Ty (zjwei)

Race #73

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Official speed 72.70 wpm (142.61 seconds elapsed during race)
Without ending ping 72.81 wpm (224 ms delay sending score to TypeRacer’s server)
Timerless 72.98 wpm (314 ms elapsed before first character typed; 142.08 seconds elapsed during race)
Timerless minus one 72.89 wpm, ignoring the first character typed
Race Start February 9, 2024 1:24:27am UTC
Race Finish February 9, 2024 1:26:49am UTC
Outcome No win (4 of 5)
Accuracy 93.5%
Points 196.29
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 calcCalculus is a tool that helps us understand how a cahnge inhange in one quantity is reallated ot ato a change in another. hHwoow does thes sp speed of a falling ojbject chage =ngenge as a fucmnction of time? How does the leve o l of water in a barreel cahnge hange as a function of the amount of liquid poured into it? We see chagne nge occuring iring in ennearly rebreveveryhthing we objseserve int he the world and universe, and poweruflful modern insturmrruments help us see more and more . In this sectionw e we inotroduce the ideas of average and instantaneuous rates of change, and sho ww taht that theya re are closely related to the slpoeope aof a curve at paa POpoint P on the curve. WEe give precide deise developemenments o ff these important conecepts int he the next chaperter, forbuyt fort nofor nmow weow we suuse an informal apporu=roach so you will see how they lead naturally to the main idea of this chapete,r r,t h , the limit. The heaidea of a limit playd as a foundtaionational role throughout calculauus.
Timing
Character c a l c -c -l -a -c C a l c u l u s i s a t o o
Milliseconds 314 60 75 124 283 135 150 133 283 108 409 435 120 150 274 74 56 68 84 116 61 94 124 17 120
Character l t h a t h e l p s u s u n d e r s t a n
Milliseconds 130 125 17 119 12 59 57 52 89 104 50 55 75 54 109 81 192 4 84 96 112 92 79 82 42
Character d h o w a c a h n g e i n -n -i - -e -g -n -h -a
Milliseconds 106 51 100 101 13 88 51 136 48 115 0 119 14 61 56 39 53 178 249 31 33 37 85 158 136
Character h a n g e i n o n e q u a n t i t y i s
Milliseconds 145 45 74 59 43 40 35 56 209 202 37 65 82 111 60 134 164 185 116 70 182 130 81 101 90
Character r e a l -l -a l a t e d o t a -a - -t -o t o a
Milliseconds 63 45 69 0 329 131 142 78 68 85 89 80 74 27 149 135 176 135 140 123 93 51 106 64 115
Character c h a n g e i n a n o t h e r . h -h H w o -o
Milliseconds 59 115 117 47 92 67 40 28 56 194 100 61 103 72 107 48 43 68 175 215 410 140 112 17 388
Character -w o w d o e s t h e s s p -p -s - -s s p e e
Milliseconds 112 136 95 54 128 42 183 74 76 96 47 64 60 11 140 8 288 148 344 141 121 56 89 84 122
Character d o f a f a l l i n g o j -j b j e c t c
Milliseconds 80 89 50 174 321 59 133 68 67 56 135 198 19 60 64 43 53 322 126 157 88 80 71 64 140
Character h a g e = -= - -e n g e -e -g -n -g n g e a s a
Milliseconds 90 127 403 105 134 228 135 131 121 151 104 60 132 139 144 143 144 54 31 73 75 84 79 91 126
Character f u c m -m -c n c t i o n o f t i m e ? H o w
Milliseconds 88 116 63 113 271 144 241 110 97 62 33 124 99 63 49 95 84 39 46 34 162 230 351 126 93
Character d o e s t h e l e v e o - -o - l o f
