Armamagedon (_m_o_t_h_)

Race #637

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Official speed 90.20 wpm (114.94 seconds elapsed during race)
Without ending ping 90.33 wpm (166 ms delay sending score to TypeRacer’s server)
Timerless 90.63 wpm (379 ms elapsed before first character typed; 114.40 seconds elapsed during race)
Timerless minus one 90.52 wpm, ignoring the first character typed
Race Start January 29, 2025 7:45:08pm UTC
Race Finish January 29, 2025 7:47:03pm UTC
Outcome Win (1 of 2)
Accuracy 98.4%
Points 243.55
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 toll thlol that helps us understand how a change in oner quantity is related to a chnageange 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 tiit? We see change occurrin ging in nearly everything we obsereverve in the world and universe, and powerful modern instrucmements help us see more and more . In this section we introduce the ideas of average and instantaneuoous rates of change , and wshow 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 chanpter, 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.
Timing
Character C a l c u l u s i s a t o l l t h -h -t - -l
Milliseconds 379 163 136 159 95 140 173 104 55 100 110 62 97 99 113 76 196 143 92 118 42 218 77 82 72
Character -l l -l o l t h a t h e l p s u s u n d e r
Milliseconds 87 503 334 194 149 142 116 65 76 63 39 132 120 46 257 102 127 162 127 110 353 96 64 81 111
Character s t a n d h o w a c h a n g e i n o n e
Milliseconds 167 69 59 98 96 80 105 42 71 77 99 79 114 41 174 2 149 74 51 145 26 75 611 44 103
Character r - -r q u a n t i t y i s r e l a t e d
Milliseconds 2 122 346 114 762 243 86 48 194 218 46 107 101 114 146 112 103 147 78 106 109 168 151 217 140
Character t o a c h n a g e -e -g -a -n a n g e i n a n
Milliseconds 119 89 89 100 113 102 69 159 17 210 94 170 95 115 143 159 59 222 37 84 129 108 84 89 88
Character o t h e r . H o w d o e s t h e s p e e d
Milliseconds 69 121 79 97 64 103 148 216 72 86 106 108 77 80 93 66 123 42 127 107 126 90 683 131 168
Character o f a f a l l i n g o b j e c t c h a n
Milliseconds 175 158 46 137 124 139 510 185 71 172 66 105 79 82 99 197 152 44 112 197 97 111 105 248 112
Character g e a s a f u n c t i o n o f t i m e ?
Milliseconds 176 78 77 115 61 128 92 107 89 82 102 61 182 76 48 56 82 132 42 406 166 67 93 56 660
Character H o w d o e s t h e l e v e l o f w a
Milliseconds 177 217 94 73 323 102 86 90 88 61 122 59 134 42 103 93 219 62 101 91 128 46 113 78 134
Character t e r i n a b a r r e l c h a n g e a s
Milliseconds 144 132 86 61 113 49 132 90 140 160 88 289 233 191 135 201 134 73 108 77 164 79 140 153 79
Character a f u n c t i o n o f t h e a m o u n t
Milliseconds 125 113 124 82 75 90 99 213 80 61 60 109 126 101 91 108 44 133 99 110 93 102 131 172 65
Character o f l i q u i d p o u r e d i n t o t i
Milliseconds 96 87 88 107 98 147 143 113 102 117 118 618 180 195 106 70 137 85 115 116 114 123 175 193 21
Character -i -t i t ? W e s e e c h a n g e o c c u r
Milliseconds 336 101 164 59 207 224 239 178 141 105 48 133 136 143 43 99 58 181 106 60 96 97 135 122 104
Character r i n g i n -n -i -g - g i n n e a r l y e v
Milliseconds 139 43 77 150 12 162 171 206 111 123 124 150 113 161 88 97 157 160 73 84 211 105 479 249 99
Character e r y t h i n g w e o b s e r e -e -r v e -e -v r
Milliseconds 68 42 123 113 69 70 113 76 107 98 86 76 120 149 120 93 142 348 381 118 79 29 307 107 114
Character v e i n t h e w o r l d a n d u n i v e
Milliseconds 235 71 153 126 86 88 134 32 123 32 114 101 92 28 146 100 127 98 142 28 137 171 134 224 67
Character r s e , a n d p o w e r f u l m o d e r n
Milliseconds 73 204 32 54 144 73 90 78 79 111 109 43 88 79 223 86 120 151 152 94 137 71 180 197 255
