Rawneedee (rawneedee)

Race #251

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Official speed 80.05 wpm (129.52 seconds elapsed during race)
Without ending ping 80.09 wpm (61 ms delay sending score to TypeRacer’s server)
Timerless 80.34 wpm (414 ms elapsed before first character typed; 129.04 seconds elapsed during race)
Timerless minus one 80.25 wpm, ignoring the first character typed
Race Start October 14, 2023 10:40:36pm UTC
Race Finish October 14, 2023 10:42:46pm UTC
Outcome No win (3 of 5)
Opponents 1. zak389 (90.33 wpm)
Accuracy 96.8%
Points 216.13
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 one quantity is related to a change in another. How does the seepeed of a falling object change as a function of time? Ho ww does the level of water in a pbarrel change as a function of the amount of liquid poured into it? We se ee change occuring rirring in nearly everything we observe in the world and unicverse, and wpower fful modern instruments help us tsee more and moerre. AInl thi hithis section we introduce the idead ofs of average and instantaneious rates of change, and show that hteythey are vclosely related intto the slope of a curve at tha point P on the curve. We give precise developments of these improortant concepts in the next chapetter, but for now we use an informal arpproach so you will see how the yy lead naturally to the main idea of this chapter, the limmiit . The idea of a limit plays a vfiououndational role throughout calcusllus.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 414 191 154 135 187 262 185 105 108 119 85 101 112 98 134 134 115 149 107 95 83 53 63 72 67
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 328 135 164 68 133 135 97 100 186 149 86 136 79 116 115 108 145 86 80 106 74 91 126 88 112
Character c h a n g e i n o n e q u a n t i t y i s
Milliseconds 218 137 132 82 120 143 89 114 87 47 230 91 120 77 347 127 158 122 114 166 120 174 129 172 91
Character r e l a t e d t o a c h a n g e i n a
Milliseconds 99 195 119 116 120 80 84 186 63 107 79 78 120 115 242 109 106 110 119 200 114 133 97 70 139
Character n o t h e r . H o w d o e s t h e s e e -e
Milliseconds 129 117 83 103 40 87 178 141 218 118 132 102 184 94 123 166 78 89 84 86 64 132 147 168 263
Character -e p e e d o f a f a l l i n g o b j e c t
Milliseconds 136 182 123 130 213 121 46 419 199 215 134 151 163 121 115 153 132 132 68 268 232 138 126 187 148
Character c h a n g e a s a f u n c t i o n o f
Milliseconds 70 177 76 80 135 67 198 152 145 126 90 115 140 150 142 154 104 144 90 89 64 79 132 100 101
Character t i m e ? H o w -w - w d o e s t h e l e
Milliseconds 130 104 103 113 213 235 240 157 118 465 123 148 139 130 165 66 104 97 84 81 79 43 63 82 73
Character v e l o f w a t e r i n a p -p b a r r e
Milliseconds 199 166 215 110 121 95 91 78 122 94 104 78 75 146 133 64 200 123 160 252 64 203 183 168 104
Character l c h a n g e a s a f u n c t i o n o f
Milliseconds 143 137 415 118 66 134 46 254 102 97 132 108 63 95 121 94 153 59 166 124 107 81 96 200 89
Character t h e a m o u n t o f l i q u i d p o u
Milliseconds 108 105 35 55 112 132 133 166 116 140 95 73 125 90 62 102 133 214 124 247 510 119 122 168 173
Character r e d i n t o i t ? W e s e e -e - e c
Milliseconds 102 124 161 71 81 79 89 129 150 163 139 202 167 184 160 105 132 149 163 87 180 117 108 97 165
Character h a n g e o c c u r i n g - -g -n -i -r r i -i -r r
Milliseconds 95 74 130 19 338 129 366 234 148 98 104 106 109 50 105 233 117 111 216 79 106 169 248 119 162
Character r i n g i n n e a r l y e v e r y t h i n g
Milliseconds 222 168 96 89 111 154 92 70 130 104 116 101 133 149 70 113 182 119 98 106 125 87 82 103 81
Character w e o b s e r v e i n t h e w o r l d
Milliseconds 84 99 121 95 171 117 146 132 91 210 133 103 134 100 64 270 129 72 80 106 79 95 119 101 101
Character a n d u n i c -c v e r s e , a n d w -w p o w
Milliseconds 116 97 71 50 246 153 113 137 239 96 145 86 135 163 149 89 111 133 92 96 166 250 168 178 87
Character e r f -f - f u l m o d e r n i n s t r u m e
Milliseconds 51 114 92 122 220 136 113 104 150 130 136 150 362 172 81 123 92 101 84 134 112 308 141 185 133
