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Race #5

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Official speed 85.85 wpm (120.77 seconds elapsed during race)
Without ending ping 86.03 wpm (248 ms delay sending score to TypeRacer’s server)
Timerless 86.31 wpm (396 ms elapsed before first character typed; 120.13 seconds elapsed during race)
Timerless minus one 86.21 wpm, ignoring the first character typed
Race Start March 27, 2025 4:56:29pm UTC
Race Finish March 27, 2025 4:58:30pm UTC
Outcome No win (1 of 1)
Accuracy 98.8%
Points 231.80
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 tol thol that helps us understand how a change in one quanity ttity 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? Wee see change occurring in nearly neeverything 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 averages and and instanteaneous rates of change, and nshow that they are closely related to the slope of a curve at a point P on the cursve. We give precise developments of these important concetspts in the next chapter, but for now we use an inforrmal approach so you will see how they lead naturally to the main idea of the chis 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 l t h -h -t - -l o
Milliseconds 396 153 109 471 143 236 240 81 109 86 142 80 103 91 133 211 200 123 67 71 237 210 220 193 52
Character l t h a t h e l p s u s u n d e r s t a n
Milliseconds 222 98 97 71 160 73 87 145 214 34 63 91 94 126 110 51 183 133 78 135 78 145 98 86 95
Character d h o w a c h a n g e i n o n e q u a
Milliseconds 66 101 100 86 87 95 99 117 105 98 26 267 89 64 169 130 94 110 332 160 26 121 43 122 162
Character n i t y - -y -t t -t -i t i t y i s r e l a t e
Milliseconds 67 302 0 50 201 315 175 393 283 278 176 209 43 160 112 326 146 98 79 84 59 108 108 108 77
Character d t o a c h a n g e i n a n o t h e r .
Milliseconds 161 45 184 105 103 130 138 105 224 132 104 74 127 111 115 88 54 90 127 176 133 73 192 57 111
Character H o w d o e s t h e s p e e d o f a
Milliseconds 65 215 145 105 38 253 186 56 56 89 113 91 121 91 107 102 97 175 151 79 136 43 102 88 119
Character f a l l i n g o b j e c t c h a n g e a s
Milliseconds 109 79 93 212 149 57 56 110 47 154 129 54 157 208 144 91 136 98 144 87 96 135 106 104 86
Character a f u n c t i o n o f t i m e ? H o w d
Milliseconds 119 105 162 130 109 112 207 57 73 79 133 109 108 91 130 60 57 96 280 135 423 188 56 82 175
Character o e s t h e l e v e l o f w a t e r i n
Milliseconds 145 82 18 180 84 148 60 144 208 144 153 64 89 91 158 78 72 107 119 159 112 95 134 390 27
Character a b a r r e l c h a n g e a s a f u n
Milliseconds 168 72 132 101 156 88 183 246 110 151 181 76 121 125 69 38 130 65 92 96 130 85 155 94 105
Character c t i o n o f t h e a m o u n t o f l i
Milliseconds 120 230 65 57 95 128 150 75 91 136 82 152 118 86 76 139 154 94 119 186 143 101 65 91 232
Character q u i d p o u r e d i n t o i t ? W e e -e
Milliseconds 121 126 71 137 63 161 136 270 130 63 180 76 127 90 124 108 119 160 120 285 117 145 219 229 342
Character s e e c h a n g e o c c u r r i n g i n
Milliseconds 113 151 211 172 119 265 94 58 135 59 107 77 63 151 181 102 141 402 166 75 69 152 88 80 95
Character n e a r l y n e -e -n e v e r y t h i n g w e
Milliseconds 318 63 52 104 95 123 150 64 96 159 199 172 187 103 132 296 273 57 105 110 41 159 157 58 80
Character o b s e r v e i n t h e w o r l d a n d
Milliseconds 362 175 214 178 76 221 95 105 63 79 97 100 78 165 186 102 121 147 149 105 95 116 75 113 55
Character u n i v e r s e , a n d p o w e r f u l m o
Milliseconds 146 134 178 81 173 64 151 180 294 129 102 74 102 73 92 75 174 189 101 224 41 233 115 132 82
Character d e r n i n s t r u m e n t s h e l p u s
