Jake (bluewater800)

Race #1698

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Official speed 82.43 wpm (125.78 seconds elapsed during race)
Without ending ping 82.55 wpm (187 ms delay sending score to TypeRacer’s server)
Timerless 82.80 wpm (370 ms elapsed before first character typed; 125.22 seconds elapsed during race)
Timerless minus one 82.70 wpm, ignoring the first character typed
Race Start October 3, 2023 4:51:01pm UTC
Race Finish October 3, 2023 4:53:07pm UTC
Outcome Win (1 of 5)
Opponents 5. a_fl_1204 (68.31 wpm)
Accuracy 98.7%
Points 222.57
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 helpsu 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 ina a barrel change a s a function of the amount of liquid poirured into it? We see change occuring ring in heanearly everythin g we ibobserve in the world and universe, and powerful modern instruments help us see more and more. In this section we introduce the diideas of average and instantaneous rates of change, and show that they are closely related to the slopde of a curve at a point p P on the curve. We give precise developments of these important concepts in the next chapter, but for now we use an infomrrmal 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 o l t h a t h
Milliseconds 370 184 118 199 173 210 204 96 85 181 69 72 129 112 149 36 159 190 142 129 90 103 148 91 216
Character e l p s u -u u s u n d e r s t a n d h o w
Milliseconds 188 91 207 352 141 309 116 105 112 114 179 163 74 184 152 171 171 161 120 79 37 170 60 44 73
Character a c h a n g e i n o n e q u a n t i t y
Milliseconds 149 103 173 61 111 115 87 184 83 89 56 137 116 190 77 67 280 181 217 109 153 109 129 291 84
Character i s r e l a t e d t o a c h a n g e i n
Milliseconds 206 98 64 174 171 93 109 183 186 156 92 153 26 233 184 128 193 120 85 110 105 182 100 51 84
Character a n o t h e r . H o w d o e s t h e s p
Milliseconds 90 168 57 82 124 117 104 139 90 100 230 202 66 109 159 88 92 191 128 169 95 95 77 168 80
Character e e d o f a f a l l i n g o b j e c t c
Milliseconds 117 128 159 93 143 43 26 180 69 204 75 106 187 148 64 46 86 182 251 234 220 193 182 80 162
Character h a n g e a s a f u n c t i o n o f t i
Milliseconds 75 100 106 83 178 84 146 90 103 139 124 173 134 138 178 197 20 52 83 107 167 45 96 123 32
Character m e ? H o w d o e s t h e l e v e l o f
Milliseconds 184 96 254 195 339 260 53 95 167 107 85 172 97 194 92 95 92 242 106 217 209 94 103 168 34
Character w a t e r i n a - -a a b a r r e l c h
Milliseconds 87 156 61 193 188 155 86 116 63 144 160 302 142 98 138 73 129 127 152 157 149 74 97 182 66
Character a n g e a - s a f u n c t i o n o f t
Milliseconds 91 110 91 193 91 143 150 394 156 95 118 103 192 77 172 175 180 25 52 83 121 158 40 88 125
Character h e a m o u n t o f l i q u i d p o i r -r
Milliseconds 82 82 94 137 41 74 208 88 93 84 110 74 86 154 143 218 124 54 215 114 605 186 352 329 177
Character -i u r e d i n t o i t ? W e s e e c h a
Milliseconds 156 212 146 230 159 88 98 56 127 119 101 177 95 257 194 185 144 81 166 185 124 172 187 247 76
Character n g e o c c u r i n g - -g -n -i r i n g i n
Milliseconds 125 79 193 95 150 117 135 161 99 132 86 64 98 214 161 148 94 167 117 60 78 90 166 80 175
Character h e a -a -e -h n e a r l y e v e r y t h i n - g
Milliseconds 126 88 101 202 160 126 175 119 109 165 107 173 64 154 206 69 181 210 201 115 38 160 210 450 328
Character w e i b -b -i o b s e r v e i n t h e w o
Milliseconds 266 206 85 203 367 133 310 143 186 113 291 183 171 177 167 90 49 54 127 162 72 98 83 134 122
Character r l d a n d u n i v e r s e , a n d p o w
Milliseconds 134 126 115 86 143 90 92 93 461 184 115 145 230 163 181 139 91 156 186 160 67 72 137 98 95
Character e r f u l m o d e r n i n s t r u m e n t s
