rkang13 (rkang13)

Race #187

View Pit Stop page for race #187 by rkang13 — Ghost race

View profile for rkang13 (rkang13)

Official speed 81.85 wpm (126.67 seconds elapsed during race)
Without ending ping 81.91 wpm (89 ms delay sending score to TypeRacer’s server)
Timerless 82.15 wpm (368 ms elapsed before first character typed; 126.21 seconds elapsed during race)
Timerless minus one 82.05 wpm, ignoring the first character typed
Race Start October 27, 2023 7:48:09am UTC
Race Finish October 27, 2023 7:50:16am UTC
Outcome Win (1 of 5)
Opponents 2. shervin123_312 (69.18 wpm)
Accuracy 95.9%
Points 220.99
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 quantiy iity is realtelated to a change in another. How does the speed of a faillin gg object change as a function of time? howHow does the level of water in a barerrl chel rel change as a function of the maaamount of liquid poured into it? We seee chanege occurring tin nearly everything we soobserve in the world an dd universe, and powerrful modenrn instruments help us see more and more. In this section we introduce the ideas ofa v average and instanttaneous reatesates or f chaange, and show taht that they are closely realtelated to the sleop leopope orf a f a curve at ta point P on the curve. We give preceiise developments of these important concepts int he the next chanpter, but for now we suuse an informal apporroach so you will see howht they lead naturally to the main idea of this hcchpater,apter, the lmiimit. The idea of al limit plays a foundational role thoruroughout ocalculous.
Timing
Character C a l c u l u s i s a t o o l t h a t h
Milliseconds 368 222 95 134 101 174 77 197 90 113 212 93 112 104 140 102 129 177 70 80 92 37 45 115 111
Character e l p s u s u n d e r s t a n d h o w a
Milliseconds 113 103 72 105 68 156 119 96 137 68 75 153 51 181 80 103 138 96 95 120 72 111 97 87 64
Character c h a n g e i n o n e q u a n t i y i -i -
Milliseconds 144 27 177 37 158 130 39 155 42 84 198 245 101 96 176 91 124 69 148 45 133 95 142 289 115
Character -y -i i t y i s r e a l t e -e -t -l -a l a t e d
Milliseconds 146 162 383 134 149 111 128 88 142 39 75 40 71 130 96 218 149 117 154 168 33 88 81 182 89
Character t o a c h a n g e i n a n o t h e r . H
Milliseconds 94 46 83 496 113 131 59 87 83 52 124 49 134 48 73 319 60 117 119 53 75 72 104 61 181
Character o w d o e s t h e s p e e d o f a f a
Milliseconds 59 124 72 119 81 79 21 101 131 36 104 88 60 125 138 101 177 94 131 117 78 186 548 124 80
Character i -i l l i n g -g - g o b j e c t c h a n g e
Milliseconds 122 479 241 112 159 44 180 88 288 120 135 62 115 87 217 122 40 175 89 170 40 107 105 92 101
Character a s a f u n c t i o n o f t i m e ? h
Milliseconds 142 106 75 91 106 95 183 129 45 138 129 64 39 176 81 152 127 62 202 64 73 121 191 166 203
Character o w -w -o -h H o w d o e s t h e l e v e l o
Milliseconds 96 143 139 127 136 177 86 111 95 114 78 94 65 74 80 40 107 51 130 20 154 123 87 68 147
Character f w a t e r i n a b a r e r -r -e r l c h
Milliseconds 81 88 70 82 81 119 52 75 121 64 80 96 92 140 128 89 222 345 183 145 112 105 70 145 68
Character -h -c - -l -r e l - -l -e r e l c h a n g e a s
Milliseconds 251 112 249 151 105 101 91 65 182 144 156 120 38 86 64 124 93 79 81 72 81 77 156 63 72
Character a f u n c t i o n o f t h e m a -a a -a -m a
Milliseconds 111 55 103 91 45 72 174 56 45 142 80 104 105 87 82 48 94 56 136 64 322 329 215 136 150
Character m o u n t o f l i q u i d p o u r e d i n
Milliseconds 105 80 79 159 81 105 99 85 72 136 87 185 88 71 178 120 264 300 77 151 151 153 44 100 43
Character t o i t ? W e s e -e e e c h a n e -e g e
Milliseconds 123 72 58 142 98 247 66 198 208 157 132 207 239 257 175 137 120 73 86 80 216 247 105 89 111
Character o c c u r r i n g t -t i n n e a r l y e v e
Milliseconds 113 157 106 136 128 128 137 39 124 204 128 834 206 22 131 455 144 121 96 111 105 79 224 129 151
Character r y t h i n g w e s o -o -s o b s e r v e i n
Milliseconds 54 186 192 62 75 111 80 128 89 78 123 118 113 167 129 200 87 106 95 71 219 94 128 96 59
Character t h e w o r l d a n d -d - d u n i v e r
Milliseconds 83 26 103 21 115 64 129 52 108 87 104 88 66 230 64 326 123 111 89 112 66 158 81 174 89
Character s e , a n d p o w e r r -r f u l m o d e n -n
Milliseconds 112 72 127 41 97 79 96 80 86 74 112 41 111 112 330 125 96 129 96 161 135 79 164 102 243
Character r n i n s t r u m e n t s h e l p u s s e
