Official speed |
92.49 wpm (112.10 seconds elapsed during race) |
Without ending ping |
92.87 wpm (196 ms delay sending score to TypeRacer’s server) |
Timerless |
93.16 wpm (356 ms elapsed before first character typed; 111.55 seconds elapsed during race) |
Timerless minus one |
93.05 wpm, ignoring the first character typed |
Race Start |
October 23, 2023 8:45:33pm UTC |
Race Finish |
October 23, 2023 8:47:25pm UTC |
Outcome |
Win (1 of 4) |
Opponents |
3. iamsincan (85.87 wpm)
4. sekasmeowmix (73.96 wpm)
|
Accuracy |
96.3% |
Points |
249.71 |
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 s a tool that helps us understand how a change in one quantity is realteelated to a change in antoother. How odoes the speed of a falling object change as af function of time? How does the level lof water in a barrel cahhangaee as a function of the amount of liquid poutred into it? We see change occurring in nearly everything we obsetrve in the world and universe, and powerful modern instruments help uis s see more and more. In thusis section wwe e intoroduce the ideas of average and instantenaneous rates of change, and show thtat they are closely realteelated to the slopeo f of a curve at a point pP on teh he curve. We give preceiseise developments of these important concepts in the next chapterm u, but for now we use an informal ppapproach so you will see how they lead natufrally to the main idea of this chapterm, the limit,.. The idaea ofdea of a mlimit plays a foundational role through t hout calculus. |
Timing |
Character |
C |
a |
l |
c |
u |
l |
u |
s |
|
i |
s |
|
s |
|
a |
-s |
- |
|
t |
o |
o |
l |
|
t |
h |
Milliseconds |
356 |
276 |
80 |
102 |
82 |
92 |
144 |
105 |
120 |
79 |
60 |
76 |
108 |
101 |
103 |
601 |
0 |
122 |
79 |
89 |
95 |
139 |
133 |
121 |
143 |
Character |
a |
t |
|
h |
e |
l |
p |
s |
|
u |
s |
|
u |
n |
d |
e |
r |
s |
t |
a |
n |
d |
|
h |
o |
Milliseconds |
78 |
66 |
81 |
81 |
95 |
105 |
61 |
55 |
108 |
78 |
234 |
118 |
106 |
54 |
24 |
80 |
489 |
103 |
81 |
79 |
65 |
119 |
80 |
53 |
83 |
Character |
w |
|
a |
|
c |
h |
a |
n |
g |
e |
|
i |
n |
|
o |
n |
e |
|
q |
u |
a |
n |
t |
i |
t |
Milliseconds |
22 |
123 |
104 |
96 |
136 |
37 |
123 |
61 |
123 |
63 |
96 |
22 |
42 |
120 |
54 |
67 |
39 |
120 |
286 |
83 |
104 |
79 |
481 |
63 |
96 |
Character |
y |
|
i |
s |
|
r |
e |
a |
l |
t |
e |
-e |
-a |
-l |
-t |
-e |
e |
l |
a |
t |
e |
d |
|
t |
o |
Milliseconds |
102 |
124 |
94 |
24 |
120 |
120 |
80 |
104 |
64 |
161 |
54 |
418 |
0 |
0 |
0 |
0 |
63 |
106 |
135 |