Milliseconds 182 218 54 138 133 114 70 179 179 68 102 200 152 80 135 137 81 181 155 113 64 110 129 131 84
Character s e e m o r e a n d m o r e . I n t h i
Milliseconds 145 185 188 92 110 92 44 56 105 96 151 89 191 136 81 39 66 163 116 159 182 102 110 87 136
Character s s e c t i o n w e i n t r o d u c e t h
Milliseconds 112 104 109 189 333 193 85 59 63 178 270 83 99 125 124 238 85 431 220 410 107 95 88 121 71
Character e i d e a s o f a v e r a g e s a n d -d -n
Milliseconds 116 84 164 51 105 32 180 118 131 90 89 199 158 117 98 103 125 97 193 103 97 125 159 354 213
Character -a - -s a n d i n s t a n t e -e a n e o u s r
Milliseconds 206 181 199 181 91 105 136 120 253 108 538 190 88 174 64 153 385 167 78 213 85 66 111 88 171
Character a t e s o f c h a n g e , a n d n -n s h o
Milliseconds 79 122 78 166 95 121 61 94 118 121 75 172 174 0 208 57 74 117 97 72 102 317 141 169 110
Character w t h a t t h e y a r e c l o s e l y r
Milliseconds 63 88 109 96 43 81 78 121 106 62 91 126 61 83 88 65 146 73 99 80 185 99 115 122 97
Character e l a t e d t o t h e s l o p e o f a
Milliseconds 97 121 116 104 95 181 76 123 101 85 99 88 169 95 147 117 235 64 93 80 152 136 140 117 115
Character c u r v e a t a p o i n t P o n t h e
Milliseconds 125 135 81 502 92 125 124 88 132 64 136 224 246 94 68 98 118 147 121 140 144 170 310 73 288
Character c u r s -s v e . W e g i v e p r e c i s e
Milliseconds 178 101 104 90 102 249 200 74 61 166 202 233 89 109 93 122 28 124 102 71 47 232 148 69 239
Character d e v e l o p m e n t s o f t h e s e i m
Milliseconds 170 169 136 168 82 91 212 68 294 120 116 87 135 103 109 31 99 90 88 173 194 162 71 108 123
Character p o r t a n t c o n c e t s -s -t p t s i n t
Milliseconds 213 63 70 82 143 96 103 63 153 108 35 170 63 256 198 232 200 82 113 118 121 47 104 92 119
Character h e n e x t c h a p t e r , b u t f o r
Milliseconds 53 162 100 122 88 229 147 99 133 314 142 48 152 137 63 97 71 144 65 114 106 112 103 79 378
Character n o w w e u s e a n i n f o r -r r m a l
Milliseconds 183 108 118 83 336 115 157 185 112 170 101 96 137 140 193 129 104 350 146 207 464 93 154 125 109
Character a p p r o a c h s o y o u w i l l s e e
Milliseconds 112 76 177 163 120 153 231 114 121 207 70 84 236 72 40 83 77 80 225 176 77 76 210 243 0
Character h o w t h e y l e a d n a t u r a l l y t
Milliseconds 162 103 96 117 94 101 110 87 124 199 91 109 216 64 162 79 105 141 218 95 82 159 95 48 128
Character o t h e m a i n i d e a o f t h e c h
Milliseconds 66 110 144 89 152 95 153 103 96 128 76 142 64 110 56 104 145 78 91 102 82 167 104 129 232
Character -h -c - -e i s c h a p t e r , t h e l i m i t
Milliseconds 187 188 207 192 245 163 89 129 111 144 119 169 176 64 99 93 122 86 152 131 73 243 595 205 121
Character . T h e i d e a o f a l i m i t p l a
Milliseconds 191 73 167 104 105 95 129 82 77 81 115 164 97 103 104 121 395 222 478 153 106 69 121 112 65
Character y s a f o u n d a t i o n a l r o l e t h
Milliseconds 126 201 123 93 80 136 80 72 240 87 96 145 48 77 98 131 136 126 79 60 190 86 128 130 118
Character r o u g h o u t c a l c u l u s .
Milliseconds 120 88 41 104 88 135 48 80 233 265 39 159 115 150 303 514 224 87
WPM Timing
Seconds WPM
2.42 64.59
4.83 54.65
7.25 74.52
9.66 81.97
12.08 67.57
14.49 72.87
16.91 76.65
19.32 80.11
21.74 82.8
24.15 85.45
26.57 85.81
28.98 86.53
31.4 87.52
33.82 88.72
36.23 89.1
38.65 87.25
41.06 87.09
43.48 86.39
45.89 86.03
48.31 86.94
50.72 87.06
53.14 87.39
55.55 87.48
57.97 88.39
60.38 88.04
62.8 87.9
65.22 86.3
67.63 84.99
70.05 85.14
72.46 85.29
74.88 86.38
77.29 86.94
79.71 86.72
82.12 86.36
84.54 86.45
86.95 86.8
89.37 87.01
91.78 86.68
94.2 86.75
96.62 86.69
99.03 86.03
101.45 86.23
103.86 86.42
106.28 87.06
108.69 86
111.11 85.75
113.52 85.94
115.94 85.8
118.35 86.49
120.77 85.85