Official speed |
130.40 wpm (79.51 seconds elapsed during race) |
Without ending ping |
130.62 wpm (135 ms delay sending score to TypeRacer’s server) |
Timerless |
131.15 wpm (321 ms elapsed before first character typed; 79.05 seconds elapsed during race) |
Timerless minus one |
131.00 wpm, ignoring the first character typed |
Race Start |
October 23, 2023 1:24:51pm UTC |
Race Finish |
October 23, 2023 1:26:10pm UTC |
Outcome |
Win (1 of 4) |
Opponents |
2. whathaha3 (117.41 wpm)
3. arkosammy_1208 (117.26 wpm)
|
Accuracy |
97.7% |
Points |
352.08 |
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 tool that helps us understand how a change in one qunaanititity is related to a change in another. How does the speed of a falling object change aas a function of tine?me? Hoow w doe the s the level of water in a barrel change as a function of the amontunt of liquid poured into it? We see change occuring inring in nearly soeeverything ewe observe in the world and universe, and powerful modern instruments help us see more and more. In this section we tiintroduce the ideas of average and instantaenous neous rates of change, and show that they ware closely related toth the lsopslope 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 approcach so you will see how they lead naturally to the main idea of this cahhapter, the limit. The idea of a limit plays a foundational role throughout chalculus. |
Timing |
Character |
C |
a |
l |
c |
u |
l |
u |
s |
|
i |
s |
|
a |
|
t |
o |
o |
l |
|
t |
h |
a |
t |
|
h |
Milliseconds |
321 |
66 |
58 |
92 |
76 |
156 |
66 |
153 |
231 |
75 |
132 |
52 |
82 |
79 |
55 |
61 |
125 |
117 |
31 |
59 |
72 |
12 |
81 |
20 |
57 |
Character |
e |
l |
p |
s |
|
u |
s |
|
u |
n |
d |
e |
r |
s |
t |
a |
n |
d |
|
h |
o |
w |
|
a |
|
Milliseconds |
73 |
52 |
98 |
83 |
50 |
60 |
83 |
42 |
198 |
126 |
40 |
147 |
20 |
90 |
79 |
58 |
47 |
84 |
78 |
61 |
32 |
49 |
51 |
573 |
62 |
Character |
c |
h |
a |
n |
g |
e |
|
i |
n |
|
o |
n |
e |
|
q |
u |
n |
a |
-a |
-n |
a |
n |
i |
t |
i |
Milliseconds |
72 |
46 |
79 |
48 |
68 |
39 |
40 |
11 |
42 |
98 |
40 |
50 |
49 |
35 |
268 |
77 |
168 |
85 |
157 |
111 |
57 |
38 |
108 |
11 |
138 |
Character |
-i |
-t |
-i |
t |
i |
t |
y |
|
i |
s |
|
r |
e |
l |
a |
t |
e |
d |
|
t |
o |
|
a |
|
c |
Milliseconds |
243 |
133 |
336 |
119 |
64 |
94 |
60 |
92 |
76 |
31 |
61 |
127 |
29 |
82 |
118 |
69 |
55 |
131 |
25 |
133 |
59 |
82 |
47 |
98 |
83 |
Character |
h |
a |
n |
g |
e |
|
i |
n |
|
a |
n |
o |
t |
h |
e |
r |
. |
|
H |
o |
w |
|
d |
o |
e |
Milliseconds |
84 |
106 |
21 |
82 |
50 |
49 |
36 |
27 |
94 |
56 |
58 |
36 |
69 |
26 |
75 |
39 |
51 |
34 |
181 |
52 |
71 |
54 |
