerless 94.40 wpm (1,499 ms elapsed before first character typed; 109.83 seconds elapsed during race)
Timerless minus one 94.29 wpm, ignoring the first character typed
Race Start February 21, 2025 5:17:04pm UTC
Race Finish February 21, 2025 5:18:57pm UTC
Outcome No win (4 of 4)
Opponents 1. anthonywspt (116.60 wpm)
2. mpb10 (102.92 wpm)
3. steffin02 (98.77 wpm)
Accuracy 96.9%
Points 248.76
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 ndeudnnderstand how a change in one quanitttiittity is related to a change n in another. How does th e speed of falla falling object change a ss a funciton tion of time/ H? ow HHow does the level of water in a barrel change as a funcitontion of the maamount of liquid poured into it? We see change occuring iring in enerarly everythihng we observe in the world andun universe, and powerful modern instruments help us see more and more. In this section we intrucoduce the idease o of average and instantenaneous rates of change, and show tehhat they are closely related to the slope of a cruurve at a point Pon on the curve. We give precise developments of these importants c concepts in the next chapter, but for now we use an informal approach so you will see how they lead naturally to the jamain idea of this chapter, the limit. The idea of a limit plays a foundational role throughout calcuulus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 1499 167 72 159 233 135 132 117 82 70 71 76 85 82 62 96 103 144 161 56 104 41 66 36 116
Character e l p s u s n d e -e -d -n u d n -n -d n d e r s t
Milliseconds 141 90 93 91 86 88 87 65 232 75 124 227 85 105 232 136 15 337 127 97 87 152 65 119 92
Character a n d h o w a c h a n g e i n o n e q
Milliseconds 61 57 98 37 88 43 93 57 71 113 174 108 68 67 77 80 76 53 71 63 185 60 55 53 345
Character u a n i t t -t -t t i -i -t -i i t -t -i t i t y i s
Milliseconds 87 129 131 69 135 153 183 89 224 56 247 243 270 168 119 227 94 122 93 80 120 65 103 96 28
Character r e l a t e d t o a c h a n g e n - -n i
Milliseconds 124 26 151 199 70 67 151 49 104 64 48 178 110 131 69 90 54 71 65 71 180 37 307 101 160
Character n a n o t h e r . H o w d o e s t h - e
Milliseconds 63 65 88 108 19 81 55 64 57 139 60 176 147 86 71 129 71 105 63 32 105 47 112 379 93
Character s p e e d o f f a l l -l -l -a -f a f a l l i
Milliseconds 48 105 79 120 129 160 56 48 104 32 200 87 96 115 278 96 111 214 291 31 168 144 121 111 57
Character n g o b j e c t c h a n g e a s -s - s a
Milliseconds 91 36 66 71 135 107 72 149 81 151 122 111 84 59 57 48 55 89 97 78 272 92 124 226 126
Character f u n c i t o n - -n -o -t -i t i o n o f t i
Milliseconds 91 89 116 113 87 97 7 48 59 85 232 176 108 108 124 109 95 42 62 44 149 104 80 99 53
Character m e / H -H - -/ ? o w - -w H -H -o H o w d o e
Milliseconds 48 39 169 80 223 216 172 92 227 81 340 113 65 166 83 299 235 98 268 169 168 120 121 47 120
Character s t h e l e v e l o f w a t e r i n a
Milliseconds 54 51 112 72 34 53 212 76 113 88 223 129 105 66 72 148 148 48 109 74 70 55 76 45 106
Character b a r r e l c h a n g e a s a f u n c i
Milliseconds 85 131 133 100 135 141 112 79 200 73 88 41 99 77 95 60 108 64 95 73 80 120 104 168 122
Character t o n -n -o -t -i t i o n o f t h e m a -a -m a m
Milliseconds 38 11 53 313 80 122 94 124 98 18 55 65 87 77 67 115 85 49 66 133 132 183 445 125 99
Character o u n t o f l i q u i d p o u r e d i n t
Milliseconds 83 77 124 52 97 68 99 66 135 32 143 97 43 165 121 134 153 79 135 362 424 115 85 59 60
Character o i t ? W e s e e c h a n g e o c c u r
Milliseconds 64 89 143 43 237 48 136 234 114 117 207 154 79 151 113 80 55 105 111 65 183 147 123 97 81
Character i n g i -i - -g -n -i r i n g i n e -e n e r -r a
Milliseconds 132 52 57 80 99 249 95 102 118 104 132 99 57 64 82 116 62 48 119 293 139 69 131 341 80
Character r l y e v e r y t h i h -h n g w e o b s e r
Milliseconds 48 130 79 64 111 200 57 125 123 96 73 62 152 432 153 47 76 77 111 85 204 128 80 104 96
Character v e i n t h e w o r l d a n d u n -n -u u