Milliseconds 116 196 176 16 181 92 256 107 172 358 170 107 107 248 192 117 167 255 93 249 139 102 126 199 87
Character h e l p u s s e e m o r e a n d m o r e
Milliseconds 153 244 199 157 157 151 75 97 134 173 136 83 124 55 95 145 79 136 104 125 82 133 79 141 161
Character . I n t h i s s e c t i o n w e i n t r
Milliseconds 58 131 196 203 64 154 61 67 104 91 151 177 176 168 52 51 83 133 143 70 90 158 79 124 168
Character o d u c e t h e d i -i -d i d e a s o f a v
Milliseconds 106 332 116 111 173 93 113 76 99 82 186 118 312 146 177 63 179 75 189 197 148 85 97 293 202
Character e r a g e a n d i n s t a n t a n e o u s r
Milliseconds 202 165 86 205 187 89 134 112 64 74 297 66 193 191 270 252 170 358 145 259 114 177 124 99 215
Character a t e s o f c h a n g e , a n d s h o w
Milliseconds 162 192 181 193 111 142 46 81 157 92 84 110 91 187 66 106 144 78 86 68 229 87 59 73 87
Character t h a t t h e y a r e c l o s e l y r e l
Milliseconds 206 74 109 188 65 121 67 109 190 74 165 108 189 84 163 70 196 91 214 95 189 80 191 194 102
Character a t e d t o t h e s l o p d -d e o f a
Milliseconds 113 171 191 144 87 155 65 96 143 32 169 81 197 97 196 176 223 432 120 75 211 96 69 134 95
Character c u r v e a t a p o i n t p - -p P o n
Milliseconds 166 147 115 207 206 94 130 179 76 133 91 182 158 256 87 123 69 193 291 164 158 198 275 187 179
Character t h e c u r v e . W e g i v e p r e c i
Milliseconds 63 136 74 96 86 154 134 69 203 174 41 194 207 101 136 185 112 88 169 86 165 83 151 179 81
Character s e d e v e l o p m e n t s o f t h e s e
Milliseconds 130 149 82 152 162 189 178 224 285 103 239 409 198 106 193 106 48 112 99 142 51 185 190 74 100
Character i m p o r t a n t c o n c e p t s i n t h e
Milliseconds 79 135 110 150 200 204 164 87 89 123 214 74 173 98 201 89 123 197 88 50 62 161 190 100 86
Character n e x t c h a p t e r , b u t f o r n o
Milliseconds 90 106 68 202 229 82 196 134 127 121 172 197 154 96 157 175 66 140 89 137 103 102 93 115 70
Character w w e u s e a n i n f o m r -r -m r m a l
Milliseconds 67 84 150 106 104 195 83 159 87 169 93 80 177 73 232 103 143 45 340 148 119 71 146 48 112
Character a p p r o a c h s o y o u w i l l s e e
Milliseconds 174 62 158 143 137 104 159 109 94 201 254 122 150 57 164 83 154 57 111 142 85 144 241 154 88
Character h o w t h e y l e a d n a t u r a l l y t
Milliseconds 132 70 51 65 195 145 91 173 62 127 80 80 167 101 164 80 154 77 163 66 108 150 83 54 165
Character o t h e m a i n i d e a o f t h i s c
Milliseconds 56 152 141 89 109 82 181 132 99 66 81 210 39 198 64 176 215 108 99 139 54 62 126 83 163
Character h a p t e r , t h e l i m i t . T h e i d
Milliseconds 98 97 120 218 189 131 87 94 133 55 119 93 148 184 202 114 147 131 120 208 443 115 98 198 75
Character e a o f a l i m i t p l a y s a f o u
Milliseconds 183 71 209 148 81 89 156 86 159 139 210 141 84 69 138 133 64 243 244 96 141 100 228 101 188
Character n d a t i o n a l r o l e t h r o u g h o u t
Milliseconds 123 101 166 199 33 73 53 113 133 332 243 78 184 90 78 157 357 158 101 164 130 85 193 187 75
Character c a l c u l u s .
Milliseconds 90 155 73 98 219 81 199 188 161 81
WPM Timing
Seconds WPM
2.52 76.32
5.03 69.17
7.55 79.5
10.06 82.29
12.58 83
15.09 85.86
17.61 88.59
20.12 87.65
22.64 89.04
25.16 88.73
27.67 88.47
30.19 87.45
32.7 86.6
35.22 88.25
37.73 84.27
40.25 84.37
42.76 83.34
45.28 81.36
47.8 80.59
50.31 78.23
52.83 79.28
55.34 78.93
57.86 79.02
60.37 78.71
62.89 79.57
65.41 80.54
67.92 80.03
70.44 79.73
72.95 79.45
75.47 79.66
77.98 80.48
80.5 80.65
83.01 80.23
85.53 80.53
88.05 79.73
90.56 80.17
93.08 79.81
95.59 80.09
98.11 80.48
100.62 80.62
103.14 81.09
105.65 80.98
108.17 81.32
110.69 81.85
113.2 82.26
115.72 82.44
118.23 82.41
120.75 82.39
123.26 82.36
125.78 82.43