Theodore (theo52)

Race #4220

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Official speed 93.58 wpm (110.79 seconds elapsed during race)
Without ending ping 93.82 wpm (280 ms delay sending score to TypeRacer’s server)
Timerless 94.01 wpm (232 ms elapsed before first character typed; 110.28 seconds elapsed during race)
Timerless minus one 93.91 wpm, ignoring the first character typed
Race Start April 8, 2024 4:29:17pm UTC
Race Finish April 8, 2024 4:31:08pm UTC
Outcome Win (1 of 5)
Accuracy 98.1%
Points 252.67
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 tolol that help sus s us understand how a change in one quantity is related to a change in another . How does the pspeed of a falling object change as a function of time? How does the level of water in a barrael change as a function of the amount of ilquliquid poured into it? We csee 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 introduc e the ideas of average and instanteaaneous rates o f change, and show that they are closely related to the slope of a curve at a point P on the curve. AWe give precise developments of thes ims e important concepts in the next chapter, but for now we use an informal approach so you will see how they lead nautturally to the main idea of this chapter, the limit . The ideaof a of a limit plays a foundatioanal role throughout calculus.
Timing
Character C a l c u l u s i s a t o l -l o l t h a t
Milliseconds 232 202 125 108 108 122 66 104 109 1387 93 94 108 93 109 63 294 281 204 156 139 63 62 77 48
Character h e l p s u s - -s -u -s - s u s u n d e r
Milliseconds 75 124 112 75 160 150 18 167 108 140 139 127 138 142 151 126 93 133 131 66 277 188 121 171 62
Character s t a n d h o w a c h a n g e i n o n e
Milliseconds 244 203 180 61 129 72 82 74 78 92 142 59 147 73 100 76 75 78 80 103 64 138 137 79 100
Character q u a n t i t y i s r e l a t e d t o a
Milliseconds 87 327 63 170 48 123 77 92 109 77 78 78 93 144 164 171 129 90 62 203 78 99 55 63 110
Character c h a n g e i n a n o t h e r - . H o w
Milliseconds 92 124 62 129 57 106 157 0 96 75 62 79 76 124 48 53 130 36 168 296 204 47 171 110 62
Character d o e s t h e p -p s p e e d o f a f a
Milliseconds 138 95 63 121 61 94 68 57 94 85 133 298 104 93 93 144 200 62 92 96 108 111 77 246 95
Character l l i n g o b j e c t c h a n g e a s a
Milliseconds 101 131 120 69 108 79 107 112 106 122 187 107 126 121 95 91 94 76 77 99 103 184 124 79 100
Character f u n c t i o n o f t i m e ? H o w d o e
Milliseconds 89 93 187 108 156 93 17 76 61 115 196 124 123 53 150 135 256 60 174 147 177 158 244 156 31
Character s t h e l e v e l o f w a t e r i n a
Milliseconds 79 138 126 35 165 123 163 74 160 120 109 105 113 93 97 92 77 48 156 32 45 112 28 77 79
Character b a r r a -a e l c h a n g e a s a f u n
Milliseconds 115 43 263 154 190 90 311 123 80 80 73 77 80 115 69 87 131 172 167 79 114 73 124 76 173
Character c t i o n o f t h e a m o u n t o f i l
Milliseconds 113 173 42 54 55 80 75 64 111 111 30 126 59 170 78 133 66 184 87 123 77 110 65 140 14
Character q u -u -q -l -i l i q u i d p o u r e d i n t o
Milliseconds 148 164 265 124 158 121 204 93 76 362 105 141 673 210 233 77 62 77 187 64 93 82 130 65 95
Character i t ? W e c -c s e e c h a n g e o c c u r
Milliseconds 77 113 263 48 140 218 108 127 257 123 158 135 76 173 110 93 125 170 141 110 159 115 362 155 111
Character r i n g i n n e a r l y e v e r y t h i n g
Milliseconds 186 110 59 97 94 75 80 56 223 528 110 79 33 138 95 54 164 105 61 109 95 80 58 143 39
Character w e o b s e r v e i n t h e w o r l d
Milliseconds 115 77 48 109 200 94 264 157 223 204 106 130 88 50 91 111 58 111 122 93 124 19 168 77 71
Character a n d u n i v e r s e , a n d p o w e r f u
Milliseconds 147 36 134 80 94 173 48 76 108 45 172 17 90 66 78 75 127 75 495 203 124 20 58 161 102
Character l m o d e r n i n s t r u m e n t s h e l p