65 |
54 |
95 |
Character |
s |
|
t |
h |
e |
|
s |
p |
e |
e |
d |
|
o |
f |
|
a |
|
f |
a |
l |
l |
i |
n |
g |
|
Milliseconds |
22 |
37 |
84 |
58 |
49 |
57 |
62 |
81 |
101 |
132 |
125 |
44 |
48 |
78 |
76 |
74 |
75 |
74 |
50 |
96 |
108 |
54 |
42 |
35 |
52 |
Character |
o |
b |
j |
e |
c |
t |
|
c |
h |
a |
n |
g |
e |
|
a |
a |
-a |
s |
|
a |
|
f |
u |
n |
c |
Milliseconds |
72 |
84 |
115 |
54 |
172 |
97 |
54 |
100 |
50 |
51 |
77 |
35 |
47 |
53 |
82 |
131 |
335 |
51 |
54 |
87 |
80 |
49 |
78 |
127 |
50 |
Character |
t |
i |
o |
n |
|
o |
f |
|
t |
i |
n |
e |
? |
-? |
-e |
-n |
m |
e |
? |
|
H |
o |
o |
w |
|
Milliseconds |
112 |
24 |
22 |
50 |
54 |
84 |
72 |
141 |
68 |
49 |
44 |
82 |
182 |
175 |
114 |
107 |
115 |
55 |
202 |
79 |
296 |
52 |
190 |
99 |
49 |
Character |
- |
-w |
-o |
w |
|
d |
o |
e |
|
t |
h |
e |
|
- |
-t |
-h |
-e |
- |
s |
|
t |
h |
e |
|
l |
Milliseconds |
183 |
122 |
103 |
36 |
25 |
67 |
52 |
83 |
57 |
79 |
80 |
34 |
57 |
161 |
143 |
0 |
0 |
350 |
207 |
75 |
126 |
63 |
73 |
27 |
73 |
Character |
e |
v |
e |
l |
|
o |
f |
|
w |
a |
t |
e |
r |
|
i |
n |
|
a |
|
b |
a |
r |
r |
e |
l |
Milliseconds |
50 |
109 |
25 |
35 |
68 |
125 |
74 |
44 |
94 |
65 |
178 |
56 |
73 |
28 |
48 |
34 |
81 |
9 |
128 |
68 |
100 |
121 |
126 |
23 |
56 |
Character |
|
c |
h |
a |
n |
g |
e |
|
a |
s |
|
a |
|
f |
u |
n |
c |
t |
i |
o |
n |
|
o |
f |
|
Milliseconds |
43 |
69 |
86 |
44 |
90 |
28 |
36 |
45 |
64 |
124 |
64 |
84 |
81 |
84 |
90 |
131 |
30 |
154 |
15 |
34 |
24 |
140 |
70 |
68 |
62 |
Character |
t |
h |
e |
|
a |
m |
o |
n |
t |
-t |
-n |
u |
n |
t |
|
o |
f |
|
l |
i |
q |
u |
i |
d |
|
Milliseconds |
112 |
14 |
53 |
57 |
67 |
77 |
91 |
182 |
75 |
211 |
112 |
464 |
151 |
70 |
40 |
60 |
87 |
36 |
104 |
80 |
86 |
78 |
35 |
80 |
64 |
Character |
p |
o |
u |
r |
e |
d |
|
i |
n |
t |
o |
|
i |
t |
? |
|
W |
e |
|
s |
e |
e |
|
c |
h |
Milliseconds |
74 |
110 |
24 |
47 |
34 |
119 |
48 |
44 |
13 |
88 |
44 |
291 |
108 |
29 |
147 |
121 |
168 |
99 |
87 |
73 |
190 |
147 |
30 |
87 |
38 |
Character |
a |
n |
g |
e |
|
o |
c |
c |
u |
r |
i |
n |
g |
|
i |
n |
-i |
-n |
- |
-g |
-n |
-i |
r |
i |
n |
Milliseconds |
62 |
68 |
45 |
13 |
52 |
54 |
90 |
142 |
89 |
86 |
71 |
49 |
43 |
63 |
56 |
47 |
302 |
0 |
170 |
120 |
125 |
107 |
85 |
67 |
44 |
Character |
g |
|
i |
n |
|
n |
e |
a |
r |
l |
y |
|
s |
o |
-o |
e |
-e |
-s |
e |
v |
e |
r |
y |
t |
h |
Milliseconds |
56 |
25 |
59 |
33 |
89 |
76 |
61 |
30 |
34 |
39 |
112 |
52 |
95 |
62 |
213 |
50 |
154 |
150 |
84 |
72 |
67 |
91 |
88 |
121 |
33 |
Character |
i |
n |
g |
|
e |
-e |
w |
e |
|
o |
b |
s |
e |
r |
v |
e |
|
i |
n |
|
t |
h |
e |
|
w |
Milliseconds |
49 |
94 |