64 |
79 |
137 |
105 |
127 |
56 |
Character |
|
a |
|
c |
h |
a |
n |
g |
e |
|
i |
n |
|
a |
n |
t |
o |
-o |
-t |
o |
t |
h |
e |
r |
. |
Milliseconds |
80 |
82 |
100 |
107 |
52 |
105 |
81 |
170 |
78 |
104 |
64 |
56 |
80 |
105 |
80 |
119 |
40 |
313 |
136 |
80 |
96 |
128 |
53 |
24 |
123 |
Character |
|
H |
o |
w |
|
o |
-o |
d |
o |
e |
s |
|
t |
h |
e |
|
s |
p |
e |
e |
d |
|
o |
f |
|
Milliseconds |
160 |
183 |
137 |
53 |
275 |
176 |
240 |
104 |
80 |
95 |
86 |
58 |
81 |
104 |
16 |
220 |
67 |
122 |
104 |
119 |
136 |
79 |
63 |
82 |
119 |
Character |
a |
|
f |
a |
l |
l |
i |
n |
g |
|
o |
b |
j |
e |
c |
t |
|
c |
h |
a |
n |
g |
e |
|
a |
Milliseconds |
57 |
127 |
249 |
63 |
55 |
120 |
162 |
64 |
53 |
67 |
104 |
80 |
120 |
96 |
80 |
192 |
103 |
129 |
61 |
58 |
81 |
80 |
61 |
123 |
96 |
Character |
s |
|
a |
f |
-f |
|
f |
u |
n |
c |
t |
i |
o |
n |
|
o |
f |
|
t |
i |
m |
e |
? |
|
H |
Milliseconds |
46 |
122 |
57 |
231 |
304 |
87 |
54 |
83 |
81 |
63 |
176 |
22 |
55 |
106 |
81 |
80 |
144 |
53 |
107 |
63 |
81 |
120 |
136 |
119 |
146 |
Character |
o |
w |
|
d |
o |
e |
s |
|
t |
h |
e |
|
l |
e |
v |
e |
l |
|
l |
$o |
f |
|
w |
a |
t |
Milliseconds |
151 |
64 |
121 |
53 |
122 |
104 |
63 |
96 |
63 |
57 |
208 |
103 |
81 |
38 |
233 |
18 |
455 |
80 |
105 |
520 |
41 |
119 |
56 |
76 |
107 |
Character |
e |
r |
|
i |
n |
|
a |
|
b |
a |
r |
r |
e |
l |
|
c |
a |
h |
-a |
-h |
h |
a |
n |
g |
a |
Milliseconds |
102 |
99 |
105 |
135 |
64 |
80 |
64 |
120 |
136 |
160 |
184 |
113 |
61 |
81 |
121 |
119 |
104 |
40 |
520 |
0 |
81 |
23 |
217 |
165 |
108 |
Character |
e |
-e |
-a |
e |
|
a |
s |
|
a |
|
f |
u |
n |
c |
t |
i |
o |
n |
|
o |
f |
|
t |
h |
e |
Milliseconds |
78 |
217 |
168 |
96 |
120 |
61 |
136 |
203 |
80 |
119 |
38 |
106 |
65 |
80 |
176 |
13 |
82 |
103 |
82 |
80 |
117 |
82 |
63 |
57 |
105 |
Character |
|
a |
m |
o |
u |
n |
t |
|
o |
f |
|
l |
i |
q |
u |
i |
d |
|
p |
o |
u |
t |
-t |
r |
e |
Milliseconds |
53 |
148 |
148 |
82 |
138 |
158 |
161 |
376 |
39 |
105 |
80 |
40 |
81 |
119 |
80 |
77 |
195 |
79 |
54 |
68 |
199 |
103 |
233 |
80 |
53 |
Character |
d |
|
i |
n |
t |
o |
|
i |
t |
? |
|
W |
e |
|
s |
e |
e |
|
c |
h |
a |
n |
g |
e |
|
Milliseconds |
146 |
106 |
52 |
67 |
119 |
38 |
275 |
248 |
80 |
223 |
78 |
183 |
237 |
159 |
80 |
78 |
162 |
96 |
120 |
119 |
106 |
79 |
337 |
53 |
106 |
Character |
o |
c |
c |
u |
r |
r |
i |
n |
g |
|
i |
n |
|
n |
e |
a |
r |
l |
y |
|
e |
v |
e |
r |
y |
Milliseconds |
136 |
119 |
128 |
95 |
120 |
106 |
144 |
13 |
82 |
106 |
119 |
