Phillip (naurwigs)

Race #271

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Official speed 87.62 wpm (118.33 seconds elapsed during race)
Without ending ping 87.82 wpm (273 ms delay sending score to TypeRacer’s server)
Timerless 88.42 wpm (803 ms elapsed before first character typed; 117.25 seconds elapsed during race)
Timerless minus one 88.32 wpm, ignoring the first character typed
Race Start March 2, 2024 10:34:45pm UTC
Race Finish March 2, 2024 10:36:43pm UTC
Outcome Win (1 of 4)
Accuracy 97.9%
Points 236.57
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 CAlalculus is a tool that helps us understand how a change in one qunaantity is related to ach change in another. How does the speed of a falling object change as a function of time? How does the level of waster in a barrel change as a functiopn n of the amount of liquid poured intio it? WE se see change occurring in nearly everything we observe in the world and universe, and powerful modern instruments helkpp us see more and more. In this section we introduce the ideas of average and instanteaneous rate of s es of change, asnnd show that thaey are closely related to the slope of a curve at a point P on the curve. W ee give [rpreceiise developments of these important concepts in thenn next chapter, but for now we used an informal approach wso you will see how they lead naturally to the main idea of this chapter, the limit. The idea of a limit plays a foudandational role throughout calculus.
Timing
Character C A l -l -A a l c u l u s i s a t o o l t h
Milliseconds 803 85 205 384 135 352 508 219 158 193 201 102 110 207 75 83 103 90 164 85 153 245 80 124 119
Character a t h e l p s u s u n d e r s t a n d h o
Milliseconds 33 67 59 179 104 113 81 82 94 165 55 95 94 68 59 92 121 78 115 63 153 15 77 111 56
Character w a c h a n g e i n o n e q u n a -a -n a
Milliseconds 64 71 97 90 98 110 81 110 342 67 85 158 77 98 296 91 62 89 232 118 254 103 225 132 89
Character n t i t y i s r e l a t e d t o a c h -h -c
Milliseconds 132 226 117 62 170 135 106 87 85 85 63 81 98 85 68 108 93 126 70 71 65 100 163 572 136
Character c h a n g e i n a n o t h e r . H o w d
Milliseconds 113 391 147 102 118 53 68 51 143 49 64 91 131 73 102 123 87 39 117 83 189 104 63 304 236
Character o e s t h e s p e e d o f a f a l l i n
Milliseconds 140 87 60 65 129 97 46 67 105 81 110 154 93 89 132 63 85 91 91 99 69 38 167 210 60
Character g o b j e c t c h a n g e a s a f u n c
Milliseconds 89 32 122 283 65 85 45 243 64 137 110 76 114 98 72 28 182 87 116 79 77 168 105 143 0
Character t i o n o f t i m e ? H o w d o e s t h
Milliseconds 159 71 49 170 103 107 85 110 158 93 60 60 255 169 368 144 84 105 99 122 85 68 72 123 113
Character e l e v e l o f w a s -s t e r i n a b
Milliseconds 27 87 123 69 109 78 114 118 144 91 45 112 82 138 354 111 76 104 86 200 78 87 81 112 91
Character a r r e l c h a n g e a s a f u n c t i o
Milliseconds 221 111 166 80 167 149 94 151 61 132 73 54 92 141 75 97 80 97 206 144 57 55 204 92 41
Character p n - -n -p n o f t h e a m o u n t o f
Milliseconds 55 156 124 269 144 141 445 89 111 61 80 271 5 3 64 109 160 100 71 189 101 68 153 150 45
Character l i q u i d p o u r e d i n t i -i o i t ?