41 |
63 |
203 |
266 |
90 |
39 |
62 |
120 |
141 |
116 |
47 |
50 |
146 |
66 |
51 |
46 |
21 |
77 |
45 |
50 |
65 |
56 |
64 |
Character |
o |
r |
l |
d |
|
a |
n |
d |
|
u |
n |
i |
v |
e |
r |
s |
e |
, |
|
a |
n |
d |
|
p |
o |
Milliseconds |
46 |
56 |
79 |
50 |
58 |
111 |
74 |
61 |
51 |
78 |
130 |
57 |
87 |
111 |
51 |
109 |
47 |
53 |
47 |
44 |
63 |
63 |
38 |
111 |
107 |
Character |
w |
e |
r |
f |
u |
l |
|
m |
o |
d |
e |
r |
n |
|
i |
n |
s |
t |
r |
u |
m |
e |
n |
t |
s |
Milliseconds |
68 |
33 |
64 |
146 |
56 |
96 |
93 |
74 |
95 |
68 |
142 |
49 |
81 |
103 |
66 |
58 |
221 |
58 |
122 |
24 |
123 |
56 |
79 |
41 |
50 |
Character |
|
h |
e |
l |
p |
|
u |
s |
|
s |
e |
e |
|
m |
o |
r |
e |
|
a |
n |
d |
|
m |
o |
r |
Milliseconds |
37 |
66 |
71 |
48 |
78 |
97 |
63 |
74 |
77 |
126 |
50 |
133 |
34 |
32 |
51 |
77 |
45 |
29 |
68 |
78 |
60 |
30 |
78 |
61 |
63 |
Character |
e |
. |
|
I |
n |
|
t |
h |
i |
s |
|
s |
e |
c |
t |
i |
o |
n |
|
w |
e |
|
t |
i |
-i |
Milliseconds |
19 |
92 |
75 |
148 |
109 |
77 |
54 |
51 |
19 |
101 |
17 |
131 |
10 |
140 |
104 |
30 |
10 |
35 |
96 |
57 |
38 |
93 |
99 |
67 |
207 |
Character |
-t |
i |
n |
t |
r |
o |
d |
u |
c |
e |
|
t |
h |
e |
|
i |
d |
e |
a |
s |
|
o |
f |
|
a |
Milliseconds |
120 |
100 |
8 |
46 |
142 |
42 |
100 |
92 |
75 |
124 |
35 |
93 |
45 |
65 |
72 |
110 |
23 |
242 |
60 |
124 |
58 |
47 |
88 |
188 |
81 |
Character |
v |
e |
r |
a |
g |
e |
|
a |
n |
d |
|
i |
n |
s |
t |
a |
n |
t |
a |
e |
n |
o |
u |
s |
|
Milliseconds |
143 |
89 |
86 |
66 |
85 |
60 |
32 |
61 |
82 |
61 |
48 |
143 |
30 |
73 |
69 |
80 |
422 |
114 |
92 |
276 |
81 |
41 |
93 |
46 |
49 |
Character |
- |
-s |
-u |
-o |
-n |
-e |
n |
e |
o |
u |
s |
|
r |
a |
t |
e |
s |
|
o |
f |
|
c |
h |
a |
n |
Milliseconds |
170 |
129 |
120 |
124 |
124 |
106 |
107 |
24 |
95 |
319 |
60 |
38 |
106 |
63 |
106 |
76 |
132 |
71 |
86 |
85 |
54 |
91 |
43 |
12 |
135 |
Character |
g |
e |
, |
|
a |
n |
d |
|
s |
h |
o |
w |
|
t |
h |
a |
t |
|
t |
h |
e |
y |
|
w |
-w |
Milliseconds |
48 |
23 |
120 |
84 |
53 |
59 |
41 |
56 |
142 |
74 |
40 |
61 |
60 |
58 |
51 |
45 |
63 |
40 |
94 |
30 |
64 |
62 |
28 |
220 |
199 |
Character |
a |
r |
e |
|
c |
l |
o |
s |
e |
l |
y |
|
r |
e |
l |
a |
t |
e |
d |
|
t |
o |
t |
h |
-h |
Milliseconds |
89 |
47 |
39 |
49 |
113 |
29 |
132 |
35 |
35 |
73 |
104 |
36 |
60 |
22 |
76 |
94 |
62 |
31 |
138 |
51 |
71 |
43 |
120 |
136 |
216 |
Character |
-t |
|
t |
h |
e |
|
l |
s |
o |
p |
-l |
-s |
-o |
-p |
s |
l |
o |
p |
e |
|
o |
f |
|
a |
|
Milliseconds |
125 |
44 |
36 |
41 |
53 |
56 |
60 |
0 |
136 |
88 |
253 |
0 |
0 |
0 |
77 |
55 |
118 |
78 |
21 |
37 |
121 |
52 |
66 |
44 |
103 |
Character |
c |
u |
r |