36 |
83 |
80 |
88 |
80 |
38 |
162 |
80 |
78 |
81 |
170 |
81 |
344 |
62 |
Character |
t |
h |
i |
n |
g |
|
w |
e |
|
o |
b |
s |
e |
t |
-t |
r |
v |
e |
|
i |
n |
|
t |
h |
e |
Milliseconds |
255 |
56 |
65 |
82 |
62 |
118 |
43 |
80 |
120 |
95 |
89 |
318 |
56 |
402 |
281 |
79 |
216 |
280 |
128 |
54 |
63 |
122 |
82 |
79 |
104 |
Character |
|
w |
o |
r |
l |
d |
|
a |
n |
d |
|
u |
n |
i |
v |
e |
r |
s |
e |
, |
|
a |
n |
d |
|
Milliseconds |
93 |
107 |
53 |
81 |
138 |
53 |
82 |
80 |
62 |
98 |
81 |
167 |
81 |
120 |
160 |
96 |
144 |
105 |
94 |
216 |
80 |
54 |
82 |
64 |
40 |
Character |
p |
o |
w |
e |
r |
f |
u |
l |
|
m |
o |
d |
e |
r |
n |
|
i |
n |
s |
t |
r |
u |
m |
e |
n |
Milliseconds |
105 |
53 |
65 |
194 |
23 |
185 |
104 |
53 |
82 |
129 |
53 |
187 |
80 |
79 |
233 |
79 |
146 |
53 |
66 |
77 |
125 |
36 |
146 |
81 |
120 |
Character |
t |
s |
|
h |
e |
l |
p |
|
u |
i |
s |
|
- |
-s |
-i |
s |
|
s |
e |
e |
|
m |
o |
r |
e |
Milliseconds |
37 |
121 |
105 |
79 |
80 |
121 |
40 |
80 |
120 |
22 |
41 |
249 |
145 |
118 |
126 |
169 |
242 |
96 |
288 |
144 |
80 |
160 |
62 |
98 |
64 |
Character |
|
a |
n |
d |
|
m |
o |
r |
e |
. |
|
I |
n |
|
t |
h |
u |
s |
-s |
-u |
i |
s |
|
s |
e |
Milliseconds |
62 |
474 |
62 |
106 |
81 |
52 |
67 |
54 |
82 |
120 |
141 |
147 |
177 |
87 |
54 |
68 |
79 |
93 |
297 |
134 |
67 |
80 |
96 |
63 |
80 |
Character |
c |
t |
i |
o |
n |
|
w |
w |
e |
|
- |
-e |
-w |
e |
|
i |
n |
t |
o |
-o |
r |
o |
d |
u |
c |
Milliseconds |
193 |
176 |
13 |
81 |
130 |
62 |
82 |
264 |
21 |
84 |
239 |
145 |
216 |
79 |
120 |
96 |
61 |
83 |
120 |
449 |
223 |
79 |
194 |
80 |
279 |
Character |
e |
|
t |
h |
e |
|
i |
d |
e |
a |
s |
|
o |
f |
|
a |
v |
e |
r |
a |
g |
e |
|
a |
n |
Milliseconds |
104 |
81 |
78 |
82 |
78 |
79 |
66 |
79 |
64 |
97 |
103 |
54 |
105 |
40 |
106 |
53 |
123 |
80 |
121 |
143 |
120 |
65 |
191 |
79 |
146 |
Character |
d |
|
i |
n |
s |
t |
a |
n |
t |
e |
n |
-n |
-e |
a |
n |
e |
o |
u |
s |
|
r |
a |
t |
e |
s |
Milliseconds |
79 |
95 |
193 |
57 |
20 |
107 |
79 |
209 |
247 |
97 |
200 |
350 |
186 |
120 |
63 |
121 |
129 |
52 |
106 |
121 |
102 |
98 |
104 |
52 |
165 |
Character |
|
o |
f |
|
c |
h |
a |
n |
g |
e |
, |
|
a |
n |
d |
|
s |
h |
o |
w |
|
t |
h |
t |
-t |
Milliseconds |
151 |
144 |
55 |
81 |
119 |
63 |
82 |
80 |
81 |
62 |
120 |
56 |
105 |
104 |
96 |
80 |
200 |
136 |
23 |
54 |
131 |
78 |
121 |
170 |
471 |
Character |
a |
t |
|
t |
h |
e |
y |
|
a |
r |
e |
|
c |
l |
o |
s |
e |
l |
y |
|
r |
e |
a |
l |
t |
Milliseconds |
232 |
80 |
120 |
