Chris (chris_p)

Race #13883

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Official speed 73.64 wpm (140.79 seconds elapsed during race)
Without ending ping 73.76 wpm (225 ms delay sending score to TypeRacer’s server)
Timerless 75.29 wpm (2,859 ms elapsed before first character typed; 137.71 seconds elapsed during race)
Timerless minus one 75.20 wpm, ignoring the first character typed
Race Start April 26, 2024 12:08:13pm UTC
Race Finish April 26, 2024 12:10:33pm UTC
Outcome No win (2 of 3)
Accuracy 97.7%
Points 198.82
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 oe ne quantitiyy is related to a change in another. How does the speed of a falling object change as a function of time? How does the leve ll of water in a gbarrel change as a faunction of theam amount of liquied poured into it? We see change occurinring 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 instantanoueous sreatates of change, and show that they are closely related to the lsslepope of a curve at a point P aon the curve. We give precise developments of these important concepts in the next chapter, but for now ewwe use an informal approach so you wil lsel see how they lead naturally to the amain idea of theis chapter, the limit. The idea of a limit plays fa fonundational role throughout calculus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 2859 186 142 634 111 188 101 186 133 145 66 120 231 127 111 124 165 242 109 160 75 74 75 32 239
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 87 112 163 16 258 377 100 107 257 227 15 185 52 124 123 87 109 99 84 167 91 59 71 145 90
Character c h a n g e i n o e - -e n e q u a n t i t
Milliseconds 166 96 120 79 150 123 105 174 100 132 90 165 463 234 158 347 69 232 493 81 197 165 131 120 121
Character i y -y -i y i s r e l a t e d t o a c h a
Milliseconds 89 180 336 108 366 134 116 109 75 129 55 174 159 79 112 211 128 137 100 49 232 122 145 100 168
Character n g e i n a n o t h e r . H o w d o e s
Milliseconds 236 166 35 247 171 80 145 91 77 80 275 165 47 73 228 66 319 194 124 109 175 84 124 61 127
Character t h e s p e e d o f a f a l l i n g o b
Milliseconds 181 119 66 90 134 99 117 159 154 79 127 114 83 167 109 442 116 132 145 87 86 82 88 163 130
Character j e c t c h a n g e a s a f u n c t i o n
Milliseconds 153 120 196 150 137 325 0 136 75 123 73 152 267 99 110 173 18 271 196 199 34 165 50 84 30
Character o f t i m e ? H o w d o e s t h e l e
Milliseconds 155 116 137 29 165 70 91 62 247 124 204 221 179 139 133 135 101 72 108 198 53 77 92 93 86
Character v e l -l - l o f w a t e r i n a g -g b
Milliseconds 137 98 168 27 420 134 255 101 180 79 142 318 230 100 102 127 90 184 81 151 122 178 148 434 118
Character a r r e l c h a n g e a s a f a -a u n c t
Milliseconds 168 149 214 83 122 127 320 70 115 102 62 83 116 162 138 118 127 89 200 112 627 415 217 69 131
Character i o n o f t h e a m -m -a a m o u n t o f
Milliseconds 91 75 36 232 149 293 193 82 101 52 292 91 536 298 276 243 115 133 111 222 79 96 187 84 50
Character l i q u i e -e d p o u r e d i n t o i t ?
Milliseconds 119 111 432 71 118 84 437 74 509 517 93 475 126 243 169 82 140 74 62 120 101 181 93 306 107
Character W e s e e c h a n g e o c c u r i n -n -i r i
Milliseconds 277 139 165 248 81 219 161 108 134 98 148 88 98 127 235 158 212 111 60 163 71 378 413 108 116
Character n g i n n e a r l y e v e r y t h i n g w
Milliseconds 87 91 185 168 54 102 146 48 129 105 183 85 106 265 198 184 93 133 57 163 104 118 331 159 229
Character e o b s e r v e i n t h e w o r l d a n
Milliseconds 93 168 251 118 364 102 136 250 112 129 170 74 134 127 109 54 72 128 77 118 100 78 129 156 96
Character d u n i v e r s e , a n d p o w e r f u l
Milliseconds 105 0 426 205 117 70 163 63 140 79 370 113 185 83 70 71 132 91 224 35 63 184 71 177 230
Character m o d e r n i n s t r u m e n t s h e l p u
