James Harper (jamesharper566)

Race #7425

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Official speed 93.74 wpm (110.60 seconds elapsed during race)
Without ending ping 93.93 wpm (220 ms delay sending score to TypeRacer’s server)
Timerless 94.16 wpm (271 ms elapsed before first character typed; 110.11 seconds elapsed during race)
Timerless minus one 94.05 wpm, ignoring the first character typed
Race Start May 13, 2024 8:13:36pm UTC
Race Finish May 13, 2024 8:15:27pm UTC
Outcome No win (2 of 4)
Opponents 1. kolock (107.33 wpm)
Accuracy 96.9%
Points 253.10
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 Calclulus is a tool that haleelps us understand how a change in one quenantity irs reallated to a chanege in another. How does theh so s speed of faa falling object change as a function of time? How does the level of water in a barrel change as a function of tha e amount of liquid poiuoured into it? We see chagne onge occuringrringrrin g in nearly everything we obvserve in the world and universe, and pwoeowerful moden irn instruments help us see more and oremore. in In this section we introduce the ideas of average and instanatanaeous 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 thse ese important concepts in th ee next chapter, but for nwow we use an informal approach so you will see how they lead naturally ito the main idea of this cphapter, the limit. The idea of a limit plays a foundaetiontional role throughout calculs.us.
Timing
Character C a l c l -l u l u s i s a t o o l t h a t
Milliseconds 271 101 135 160 354 267 167 139 78 79 70 32 115 55 113 100 100 73 114 154 43 83 54 41 56
Character h a l e -e -l -a e l p s u s u n d e r s t a n
Milliseconds 30 104 77 72 136 298 103 134 116 61 154 134 0 100 148 65 54 113 83 120 26 105 94 44 80
Character d h o w a c h a n g e i n o n e q u e
Milliseconds 103 74 55 30 85 50 104 62 106 130 132 55 90 104 0 46 87 69 46 97 143 296 166 264 88
Character n -n -e a n t i t y i r -r s r e a l -l -a l a t e
Milliseconds 99 351 104 227 106 146 25 178 69 96 182 180 191 94 33 101 54 67 26 303 116 195 36 92 65
Character d t o a c h a n e -e g e i n a n o t h e
Milliseconds 146 54 108 21 77 138 120 87 82 98 67 212 208 93 73 62 145 25 64 118 69 67 91 68 74
Character r . H o w d o e s t h e h s o -o -s - s -s
Milliseconds 58 91 30 226 54 73 108 86 40 82 94 12 107 32 105 0 50 132 136 209 93 141 239 102 232
Character - -h s p e e d o f f a -a -f a f a l l i n g
Milliseconds 114 162 201 120 87 99 118 133 44 40 82 85 125 150 175 111 67 171 26 91 248 133 103 48 94
Character o b j e c t c h a n g e a s a f u n c t
Milliseconds 38 103 313 178 71 137 180 30 158 143 123 106 54 118 171 118 62 66 152 26 243 195 184 95 168
Character i o n o f t i m e ? H o w d o e s t h e
Milliseconds 19 95 19 66 67 125 94 221 81 119 69 268 113 228 90 84 115 78 148 59 78 57 72 78 40
Character l e v e l o f w a t e r i n a b a r r
Milliseconds 107 95 97 140 114 89 33 140 69 153 114 69 131 93 80 44 69 85 82 47 68 131 122 146 120
Character e l c h a n g e a s a f u n c t i o n o
Milliseconds 70 91 69 132 69 86 63 98 78 195 110 108 62 102 34 104 70 129 78 168 48 104 33 78 97
Character f t h a - -a e a m o u n t o f l i q u i
Milliseconds 344 86 108 68 88 144 273 98 49 84 99 50 63 123 64 53 111 19 88 82 64 119 312 46 142
Character d p o i u -u -i o -o u r e d i n t o i t ? W
Milliseconds 111 72 181 205 132 332 229 122 192 367 174 47 86 164 0 65 98 116 20 71 131 85 196 153 114
Character e s e e c h a g n e o -o - -e -n -g n g e o c
Milliseconds 169 94 55 167 126 47 128 91 89 107 0 111 29 72 294 107 135 135 247 217 28 67 90 56 109
Character c u r i n g -g -n -i -r r -r r i n g -g -n r -r -i r i n
Milliseconds 148 100 83 119 113 165 172 117 113 146 90 281 339 82 140 84 270 213 142 132 199 132 515 91 54
Character - g i n n e a r l y e v e r y t h i n g w
Milliseconds 407 99 88 266 118 93 166 108 81 14 86 149 76 75 134 113 49 30 114 44 84 247 131 148 106
Character e o b v -v s e r v e i n t h e w o r l d
Milliseconds 95 70 136 95 138 255 57 68 85 181 114 89 116 52 74 47 101 21 120 53 330 0 0 75 42