Milliseconds 99 99 66 110 63 88 92 30 92 53 76 19 96 85 47 70 185 206 137 118 172 108 86 63 96
Character w a t e r i n a b a r r e e -e l c a h n g
Milliseconds 67 75 76 91 72 50 68 37 160 60 124 165 55 100 106 242 179 524 131 91 28 114 10 141 0
Character e - -e -g -n -h -a h a n g e a s a f u n c t i
Milliseconds 42 87 202 250 33 27 33 116 213 69 72 16 68 78 49 109 44 77 129 68 126 302 90 196 24
Character o n o f t h e a m o u n t o f l i q u i
Milliseconds 41 119 83 55 41 106 104 54 34 112 79 84 156 67 125 25 70 71 75 49 56 125 112 174 53
Character d p o u r e d i n t o i t ? W e s e e
Milliseconds 148 80 112 177 73 150 171 62 80 52 28 122 41 94 165 67 144 211 72 255 108 203 57 107 106
Character c h a g n e - -e -n -g n g e o c c u r i n g i
Milliseconds 66 140 42 104 7 58 135 224 132 145 119 131 49 26 55 145 108 137 103 113 36 38 89 47 99
Character -i - -g -n -i r i n g i n e n -n -e n e a r l y r
Milliseconds 244 154 152 143 394 888 49 29 110 101 289 230 127 101 119 157 131 215 111 29 70 71 120 91 64
Character e b r -r -b -e e v -v -e -r e v e r y h -h t h i n g w
Milliseconds 26 62 130 207 147 141 135 97 198 155 141 151 42 141 63 94 160 309 92 57 71 75 18 100 37
Character e o b j s e -e -s -j s e r v e i n t h e -e -h -
Milliseconds 52 100 94 84 153 74 57 325 139 128 80 13 59 203 86 110 48 47 124 10 66 28 379 141 140
Character -t t h e w o r l d a n d u n i v e r s e ,
Milliseconds 141 120 85 65 85 70 94 67 80 92 106 88 53 98 71 85 74 51 165 234 130 102 61 101 36
Character a n d p o w e r u f l -l -f -u f u l m o d e r
Milliseconds 170 55 133 52 98 263 97 137 59 43 146 19 173 273 139 139 107 32 114 133 58 63 77 64 109
Character n i n s t u r m -m -r r -r -u r u m e n t s h e l
Milliseconds 50 111 100 49 98 57 118 119 152 187 142 166 182 146 99 50 145 78 112 81 63 14 56 165 30
Character p u s s e e m o r e a n d m o r e - .
Milliseconds 18 157 75 51 109 72 50 129 54 70 46 64 31 39 113 121 63 73 73 58 80 62 65 271 154
Character I n t h i s s e c t i o n w e - -e - -w
Milliseconds 178 168 259 137 108 62 40 70 32 131 54 123 104 38 36 114 107 5 60 146 242 149 147 129 130
Character w e i n o -o t r o d u c e t h e i d e a s
Milliseconds 80 43 85 124 26 155 369 48 149 79 135 98 93 96 101 95 73 15 111 56 83 42 53 134 109
Character o f a v e r a g e a n d i n s t a n t a n e
Milliseconds 0 235 155 64 86 145 81 90 93 74 69 90 110 69 70 68 7 88 58 96 176 123 263 361 172
Character u -u o u s r a t e s o f c h a n g e , a n
Milliseconds 168 510 155 58 56 321 395 84 405 64 30 116 106 76 75 111 480 44 101 51 43 92 148 45 126
Character d s h o w -w - w t a h t t -t - -t -h -a h a t
Milliseconds 63 123 106 102 121 171 35 212 155 66 113 55 135 12 63 111 74 245 153 163 125 149 156 86 61
Character t h e y a r e - -e -r - -a a r e c l o s e
Milliseconds 33 124 35 104 68 96 11 43 76 97 207 149 149 133 130 130 82 72 67 85 109 96 145 16 71
Character l y r e l a t e d t o t h e s l p o e -e -o
Milliseconds 80 129 91 86 43 80 95 59 154 75 105 95 61 56 104 74 61 69 380 102 213 0 146 248 152
Character -p o p e a -a o f a c u r v e a t p a -a -p
Milliseconds 130 136 34 70 76 89 405 118 79 77 32 142 107 128 83 262 98 79 101 109 84 90 218 187 123
Character a P O -O -P p o i n t P o n t h e c u r v