Milliseconds 175 49 104 89 82 20 304 104 49 40 103 105 66 96 69 81 97 38 72 184 144 213 91 98 95
Character n i v e r s e , a n d p o w e r f u l m o d
Milliseconds 132 60 125 90 116 84 64 146 70 120 75 69 40 126 99 152 40 122 150 71 81 72 160 136 125
Character e r n i n s t r u m e n t s h e l p u s s
Milliseconds 155 71 136 81 183 75 125 90 134 57 115 92 92 95 89 84 123 110 66 118 119 121 113 399 130
Character e e m o r e a n d m o r e . I n t h i s
Milliseconds 135 158 80 112 32 84 64 76 137 127 229 60 90 50 107 26 151 55 201 111 120 88 97 27 68
Character s e c t i o n w e i n t r u c -c -u o d u c e
Milliseconds 57 96 119 178 64 118 40 49 87 97 47 104 217 64 106 126 146 110 328 97 160 63 127 56 144
Character t h e i d e a s e o -o - -e o f a v e r a
Milliseconds 88 80 75 62 103 81 127 392 74 161 73 85 131 248 85 116 92 392 168 55 80 224 192 88 136
Character g e a n d i n s t a n t e n -n -e a n e o u s
Milliseconds 91 81 86 114 53 117 30 157 88 111 64 256 124 188 313 143 289 88 119 72 160 136 92 92 80
Character r a t e s o f c h a n g e , a n d s h o w
Milliseconds 153 120 90 69 131 85 89 75 61 155 204 105 79 97 51 109 79 88 80 92 53 103 49 39 75
Character t e h -h -e h a t t h e y a r e c l o s e l
Milliseconds 54 87 108 0 436 113 185 114 53 71 89 96 120 112 32 101 67 47 49 208 107 124 48 49 178
Character y r e l a t e d t o t h e s l o p e o f
Milliseconds 49 76 97 210 142 112 56 79 147 53 82 71 63 74 90 44 76 113 91 160 100 108 156 53 132
Character a c r u -u -r u r v e a t a p o i n t P
Milliseconds 60 128 100 115 117 99 347 93 177 199 184 32 72 91 157 129 114 87 142 44 99 42 40 71 217
Character o n - -n -o o n t h e c u r v e . W e g
Milliseconds 429 115 23 262 122 128 115 118 65 54 80 82 40 54 144 88 81 242 38 153 38 113 111 88 168
Character i v e p r e c i s e d e v e l o p m e n t s
Milliseconds 107 93 43 64 170 275 48 184 107 93 75 101 147 152 134 50 78 156 67 184 98 81 62 168 106
Character o f t h e s e i m p o r t a n t s c -c - -s
Milliseconds 125 64 80 81 66 32 141 72 112 259 69 49 33 110 200 241 167 116 149 151 136 272 92 108 116
Character c o n c e p t s i n t h e n e x t c h a p
Milliseconds 133 119 32 241 127 57 103 81 115 94 63 47 48 99 5 66 86 43 166 87 65 147 69 135 224
Character t e r , b u t f o r n o w w e u s e a
Milliseconds 171 86 82 102 66 118 115 52 48 88 105 47 59 327 24 142 76 92 73 71 296 88 64 82 166
Character n i n f o r m a l a p p r o a c h s o y o
Milliseconds 104 88 80 72 80 104 91 142 112 79 41 263 97 97 86 84 108 112 80 64 137 112 71 137 47
Character u w i l l s e e h o w t h e y l e a d
Milliseconds 96 26 78 154 11 107 96 81 113 134 72 76 44 80 48 89 107 45 127 50 86 80 96 66 78
Character n a t u r a l l y t o t h e j a -a -j m a i n
Milliseconds 144 104 45 101 63 71 96 115 117 72 184 105 64 47 88 56 57 95 114 253 185 153 119 80 63
Character i d e a o f t h i s c h a p t e r , t h
Milliseconds 33 169 100 155 113 33 463 87 65 88 59 68 132 68 200 114 86 147 200 77 80 88 90 70 64
Character e l i m i t . T h e i d e a o f a l i
Milliseconds 53 62 85 53 116 84 102 181 81 115 76 160 114 126 74 171 165 137 78 120 39 129 95 121 31
Character m i t p l a y s a f o u n d a t i o n a l
Milliseconds 163 78 111 72 107 117 116 125 75 84 83 94 123 68 70 122 77 116 88 64 34 53 128 121 79
Character r o l e t h r o u g h o u t c a l c u u -u l u
Milliseconds 136 96 130 66 69 71 105 127 48 49 66 77 64 76 100 72 226 158 96 497 91 142 359 160 82
Character s .
Milliseconds 69 98
WPM Timing
Seconds WPM
2.25 26.66
4.5 79.97
6.75 65.76
9 85.31
11.25 72.51
13.5 74.64
15.76 79.21
18.01 81.97
20.26 78.2
22.51 82.64
24.76 79
27.01 78.2
29.26 74.64
31.51 78.07
33.76 81.4
36.01 81.64
38.26 81.54
40.51 81.75
42.76 82.22
45.01 81.31
47.27 81.24
49.52 81.67
51.77 82.06
54.02 83.75
56.27 84.88
58.52 85.51
60.77 86.89
63.02 86.64
65.27 85.31
67.52 85.48
69.77 85.48
72.02 85.81
74.27 86.92
76.52 88.13
78.78 87.59
81.03 87.23
83.28 87.61
85.53 88.39
87.78 87.77
90.03 88.64
92.28 89.21
94.53 89.62
96.78 90.76
99.03 91.73
101.28 91.35
103.53 92.14
105.78 92.34
108.04 93.19
110.29 93.36
112.54 92.13