Milliseconds 148 127 45 139 64 168 73 151 145 201 187 67 153 96 126 227 155 100 78 65 152 111 89 105 183
Character e m o r e a n d m o r e . I n t h i s
Milliseconds 120 129 314 110 96 33 134 81 52 100 52 115 59 53 50 142 80 174 234 72 120 81 48 136 70
Character s e c t i o n w e i n t r o d u c e t h e
Milliseconds 104 44 189 168 79 33 157 66 89 21 171 62 58 87 159 91 289 78 112 64 89 113 50 93 87
Character i d e a s o f a v -v - -a a v e r a g e a n
Milliseconds 87 41 160 73 112 137 110 120 96 73 151 234 141 144 89 52 85 151 55 121 64 80 129 71 72
Character d i n s t a n t t -t a n e o u s r e a t e s -s
Milliseconds 53 163 71 97 147 57 124 176 101 215 267 97 120 114 102 82 163 130 224 82 55 79 112 97 129
Character -e -t -a -e a t e s o r - -r f c h a -a a n g e ,
Milliseconds 119 153 152 135 15 129 72 64 143 162 113 85 289 127 163 59 148 118 129 305 430 72 96 104 106
Character a n d s h o w t a h t t -t -a -h -t - h a t
Milliseconds 51 314 67 110 73 111 81 40 104 111 139 78 25 73 93 45 276 551 0 0 0 82 68 47 107
Character t h e y a r e c l o s e l y r e a l t e -e -t
Milliseconds 170 94 82 88 104 166 85 101 110 184 48 165 46 205 126 116 99 140 71 49 103 73 94 178 120
Character -l -a l a t e d t o t h e s l e o p -l -e -o -p
Milliseconds 151 137 160 13 99 95 168 118 98 65 87 49 111 41 120 192 210 167 62 89 122 671 0 0 0
Character - l e o p -p -o -e o p e o r f a - -a - -f -r f
Milliseconds 0 88 161 30 103 385 130 143 119 72 64 121 176 122 14 67 92 49 215 119 154 150 125 131 90
Character a c u r v e a t t -t a p o i n t P o n
Milliseconds 87 88 112 112 106 142 121 110 146 72 107 91 217 152 89 191 57 183 33 104 127 135 166 163 135
Character t h e c u r v e . W e g i v e p r e c e
Milliseconds 96 65 96 40 106 53 121 53 267 120 88 45 195 312 119 104 89 63 118 114 97 75 51 177 65
Character i -i -e i s e d e v e l o p m e n t s o f t h
Milliseconds 111 224 138 151 96 64 112 224 128 137 136 97 118 64 151 121 80 88 87 112 96 114 102 112 139
Character e s e i m p o r t a n t c o n c e p t s i n
Milliseconds 78 112 96 79 106 39 176 63 43 133 166 82 121 104 127 66 87 121 71 112 71 106 112 104 56
Character t h e - -e -h - -t t h e n e x t c h a n -n
Milliseconds 52 64 84 22 81 247 114 143 135 146 55 136 88 72 80 84 67 150 138 153 111 104 66 118 339
Character p t e r , b u t f o r n o w w e s u -u -s
Milliseconds 158 72 128 65 63 72 507 78 142 89 177 88 167 369 374 62 165 118 129 96 120 127 88 225 136
Character u s e a n i n f o r m a l a p p o r -r -o r o
Milliseconds 136 47 55 103 117 125 72 121 64 68 122 125 65 107 39 81 174 122 127 177 160 190 90 112 80
Character a c h s o y o u w i l l s e e h o w h t
Milliseconds 63 113 79 73 113 60 99 72 48 63 89 303 49 169 128 40 135 191 129 44 140 24 145 199 207
Character -t -h t h e y l e a d n a t u r a l l y t o
Milliseconds 184 155 262 135 234 127 128 128 173 66 75 117 130 166 104 65 183 121 44 123 97 126 90 129 94
Character t h e m a i n i d e a o f t h i s h c
Milliseconds 82 59 88 90 58 147 124 32 64 88 144 104 154 43 134 102 104 78 200 44 71 134 64 232 113
Character -c -h c h p a t e r , -, -r -e -t -a -p a p t e r , t h
Milliseconds 142 122 96 64 129 27 80 164 48 71 145 144 135 159 134 132 145 56 120 135 53 122 54 99 53
Character e l m i -i -m i m i t . T h e i d e a o f
Milliseconds 92 48 96 199 97 263 120 186 39 125 114 87 80 216 105 72 96 95 90 142 55 115 79 121 127
Character a l -l l i m i t p l a y s a f o u n d a t
Milliseconds 48 385 326 152 137 165 24 133 114 101 86 45 35 105 173 98 113 87 97 130 38 183 71 91 71
Character i o n a l r o l e t h o r u -u -r -o r o u g h o
Milliseconds 35 40 134 102 41 95 63 124 133 87 129 129 21 203 103 37 195 144 103 110 59 45 124 88 88
Character u t o -o c a l c u l o -o u s .
Milliseconds 53 90 80 96 512 89 79 73 144 20 100 21 483 264 136 672
WPM Timing
Seconds WPM
2.53 80.52
5.07 99.47
7.6 102.63
10.13 88.81
12.67 82.42
15.2 89.21
17.73 90
20.27 84.67
22.8 87.89
25.33 85.26
27.87 90
30.4 84.08
32.93 84.9
35.47 83.57
38 84
40.53 83.48
43.07 83.59
45.6 81.58
48.13 81.52
50.67 82.66
53.2 83.46
55.74 83.32
58.27 83.41
60.8 85.06
63.34 86.4
65.87 86.17
68.4 85.79
70.94 84.25
73.47 84.12
76 83.37
78.54 82.97
81.07 81.86
83.6 80.24
86.14 80.66
88.67 81.2
91.2 81.31
93.74 82.19
96.27 82.02
98.8 81.86
101.34 81.47
103.87 81.68
106.4 82.44
108.94 81.85
111.47 82.78
114 82.1
116.54 81.76
119.07 81.73
121.6 82.69
124.14 82.65
126.67 81.85