Milliseconds 81 88 209 75 357 118 111 23 195 128 70 229 200 189 103 55 205 131 48 58 135 76 146 54 185
Character e . W E -E e g i v e p r e c i d e d e -e -d
Milliseconds 45 88 177 125 57 403 129 98 119 90 183 75 142 91 114 450 195 111 104 69 102 123 73 195 251
Character - -e -d -i i s e d e v e l o p e m -m -e e n -n -e m e
Milliseconds 30 38 31 160 607 116 76 80 90 105 126 74 24 160 41 135 41 380 127 529 117 206 126 165 78
Character n t s o f -f - f t h e s e i m p o r t a n
Milliseconds 81 103 57 27 64 121 245 209 134 50 116 58 136 23 89 108 52 83 9 174 39 73 175 52 112
Character t c o n e -e c e p t s i n t h e - -e -h - -t
Milliseconds 79 108 103 69 31 173 302 87 71 75 116 78 70 60 36 131 36 74 26 144 216 250 33 93 158
Character t h e n e x t c h a p e r -r -e t e r , f o
Milliseconds 155 100 66 31 94 59 48 49 90 91 154 404 64 104 96 43 409 130 128 195 43 139 156 85 94
Character r -r -o -f b u y t f o r -r -o -f - -t -y t n o -o -n f
Milliseconds 49 277 141 139 188 141 0 80 48 128 80 101 333 251 36 135 165 129 120 72 142 135 283 134 91
Character o r n m o w w e -e -w - -w -o -m o w w e s u -u
Milliseconds 79 80 58 63 56 18 54 86 98 85 155 251 35 27 35 34 331 45 88 99 78 101 99 100 233
Character -s u s e a n i n f o r m a l a p p o r u = -=
Milliseconds 132 141 37 23 126 16 8669 172 138 62 235 88 125 35 103 40 101 182 86 119 206 16 113 268 148
Character -u -r -o r o a c h s o y o u w i l l s e e
Milliseconds 139 135 141 114 111 104 45 66 125 28 52 138 115 90 61 43 99 33 143 132 197 116 66 124 118
Character h o w t h e y l e a d n a t u r a l l y t
Milliseconds 73 71 98 56 131 37 93 69 77 95 34 73 97 31 134 73 157 90 198 37 50 135 123 59 104
Character o t h e m a i n i d e a o f t h i s c
Milliseconds 40 114 95 28 98 53 59 84 89 56 75 69 76 70 25 81 32 116 88 111 42 55 43 167 40
Character h a p e -e t e , r - -r -, r , t h -h - -t -, - ,
Milliseconds 105 60 136 95 214 63 101 55 10 175 266 135 138 147 87 126 23 186 378 145 230 173 183 220 110
Character t h e l i m i t . T h e h e a -a -e -h i d e
Milliseconds 207 99 60 88 36 223 184 49 126 102 91 191 134 71 55 69 63 44 76 147 129 154 161 37 38
Character a o f a l i m i t p l a y d a -a - -d s
Milliseconds 42 73 12 117 93 73 95 605 179 18 155 84 91 63 51 48 147 91 162 57 163 140 134 444 112
Character a f o u n d t a i o n -n -o -i -a -t a t i o n a l
Milliseconds 69 347 136 64 57 114 58 185 67 65 35 138 212 117 354 151 147 120 26 75 38 117 66 102 135
Character r o l e t h r o u g h o u t c a l c u l a u -u
Milliseconds 116 48 129 48 62 87 27 110 16 53 77 31 120 66 5 140 81 99 192 189 68 129 154 74 165
Character -a u s .
Milliseconds 124 137 52 326
WPM Timing
Seconds WPM
2.85 25.24
5.7 82.04
8.56 82.74
11.41 85.2
14.26 87.51
17.11 84.14
19.97 81.74
22.82 78.88
25.67 76.66
28.52 81.62
31.37 82.23
34.23 80.29
37.08 84.14
39.93 85.65
42.78 83.3
45.64 80.2
48.49 78.45
51.34 78.53
54.19 78.83
57.05 79.31
59.9 79.54
62.75 81.27
65.6 80.85
68.45 82.92
71.31 82.12
74.16 82.69
77.01 81.49
79.86 81.59
82.72 80.81
85.57 80.36
88.42 80.75
91.27 79.8
94.12 78.79
96.98 78.33
99.83 78.61
102.68 78.18
105.53 76.75
108.39 75.73
111.24 74.76
114.09 72.89
116.94 71.11
119.8 70.82
122.65 70.93
125.5 72.48
128.35 73.3
131.2 72.35
134.06 72.69
136.91 72.4
139.76 72.29
142.61 72.7