Milliseconds 93 124 159 108 173 191 368 78 71 84 78 92 111 154 109 187 93 104 98 292 129 136 140 77 106
Character u s s e e m o r e a n d m o r e . I n
Milliseconds 125 82 81 136 75 139 130 73 147 56 32 61 99 74 93 101 85 112 57 80 47 125 51 148 186
Character t h i s s e c t i o n w e i n t r o d u c
Milliseconds 47 199 20 107 140 143 107 136 192 172 0 25 72 70 109 33 136 63 78 206 150 94 173 139 48
Character - e t h e i d e a s o f a v e r a g e
Milliseconds 251 381 132 73 125 48 90 94 111 105 154 117 167 89 109 106 82 195 126 172 206 72 108 62 112
Character a n d i n s t a n t e a -a -e a n e o u s r a t
Milliseconds 92 80 107 129 102 85 86 233 141 94 155 155 270 121 171 156 77 186 125 66 144 56 93 98 90
Character e s o - f c h a n g e , a n d s h o w
Milliseconds 69 141 90 109 205 355 130 93 136 97 74 109 77 92 106 52 149 83 156 92 154 92 64 106 109
Character t h a t t h e y a r e c l o s e l y r e l
Milliseconds 77 49 90 77 59 120 16 231 201 76 79 92 34 125 201 78 124 338 159 122 138 80 90 47 157
Character a t e d t o t h e s l o p e o f a c u
Milliseconds 108 32 68 231 106 123 124 80 125 44 125 78 146 24 186 109 155 123 110 124 90 110 77 467 140
Character r v e a t a p o i n t P o n t h e c
Milliseconds 62 193 129 109 143 59 140 66 121 263 192 79 58 91 127 136 110 77 86 64 116 78 43 91 129
Character u r v e . A -A W e g i v e p r e c i s e d
Milliseconds 91 64 174 150 112 72 177 412 93 171 141 216 46 125 93 139 142 125 93 205 92 137 65 87 164
Character e v e l o p m e n t s o f t h e s i m -m -i -
Milliseconds 134 142 187 63 160 121 187 123 99 107 121 73 117 91 92 116 56 144 25 125 122 175 336 126 122
Character s - -s e i m p o r t a n t c o n c e p t s
Milliseconds 141 109 372 108 46 128 76 170 102 102 31 155 62 51 104 94 110 45 68 65 153 75 109 154 62
Character i n t h e n e x t c h a p t e r , b u t
Milliseconds 125 47 62 79 95 49 141 138 97 216 140 140 155 90 140 51 135 122 76 0 82 110 61 141 46
Character f o r n o w w e u s e a n i n f o r m a
Milliseconds 251 102 131 70 135 79 121 132 87 46 96 106 47 62 96 92 115 27 105 78 77 137 66 141 75
Character l a p p r o a c h s o y o u w i l l s e
Milliseconds 91 109 170 264 160 107 108 68 183 90 62 85 88 82 117 108 62 79 83 69 145 135 77 49 185
Character e h o w t h e y l e a d n a u t -t -u t u r
Milliseconds 140 18 113 70 156 48 108 62 103 91 42 201 94 62 155 126 186 114 244 138 202 126 159 75 97
Character a l l y t o t h e m a i n i d e a o f
Milliseconds 58 16 173 130 90 78 63 79 61 80 105 62 144 121 30 48 80 107 92 135 83 47 94 140 78
Character t h i s c h a p t e r , t h e l i m i t -
Milliseconds 83 28 76 410 105 188 308 156 62 123 140 52 66 44 106 27 122 48 185 125 171 110 95 264 371
Character - . T h e i d e a o f a -a - -f -o o f a
Milliseconds 298 290 218 65 136 135 101 97 149 109 141 94 140 122 94 72 225 124 138 140 171 92 109 110 92
Character l i m i t p l a y s a f o u n d a t i o a
Milliseconds 78 155 170 139 126 48 157 136 141 100 136 93 114 119 283 169 67 77 181 32 138 116 25 31 248
Character -a n a l r o l e t h r o u g h o u t c a l c
Milliseconds 279 170 93 64 71 102 73 154 170 124 97 77 137 33 75 159 34 102 88 133 93 172 138 155 142
Character u l u s .
Milliseconds 79 100 85 77 110
WPM Timing
Seconds WPM
2.22 48.74
4.43 59.57
6.65 55.96
8.86 64.99
11.08 73.65
13.3 80.33
15.51 84.33
17.73 85.97
19.94 87.85
22.16 90.98
24.37 90.09
26.59 92.51
28.81 92.9
31.02 94.77
33.24 92.06
35.45 90.03
37.67 89.52
39.89 89.06
42.1 89.5
44.32 89.9
46.53 91.55
48.75 92.06
50.96 91.83
53.18 92.74
55.4 93.36
57.61 93.11
59.83 93.27
62.04 93.03
64.26 92.44
66.48 93.33
68.69 93.29
70.91 93.93
73.12 93.87
75.34 94.29
77.56 93.61
79.77 93.57
81.99 92.36
84.2 92.78
86.42 93.45
88.63 94.09
90.85 94.44
93.07 95.16
95.28 94.58
97.5 95.51
99.71 95.43
101.93 94.42
104.15 93.56
106.36 93.53
108.58 93.39
110.79 93.58