Character n t s h e l p u s t -t s e e m o r e a n
Milliseconds 92 110 108 95 116 106 128 136 111 119 113 120 113 253 68 179 140 128 452 132 87 113 121 181 248
Character d m o e r -r -e r e . A -A I n l t h i -i -h -t -
Milliseconds 118 97 103 135 68 95 382 120 97 86 123 173 244 293 262 140 152 15 115 71 95 239 94 116 102
Character -l h i -i -h t h i s s e c t i o n w e i n t
Milliseconds 399 153 163 116 209 127 121 108 121 115 101 81 157 167 130 68 62 87 51 88 127 94 122 97 38
Character r o d u c e t h e i d e a d o f -f -o - -d s
Milliseconds 130 88 112 132 81 170 265 158 116 62 64 169 99 171 64 133 91 131 130 218 113 118 200 232 133
Character o f a v e r a g e a n d i n s t a n t a n e
Milliseconds 131 120 89 112 196 140 93 135 107 114 86 96 99 101 62 152 103 99 149 90 142 122 176 184 149
Character i -i o u s r a t e s o f c h a n g e , a n
Milliseconds 199 260 328 183 112 105 103 127 107 97 202 98 154 79 79 186 99 92 113 44 369 141 107 203 121
Character d s h o w t h a t h t e y -y -e -t -h t h e y
Milliseconds 107 56 219 80 89 79 148 117 102 62 50 103 167 66 122 95 232 119 104 109 92 96 82 118 105
Character a r e v -v c l o s e l y r e l a t e d i n -n
Milliseconds 159 86 89 93 139 248 129 118 168 47 318 155 199 97 196 92 127 137 109 75 194 83 168 90 189
Character t -t -i t o t h e s l o p e o f a c u r v
Milliseconds 88 155 119 109 101 117 78 91 49 72 111 81 181 124 134 96 110 106 88 99 101 145 199 136 199
Character e a t t h -h -t a p o i n t P o n t h e
Milliseconds 105 113 199 135 80 107 125 272 119 145 117 163 152 121 79 105 79 155 129 234 183 106 147 132 65
Character c u r v e . W e g i v e p r e c i s e d
Milliseconds 83 301 90 94 231 149 185 122 210 265 0 129 93 97 132 90 63 183 462 402 233 34 169 99 199
Character e v e l o p m e n t s o f t h e s e i m p r
Milliseconds 172 148 95 101 167 151 201 128 172 162 155 102 132 69 114 148 81 85 114 168 202 255 213 253 182
Character o -o -r o r t a n t c o n c e p t s i n t h e
Milliseconds 79 336 118 177 118 169 104 100 86 64 153 47 79 83 201 87 111 120 117 104 82 65 132 107 76
Character n e x t c h a p e t -t -e t e r , b u t f o
Milliseconds 67 94 91 168 143 103 187 111 89 133 98 150 297 116 68 85 94 93 124 138 79 105 63 125 77
Character r n o w w e u s e a n i n f o r m a l
Milliseconds 90 95 148 91 48 124 141 131 82 150 97 140 59 106 201 126 183 76 80 121 92 91 81 116 95
Character a r -r p p r o a c h s o y o u w i l l s e
Milliseconds 292 175 238 169 136 143 49 214 138 112 134 367 121 106 112 94 106 94 135 155 146 129 76 80 166
Character e h o w t h e y -y - y l e a d n a t u r
Milliseconds 129 87 99 68 162 177 246 65 118 97 198 188 119 154 92 139 108 89 122 72 154 101 89 158 82
Character a l l y t o t h e m a i n i d e a o f
Milliseconds 165 155 103 137 63 153 79 114 68 97 57 76 85 88 104 48 64 179 76 176 79 121 154 133 81
Character t h i s c h a p t e r , t h e l i m m i -i -m
Milliseconds 115 68 65 87 97 134 97 105 101 83 119 97 151 109 105 91 94 66 443 156 166 134 83 249 117
Character i t - . T h e i d e a o f a l i m i t
Milliseconds 169 65 120 293 188 110 177 113 103 81 231 73 190 85 118 168 130 82 151 136 215 123 120 142 105
Character p l a y s a v -v f i o u -u -o -i o u n d a t i
Milliseconds 97 116 164 89 127 120 113 67 137 380 270 80 450 55 32 351 129 219 370 112 139 29 113 119 90
Character o n a l r o l e t h r o u g h o u t c a l c
Milliseconds 81 79 135 104 123 156 101 147 152 83 146 92 95 65 87 61 91 280 182 107 97 180 115 120 118
Character u s l -l -s l u s .
Milliseconds 143 136 106 197 116 163 107 81 114
WPM Timing
Seconds WPM
2.59 74.12
5.18 88.02
7.77 94.19
10.36 91.49
12.95 93.58
15.54 94.19
18.13 88.02
20.72 88.02
23.31 89.56
25.9 86.63
28.49 88.44
31.08 86.47
33.67 88.37
36.27 87.69
38.86 87.4
41.45 85.7
44.04 82.3
46.63 83.9
49.22 84.85
51.81 84.54
54.4 83.16
56.99 83.81
59.58 82.98
62.17 81.46
64.76 79.12
67.35 80.18
69.94 79.27
72.53 79.91
75.12 79.55
77.71 80.14
80.3 79.35
82.89 78.75
85.48 79.45
88.07 79.16
90.66 79.28
93.25 79.01
95.84 79.25
98.43 78.87
101.02 79.35
103.62 79.8
106.21 79.77
108.8 80.08
111.39 79.83
113.98 80.75
116.57 81.43
119.16 80.57
121.75 80.82
124.34 79.81
126.93 80.17
129.52 80.05