95 |
38 |
83 |
105 |
119 |
39 |
82 |
61 |
121 |
98 |
86 |
154 |
12 |
183 |
251 |
233 |
160 |
54 |
81 |
79 |
66 |
120 |
Character |
e |
-e |
-a |
-l |
-t |
-e |
e |
l |
a |
t |
e |
d |
|
t |
o |
|
t |
h |
e |
|
s |
l |
o |
p |
e |
Milliseconds |
63 |
488 |
0 |
0 |
0 |
0 |
63 |
105 |
95 |
82 |
105 |
176 |
63 |
144 |
53 |
84 |
168 |
79 |
53 |
106 |
121 |
23 |
155 |
78 |
77 |
Character |
o |
|
f |
|
- |
-f |
- |
-o |
|
o |
f |
|
a |
|
c |
u |
r |
v |
e |
|
a |
t |
|
a |
|
Milliseconds |
108 |
15 |
200 |
78 |
378 |
136 |
143 |
137 |
80 |
95 |
89 |
78 |
98 |
119 |
105 |
160 |
176 |
167 |
62 |
139 |
64 |
224 |
103 |
54 |
107 |
Character |
p |
o |
i |
n |
t |
|
p |
-p |
P |
|
o |
n |
|
t |
e |
h |
|
- |
-h |
-e |
h |
e |
|
c |
u |
Milliseconds |
223 |
62 |
187 |
62 |
58 |
64 |
289 |
223 |
199 |
266 |
119 |
54 |
172 |
134 |
117 |
42 |
183 |
258 |
151 |
134 |
131 |
37 |
105 |
130 |
56 |
Character |
r |
v |
e |
. |
|
W |
e |
|
g |
i |
v |
e |
|
p |
r |
e |
c |
e |
i |
s |
e |
-e |
-s |
-i |
-e |
Milliseconds |
143 |
168 |
58 |
78 |
128 |
278 |
180 |
95 |
120 |
104 |
78 |
66 |
97 |
119 |
23 |
133 |
171 |
81 |
128 |
56 |
121 |
127 |
144 |
145 |
149 |
Character |
i |
s |
e |
|
d |
e |
v |
e |
l |
o |
p |
m |
e |
n |
t |
s |
|
o |
f |
|
t |
h |
e |
s |
e |
Milliseconds |
56 |
67 |
103 |
159 |
80 |
136 |
159 |
86 |
99 |
248 |
81 |
191 |
64 |
121 |
55 |
128 |
81 |
79 |
81 |
79 |
122 |
79 |
185 |
79 |
94 |
Character |
|
i |
m |
p |
o |
r |
t |
a |
n |
t |
|
c |
o |
n |
c |
e |
p |
t |
s |
|
i |
n |
|
t |
h |
Milliseconds |
81 |
105 |
62 |
162 |
80 |
40 |
64 |
144 |
40 |
97 |
79 |
141 |
58 |
64 |
104 |
40 |
81 |
120 |
144 |
61 |
83 |
65 |
52 |
82 |
104 |
Character |
e |
|
n |
e |
x |
t |
|
c |
h |
a |
p |
t |
e |
r |
m |
|
u |
-u |
- |
-m |
, |
|
b |
u |
t |
Milliseconds |
54 |
105 |
65 |
54 |
212 |
52 |
147 |
144 |
62 |
121 |
118 |
107 |
54 |
105 |
122 |
38 |
274 |
224 |
151 |
152 |
80 |
63 |
81 |
80 |
80 |
Character |
|
f |
o |
r |
|
n |
o |
w |
|
w |
e |
|
u |
s |
e |
|
a |
n |
|
i |
n |
f |
o |
r |
m |
Milliseconds |
120 |
80 |
77 |
106 |
96 |
82 |
38 |
62 |
82 |
97 |
40 |
129 |
229 |
65 |
55 |
82 |
120 |
144 |
79 |
329 |
40 |
119 |
82 |
119 |
120 |
Character |
a |
l |
|
p |
p |
-p |
-p |
a |
p |
p |
r |
o |
a |
c |
h |
|
s |
o |
|
y |
o |
u |
|
w |
i |
Milliseconds |
79 |
105 |
152 |
176 |
129 |
155 |
148 |
184 |
96 |
128 |
120 |
56 |
81 |
88 |
94 |
178 |
191 |
120 |
119 |
81 |
22 |
82 |
61 |
43 |
56 |
Character |
l |
l |
|
s |
e |
e |
|
h |
o |
w |
|
t |
h |
e |
y |
|
l |
e |
a |
d |
|