Character a n d u n i v e r s e , a n d p w o e -e -o -w
Milliseconds 85 62 115 48 83 122 104 62 134 66 48 108 78 51 85 83 86 62 44 136 23 26 250 100 101
Character o w e r f u l m o d e n i -i - -n r n i n s t
Milliseconds 221 46 52 15 172 26 148 49 163 116 77 153 150 101 228 206 134 126 110 88 37 90 95 81 73
Character r u m e n t s h e l p u s s e e m o r e
Milliseconds 153 41 152 100 87 82 86 83 95 130 54 150 115 72 109 76 382 132 111 117 62 103 41 66 100
Character a n d o r e -e -r -o m o r e . i n - -n -i I n
Milliseconds 142 117 19 71 115 96 56 181 104 132 187 83 0 35 140 115 169 137 115 263 98 139 169 126 39
Character t h i s s e c t i o n w e i n t r o d u c e
Milliseconds 136 45 37 102 65 109 76 195 154 31 51 45 103 115 87 119 83 116 84 110 121 266 112 86 185
Character t h e i d e a s o f a v e r a g e a n d
Milliseconds 85 79 73 67 96 49 101 136 78 65 68 184 167 84 119 196 117 61 93 98 103 82 111 57 127
Character i n s t a n a -a t a n a -a e o u s r a t e s
Milliseconds 89 66 119 242 105 82 115 105 439 137 83 74 144 237 97 134 81 101 95 119 58 125 66 88 79
Character o f c h a n g e , a n d s h o w t h a t
Milliseconds 186 89 118 116 248 70 128 0 119 68 45 100 100 52 79 310 0 93 85 129 90 41 44 83 44
Character t h e y a r e c l o s e l y r e l a t e d
Milliseconds 119 0 114 106 17 117 89 34 76 167 75 125 66 81 110 153 69 46 70 101 153 67 35 182 51
Character t o t h e s l o p e o f a c u r v e a
Milliseconds 146 47 63 74 68 46 115 56 147 202 133 149 113 76 324 21 150 64 130 106 46 485 144 124 146
Character t a p o i n t P o n t h e c u r v e .
Milliseconds 147 42 57 107 69 150 65 145 102 23 179 168 106 64 63 88 47 45 98 74 85 63 203 118 47
Character W e g i v e p r e c i s e d e v e l o p m
Milliseconds 48 201 135 83 148 86 71 130 40 123 35 69 212 186 110 100 133 350 127 147 100 33 179 250 264
Character e n t s o f t h s e - -e -s e s e i m p o r
Milliseconds 104 88 32 116 26 54 106 92 115 74 48 137 84 247 110 142 91 71 115 13 92 127 107 63 101
Character t a n t c o n c e p t s i n t h e -e - e
Milliseconds 239 114 91 105 71 161 20 64 101 91 138 41 116 57 75 61 92 97 53 167 0 414 103 94 20
Character n e x t c h a p t e r , b u t f o r n w -w
Milliseconds 119 23 190 137 109 188 84 102 85 149 99 63 31 84 188 82 114 114 223 66 103 27 101 320 283
Character o w w e u s e a n i n f o r m a l a p p
Milliseconds 229 71 104 63 174 38 85 48 99 86 150 62 89 200 86 117 94 115 55 103 82 67 125 87 103
Character r o a c h s o y o u w i l l s e e h o w
Milliseconds 100 103 54 207 35 101 259 90 51 185 30 48 44 113 70 136 137 106 49 218 156 50 254 49 122
Character t h e y l e a d n a t u r a l l y i -i t o
Milliseconds 82 98 17 166 0 51 133 50 53 130 55 196 104 45 335 118 94 89 129 153 15 133 280 139 108
Character t h e m a i n i d e a o f t h i s c p
Milliseconds 37 119 67 99 49 86 63 89 31 64 139 95 138 65 135 70 110 47 126 96 35 82 131 139 113
Character -p h a p t e r , t h e l i m i t . T h e i
Milliseconds 287 215 102 140 134 126 47 130 48 134 50 168 15 131 75 132 128 107 67 51 149 113 113 21 65
Character d e a o f a l i m i t p l a y s a f o
Milliseconds 265 186 103 86 59 106 67 100 39 110 162 168 135 103 51 113 166 110 100 135 91 108 141 145 34
Character u n d a e t i o n -n -o -i -t -e t i o n a l r o l e
Milliseconds 53 120 54 78 110 0 125 97 27 258 99 129 122 134 99 101 93 32 441 118 60 238 63 172 92
Character t h r o u g h o u t c a l c u l s . -. -s u s .
Milliseconds 30 91 65 137 0 77 241 97 236 75 90 111 158 123 143 201 232 328 89 239 256 120 263 88 134
WPM Timing
Seconds WPM
2.21 70.52
4.42 81.37
6.64 104.88
8.85 92.22
11.06 88.97
13.27 93.13
15.48 93
17.7 88.15
19.91 88.6
22.12 90.59
24.33 91.73
26.54 95.39
28.76 97.23
30.97 96.87
33.18 95.48
35.39 94.26
37.61 91.9
39.82 89.21
42.03 85.08
44.24 85.17
46.45 85.76
48.67 88.28
50.88 88.68
53.09 87.93
55.3 88.97
57.51 87.63
59.73 88.4
61.94 89.12
64.15 89.79
66.36 89.33
68.57 90.12
70.79 91.88
73 92.39
75.21 92.38
77.42 93.15
79.63 93.13
81.85 92.81
84.06 93.79
86.27 93.47
88.48 93.03
90.7 93.81
92.91 94.16
95.12 94.62
97.33 94.93
99.54 94.87
101.76 95.29
103.97 95.68
106.18 94.71
108.39 94.88
110.6 93.74