Character i n s t r u c m e -e -m -c m e n t s h e l p u s
Milliseconds 130 113 176 177 129 84 104 207 98 239 95 131 304 107 94 82 80 105 145 95 94 160 167 136 82
Character s e e m o r e a n d m o r e - . I n
Milliseconds 146 125 112 138 98 157 94 109 69 114 99 42 112 84 130 48 103 56 187 393 262 121 170 139 115
Character t h i s s e c t i o n w e i n t r o d u c e
Milliseconds 91 85 40 117 61 163 53 221 230 69 38 78 110 244 99 288 180 85 133 146 86 138 138 102 112
Character t h e i d e a s o f a v e r a g e a n d
Milliseconds 102 114 61 127 64 85 119 57 71 164 123 111 89 256 105 163 96 137 92 100 82 76 146 93 168
Character i n s t a n t a n e u o -o -u o u s r a t e s
Milliseconds 220 143 107 107 139 93 85 171 256 212 157 439 210 284 119 263 192 73 118 206 121 124 86 64 113
Character o f c h a n g e - , a n d w -w s h o w t
Milliseconds 121 94 112 115 93 128 42 179 115 205 307 187 99 95 88 87 78 157 327 104 78 37 90 76 106
Character h a t t h e y a r e c l o s e l y r e l a
Milliseconds 102 79 63 136 83 109 79 69 142 91 77 75 85 114 51 168 84 78 91 121 123 251 71 130 135
Character t e d t o t h e s l o p e o f a c u r
Milliseconds 105 81 153 139 106 95 160 137 97 72 70 129 65 160 102 118 330 134 117 107 198 235 118 109 121
Character v e a t a p o i n t P o n t h e c u
Milliseconds 200 224 217 120 92 206 35 55 133 259 192 96 77 137 252 150 266 199 158 127 65 95 61 119 98
Character r v e . W e g i v e p r e c i s e d e v e
Milliseconds 92 211 62 91 108 387 183 130 139 87 166 73 102 130 95 75 211 111 119 101 118 160 100 233 80
Character l o p m e n t s o f t h e s e i m p o r t a
Milliseconds 166 202 91 209 89 124 67 176 141 119 93 115 104 75 113 111 137 65 139 154 149 125 119 197 170
Character n t c o n c e p t s i n t h e n e x t c
Milliseconds 79 103 116 106 114 138 147 67 86 119 71 100 105 101 87 113 87 88 61 116 35 176 159 89 136
Character h a n -n p t e r , b u t f o r n o w w e
Milliseconds 106 98 97 432 70 115 110 69 92 124 165 82 57 150 91 77 92 84 115 37 63 98 145 66 128
Character u s e a n i n f o r m a l a p p r o a c h
Milliseconds 138 69 92 118 117 92 80 169 139 109 120 84 116 110 62 125 118 112 151 83 138 80 202 126 89
Character s o y o u w i l l s e e h o w t h e y
Milliseconds 211 101 119 136 58 93 70 61 118 169 145 81 95 76 165 53 149 62 56 167 116 162 105 67 131
Character l e a d n a t u r a l l y t o t h e m a i
Milliseconds 140 70 64 67 109 105 76 146 105 95 58 47 160 129 233 267 80 90 88 84 80 70 140 139 86
Character n i d e a o f t h i s c h a p t e r , t
Milliseconds 75 92 138 97 66 78 80 103 102 79 94 68 53 68 107 91 142 231 371 189 107 93 48 87 149
Character h e l i m i t . T h e i d e a o f a l
Milliseconds 75 101 36 112 115 119 109 107 141 158 229 110 98 56 338 109 53 76 98 87 86 93 113 101 105
Character i m i t p l a y s a f o u n d a t i o n a l
Milliseconds 147 141 93 98 126 173 151 68 136 89 87 142 82 109 64 83 150 51 86 169 69 40 109 116 63
Character r o l e t h r o u g h o u t c a l c u l u s
Milliseconds 136 90 122 127 94 107 167 145 85 55 75 221 38 189 47 96 84 161 78 66 151 91 107 277 88
Character .
Milliseconds 167
WPM Timing
Seconds WPM
2.3 83.52
4.6 49.59
6.9 66.12
9.2 78.3
11.49 70.99
13.79 76.56
16.09 74.57
18.39 80.26
20.69 77.14
22.99 78.82
25.29 82.09
27.59 81.78
29.89 84.32
32.18 84.26
34.48 86.3
36.78 86.13
39.08 84.75
41.38 85.55
43.68 84.07
45.98 84.56
48.28 82.28
50.58 83.52
52.87 84.88
55.17 84.17
57.47 83.73
59.77 83.92
62.07 84.29
64.37 85.01
66.67 85.32
68.97 84.21
71.27 84.36
73.56 83.84
75.86 84.78
78.16 85.36
80.46 85.01
82.76 84.97
85.06 85.07
87.36 85.17
89.66 85.53
91.96 86.26
94.25 86.32
96.55 87.12
98.85 87.52
101.15 88.03
103.45 88.51
105.75 88.74
108.05 89.07
110.35 89.5
112.65 90.02
114.94 90.2