Milliseconds 261 192 107 166 81 266 88 400 215 123 119 61 110 138 128 84 226 174 283 209 106 125 59 225 150
Character W E s -s - -E e s e e c h a n g e o c c u r
Milliseconds 171 105 60 161 413 157 147 66 72 135 102 170 109 281 102 121 132 129 54 64 164 100 138 122 101
Character r i n g i n n e a r l y e v e r y t h i n g
Milliseconds 144 124 75 100 33 140 43 56 150 35 63 133 115 117 57 129 128 82 115 111 92 106 11 133 75
Character w e o b s e r v e i n t h e w o r l d
Milliseconds 54 194 74 70 160 179 79 89 70 188 66 71 87 44 70 136 187 88 69 99 109 84 130 104 204
Character a n d u n i v e r s e , a n d p o w e r f u
Milliseconds 62 146 71 42 119 52 134 135 72 136 67 91 136 88 63 138 81 35 548 169 100 24 76 181 80
Character l m o d e r n i n s t r u m e n t s h e l k
Milliseconds 204 78 231 82 91 114 108 128 57 120 64 38 119 50 90 214 59 112 52 56 60 140 390 216 0
Character p -p -k p u s s e e m o r e a n d m o r e
Milliseconds 26 334 144 405 137 167 90 105 137 117 154 86 81 72 52 39 65 121 104 48 71 146 54 77 30
Character . I n t h i s s e c t i o n w e i n t r
Milliseconds 338 65 248 134 56 123 111 55 122 101 180 92 96 244 64 38 203 109 130 101 97 173 72 85 62
Character o d u c e t h e i d e a s o f a v e r a g
Milliseconds 101 99 150 50 86 80 125 202 44 51 129 52 86 55 144 143 73 124 34 208 171 167 85 101 125
Character e a n d i n s t a n t e -e a n e o u s r a t
Milliseconds 73 71 121 105 90 43 166 33 59 145 65 133 117 123 493 72 149 182 111 95 166 131 418 89 160
Character e o f - -f -o - -e s - -s e s o f c h a n g
Milliseconds 26 66 162 82 40 409 163 156 159 135 85 34 334 140 91 49 93 197 76 78 103 136 77 136 73
Character e , a s n -n -s n d s h o w t h a t t h a -a
Milliseconds 62 125 56 75 72 91 307 148 798 111 53 216 77 79 118 93 190 123 58 82 69 134 95 117 360
Character e y a r e c l o s e l y r e l a t e d t o
Milliseconds 70 141 71 107 105 66 64 134 97 171 42 84 128 108 129 219 66 134 29 107 54 125 58 179 100
Character t h e s l o p e o f a c u r v e a t
Milliseconds 101 157 141 64 45 139 74 189 164 118 51 123 69 115 31 155 62 228 314 163 84 100 125 242 101
Character a p o i n t P o n t h e c u r v e . W
Milliseconds 84 108 181 230 169 93 95 53 253 170 191 164 92 73 129 46 71 118 147 68 170 67 108 89 175
Character e -e - e g i v e [ r -r -[ p r e c e i -i -e i s
Milliseconds 188 14 470 150 64 62 409 136 65 59 65 177 117 332 154 465 91 43 200 26 120 333 144 642 90
Character e d e v e l o p m e n t s o f t h e s e i
Milliseconds 74 139 355 87 121 64 131 153 66 214 95 128 61 71 225 174 101 62 150 133 48 194 97 101 197
Character m p o r t a n t c o n c e p t s i n t h e n
Milliseconds 62 167 143 72 140 51 111 119 57 161 95 48 51 93 184 99 67 128 186 56 113 90 186 28 384
Character n -n - -n n e x t c h a p t e r , b u t f
Milliseconds 80 231 121 123 168 149 164 83 187 203 54 161 106 77 143 172 83 90 152 82 208 68 102 53 140
Character o r n o w w e u s e d -d a n i n f o r m
Milliseconds 91 85 61 125 91 122 98 261 205 110 178 79 84 114 388 108 218 128 104 134 54 126 137 154 79
Character a l a p p r o a c h w -w s o y o u w i l l
Milliseconds 89 145 149 128 113 157 142 140 104 183 134 104 97 426 136 114 141 56 91 69 64 139 336 174 135
Character s e e h o w t h e y l e a d n a t u r a
Milliseconds 66 32 107 320 123 221 59 104 64 303 137 76 181 129 100 48 177 119 151 184 90 171 136 79 47
Character l l y t o t h e m a i n i d e a o f t
Milliseconds 107 140 91 49 130 89 73 372 103 29 84 115 108 108 75 86 130 78 105 33 127 142 75 76 160
Character h i s c h a p t e r , t h e l i m i t . T
Milliseconds 152 62 81 62 169 128 62 123 121 75 117 128 72 184 139 57 76 83 180 75 137 99 142 61 191
Character h e i d e a o f a l i m i t p l a y s
Milliseconds 188 117 83 270 40 90 60 143 188 103 80 129 70 396 200 65 142 104 74 168 72 81 255 110 122
Character a f o u d a -a -d n d a t i o n a l r o l e t
Milliseconds 86 106 141 171 56 669 131 351 128 214 78 33 161 89 30 158 92 99 82 85 110 183 84 62 150
Character h r o u g h o u t c a l c u l u s .
Milliseconds 104 78 82 74 35 118 138 62 65 40 197 87 178 223 123 196 190 78 144
WPM Timing
Seconds WPM
2.37 10.14
4.73 45.64
7.1 74.37
9.47 81.13
11.83 80.12
14.2 76.06
16.57 81.13
18.93 86.2
21.3 89.58
23.67 90.26
26.03 92.65
28.4 92.12
30.77 92.05
33.13 91.27
35.5 90.26
37.87 88.42
40.23 86.8
42.6 88.74
44.97 90.2
47.33 91.52
49.7 91.51
52.06 91.27
54.43 91.71
56.8 91.9
59.16 92.89
61.53 93.81
63.9 92.21
66.26 89.82
68.63 88.65
71 88.74
73.36 89.47
75.73 89.84
78.1 89.58
80.46 89.18
82.83 87.94
85.2 86.9
87.56 87.16
89.93 87.8
92.3 86.85
94.66 87.21
97.03 86.94
99.4 86.68
101.76 86.55
104.13 87.01
106.5 87.55
108.86 87.96
111.23 87.93
113.6 87.57
115.96 87.55
118.33 87.62