n |
a |
t |
u |
Milliseconds |
78 |
131 |
52 |
83 |
80 |
80 |
128 |
95 |
38 |
42 |
80 |
105 |
121 |
56 |
127 |
96 |
104 |
95 |
82 |
103 |
79 |
249 |
160 |
121 |
86 |
Character |
f |
-f |
r |
a |
l |
l |
y |
|
t |
o |
|
t |
h |
e |
|
m |
a |
i |
n |
|
i |
d |
e |
a |
|
Milliseconds |
210 |
327 |
104 |
37 |
124 |
109 |
49 |
81 |
120 |
78 |
123 |
36 |
100 |
87 |
54 |
83 |
143 |
96 |
62 |
58 |
88 |
97 |
36 |
123 |
64 |
Character |
o |
f |
|
t |
h |
i |
s |
|
c |
h |
a |
p |
t |
e |
r |
m |
-m |
, |
|
t |
h |
e |
|
l |
i |
Milliseconds |
136 |
105 |
144 |
78 |
82 |
53 |
42 |
129 |
79 |
53 |
81 |
106 |
78 |
58 |
104 |
81 |
320 |
279 |
120 |
80 |
65 |
52 |
108 |
56 |
62 |
Character |
m |
i |
t |
, |
. |
-. |
-, |
. |
|
T |
h |
e |
|
i |
d |
a |
-a |
-d |
e |
a |
|
o |
f |
-e |
-a |
Milliseconds |
178 |
54 |
80 |
185 |
13 |
299 |
145 |
191 |
222 |
162 |
105 |
53 |
82 |
80 |
81 |
144 |
175 |
153 |
53 |
67 |
81 |
118 |
62 |
458 |
0 |
Character |
- |
-o |
-f |
d |
e |
a |
|
o |
f |
|
a |
|
m |
$l |
i |
m |
i |
t |
|
p |
l |
a |
y |
s |
|
Milliseconds |
0 |
0 |
0 |
55 |
38 |
107 |
120 |
54 |
67 |
127 |
104 |
128 |
217 |
496 |
45 |
154 |
38 |
79 |
123 |
37 |
85 |
44 |
82 |
144 |
122 |
Character |
a |
|
f |
o |
u |
n |
d |
a |
t |
i |
o |
n |
a |
l |
|
r |
o |
l |
e |
|
t |
h |
r |
o |
u |
Milliseconds |
51 |
139 |
104 |
81 |
62 |
135 |
66 |
120 |
424 |
39 |
54 |
131 |
53 |
107 |
94 |
66 |
120 |
152 |
145 |
103 |
120 |
53 |
108 |
78 |
105 |
Character |
g |
h |
|
- |
t |
|
- |
-t |
-h |
h |
o |
u |
t |
|
c |
a |
l |
c |
u |
l |
u |
s |
. |
Milliseconds |
55 |
42 |
167 |
272 |
78 |
154 |
173 |
156 |
160 |
647 |
161 |
38 |
81 |
80 |
127 |
120 |
96 |
169 |
191 |
82 |
79 |
120 |
80 |
|
WPM Timing |
Seconds |
WPM |
2.24 |
69.58 |
4.48 |
85.64 |
6.73 |
96.34 |
8.97 |
100.36 |
11.21 |
94.2 |
13.45 |
95.45 |
15.69 |
94.05 |
17.94 |
97.01 |
20.18 |
97.53 |
22.42 |
100.63 |
24.66 |
98.78 |
26.9 |
97.68 |
29.15 |
95.93 |
31.39 |
96.34 |
33.63 |
97.77 |
35.87 |
96.68 |
38.11 |
97.6 |
40.36 |
97.83 |
42.6 |
96.63 |
44.84 |
97.95 |
47.08 |
98.89 |
49.32 |
97.8 |
51.57 |
97.97 |
53.81 |
97.46 |
56.05 |
95.06 |
58.29 |
96.14 |
60.53 |
95.55 |
62.78 |
95.58 |
65.02 |
95.42 |
67.26 |
95.63 |
69.5 |
94.79 |
71.74 |
93.83 |
73.99 |
94.07 |
76.23 |
92.25 |
78.47 |
92.67 |
80.71 |
91.73 |
82.95 |
92.44 |
85.19 |
93.53 |
87.44 |
93.05 |
89.68 |
93.67 |
91.92 |
93.21 |
94.16 |
94.3 |
96.4 |
94.1 |
98.65 |
95.13 |
100.89 |
94.8 |
103.13 |
93.55 |
105.37 |
93.38 |
107.61 |
93.89 |
109.86 |
93.07 |
112.1 |
92.49 |
|