Milliseconds 184 90 79 167 51 120 162 205 80 235 83 184 122 211 99 74 80 130 180 538 103 52 161 132 135
Character s s e e m o r e a n d m o r e . I n t
Milliseconds 107 111 188 95 180 103 151 89 40 103 96 174 98 99 13 145 64 64 36 180 94 169 260 125 206
Character h i s s e c t i o n w e i n t r o d u c e
Milliseconds 144 72 34 182 154 40 241 135 81 102 26 222 112 31 211 156 92 186 173 127 328 80 114 151 108
Character t h e i d e a s o f a v e r a g e a n d
Milliseconds 268 83 61 87 114 366 135 82 155 118 158 104 96 299 261 128 96 122 119 103 113 171 114 82 32
Character i n s t a n t a n o u -u -o e o u s s -s r e a t -t
Milliseconds 137 96 156 197 120 344 198 253 165 240 82 462 120 155 101 70 244 108 224 299 76 78 280 53 280
Character -a -e a t e s o f c h a n g e , a n d s h o
Milliseconds 138 126 87 52 99 296 135 129 74 63 256 34 145 69 46 113 152 82 186 56 150 47 160 43 86
Character w t h a t t h e y a r e c l o s e l y r
Milliseconds 83 131 196 57 63 87 65 250 65 209 123 468 121 49 68 363 418 168 167 131 92 106 90 112 316
Character e l a t e d t o t h e l s -s -l s l e p -p -e o
Milliseconds 49 139 100 84 109 213 94 168 64 102 310 73 83 108 155 70 434 136 146 96 178 157 403 121 227
Character p e o f a c u r v e a t a p o i n t
Milliseconds 166 135 82 205 97 161 132 95 140 103 113 221 102 117 189 140 124 126 182 170 120 100 122 80 369
Character P a -a o n t h e c u r v e . W e g i v e
Milliseconds 202 316 89 323 218 98 89 96 126 42 111 125 101 101 308 100 109 147 469 196 104 114 143 137 120
Character p r e c i s e d e v e l o p m e n t s o f
Milliseconds 103 234 114 102 297 104 165 150 220 215 159 168 91 157 377 196 219 217 247 119 130 122 149 129 102
Character t h e s e i m p o r t a n t c o n c e p t s
Milliseconds 105 49 94 219 86 151 263 69 200 45 204 170 300 148 103 133 332 165 88 200 181 117 116 143 144
Character i n t h e n e x t c h a p t e r , b u t
Milliseconds 200 79 98 71 164 47 108 130 86 213 88 140 441 117 113 139 96 104 118 131 92 193 77 115 84
Character f o r n o w e w -w -e w e u s e a n i n f
Milliseconds 258 83 95 33 138 115 21 215 141 76 445 136 110 58 96 322 81 84 96 223 73 121 152 136 187
Character o r m a l a p p r o a c h s o y o u w i l
Milliseconds 141 68 423 108 75 115 231 54 181 103 152 166 298 63 172 302 116 94 172 118 131 66 200 83 154
Character l s e -e -s -l - l s e e h o w t h e y l e
Milliseconds 179 34 134 50 312 141 128 129 307 137 131 49 182 88 134 83 112 53 475 93 50 148 70 116 151
Character a d n a t u r a l l y t o t h e a -a m a i
Milliseconds 133 116 103 279 51 86 156 124 180 165 173 98 105 171 96 72 275 115 67 86 210 414 573 100 83
Character n i d e a o f t h e -e i s c h a p t e r ,
Milliseconds 73 141 188 119 196 51 182 91 94 111 92 100 111 431 205 72 61 167 70 103 149 126 64 120 156
Character t h e l i m i t . T h e i d e a o f a
Milliseconds 83 146 53 100 34 117 63 135 187 64 264 74 332 116 78 90 117 157 161 114 151 161 91 76 168
Character l i m i t p l a y s f -f a f o n -n u n d a
Milliseconds 79 111 114 113 155 75 173 100 113 136 155 131 116 231 483 119 104 227 103 201 304 226 232 147 160
Character t i o n a l r o l e t h r o u g h o u t c a
Milliseconds 124 159 81 119 161 97 94 201 93 149 71 47 307 144 119 87 67 81 148 585 51 76 107 152 152
Character l c u l u s .
Milliseconds 100 314 575 154 168 183 139
WPM Timing
Seconds WPM
2.82 0
5.63 36.22
8.45 51.14
11.26 64.99
14.08 59.66
16.9 60.37
19.71 64.53
22.53 67.65
25.34 69.61
28.16 72.02
30.97 74.38
33.79 72.8
36.61 72.45
39.42 72.14
42.24 69.61
45.05 69.52
47.87 69.19
50.69 69.61
53.5 69.31
56.32 69.46
59.13 70.62
61.95 71.48
64.76 72.08
67.58 72.8
70.4 73.81
73.21 74.41
76.03 74.66
78.84 73.66
81.66 72.74
84.48 74.01
87.29 73.68
90.11 73.51
92.92 73.09
95.74 72.82
98.56 73.06
101.37 72.92
104.19 73.14
107 73.12
109.82 73.54
112.63 73.51
115.45 73.69
118.27 73.36
121.08 73.44
123.9 73.61
126.71 73.39
129.53 73.84
132.35 74.26
135.16 73.69
137.98 74.01
140.79 73.64