v |
e |
|
a |
t |
|
a |
|
p |
o |
i |
n |
t |
|
P |
|
o |
n |
|
t |
h |
e |
Milliseconds |
44 |
117 |
187 |
266 |
61 |
34 |
97 |
68 |
35 |
103 |
79 |
101 |
59 |
41 |
22 |
43 |
46 |
179 |
108 |
97 |
64 |
68 |
62 |
46 |
68 |
Character |
|
c |
u |
r |
v |
e |
|
- |
. |
|
W |
e |
|
g |
i |
v |
e |
|
p |
r |
e |
c |
i |
s |
e |
Milliseconds |
42 |
96 |
54 |
66 |
143 |
25 |
419 |
275 |
148 |
56 |
106 |
74 |
124 |
109 |
72 |
82 |
35 |
28 |
68 |
106 |
58 |
108 |
79 |
83 |
21 |
Character |
|
d |
e |
v |
e |
l |
o |
p |
m |
e |
n |
t |
s |
|
o |
f |
|
t |
h |
e |
s |
e |
|
i |
m |
Milliseconds |
115 |
88 |
137 |
134 |
39 |
316 |
149 |
47 |
218 |
83 |
80 |
34 |
58 |
23 |
88 |
74 |
37 |
118 |
37 |
65 |
130 |
51 |
48 |
42 |
103 |
Character |
p |
o |
r |
t |
a |
n |
t |
|
c |
o |
n |
c |
e |
p |
t |
s |
|
i |
n |
|
t |
h |
e |
|
n |
Milliseconds |
119 |
107 |
57 |
134 |
25 |
43 |
69 |
33 |
106 |
34 |
40 |
81 |
138 |
67 |
34 |
70 |
37 |
78 |
69 |
41 |
45 |
55 |
71 |
64 |
193 |
Character |
e |
x |
t |
|
c |
h |
a |
p |
t |
e |
r |
, |
|
b |
u |
t |
|
f |
o |
r |
|
n |
o |
w |
|
Milliseconds |
41 |
117 |
78 |
23 |
94 |
44 |
55 |
65 |
66 |
72 |
54 |
35 |
38 |
102 |
68 |
84 |
52 |
71 |
51 |
108 |
81 |
12 |
45 |
70 |
67 |
Character |
w |
e |
|
u |
s |
e |
|
a |
n |
|
i |
n |
f |
o |
r |
m |
a |
l |
|
a |
p |
p |
r |
o |
c |
Milliseconds |
311 |
55 |
59 |
116 |
115 |
22 |
46 |
81 |
49 |
84 |
103 |
47 |
76 |
61 |
96 |
55 |
86 |
104 |
104 |
63 |
97 |
139 |
80 |
36 |
104 |
Character |
-c |
a |
c |
h |
|
s |
o |
|
y |
o |
u |
|
w |
i |
l |
l |
|
s |
e |
e |
|
h |
o |
w |
|
Milliseconds |
343 |
51 |
81 |
68 |
40 |
96 |
53 |
105 |
34 |
57 |
80 |
25 |
35 |
66 |
126 |
111 |
33 |
56 |
43 |
140 |
35 |
66 |
31 |
65 |
53 |
Character |
t |
h |
e |
y |
|
l |
e |
a |
d |
|
n |
a |
t |
u |
r |
a |
l |
l |
y |
|
t |
o |
|
t |
h |
Milliseconds |
264 |
66 |
79 |
55 |
51 |
83 |
36 |
29 |
111 |
38 |
79 |
59 |
58 |
60 |
76 |
47 |
60 |
108 |
103 |
28 |
56 |
51 |
106 |
15 |
76 |
Character |
e |
|
m |
a |
i |
n |
|
i |
d |
e |
a |
|
o |
f |
|
t |
h |
i |
s |
|
c |
a |
h |
-h |
-a |
Milliseconds |
67 |
93 |
32 |
94 |
29 |
87 |
46 |
129 |
105 |
119 |
9 |
68 |
47 |
143 |
103 |
75 |
49 |
15 |
57 |
58 |
95 |
85 |
35 |
228 |
110 |
Character |
h |
a |
p |
t |
e |
r |
, |
|
t |
h |
e |
|
l |
i |
m |
i |
t |
. |
|
T |
h |
e |
|
i |
d |
Milliseconds |
97 |
50 |
69 |
67 |
69 |
62 |
47 |
48 |
91 |
55 |
55 |
56 |
163 |
101 |
148 |
72 |
108 |
102 |
95 |
161 |
91 |
46 |
50 |
67 |
95 |
Character |
e |
a |
|
o |
f |
|
a |
|
l |
i |
m |
i |
t |
|
p |
l |
a |
y |
s |
|
a |
|
f |
o |
u |
Milliseconds |
265 |
83 |
105 |
117 |
141 |
97 |
80 |
140 |
138 |
99 |
127 |
48 |
97 |
52 |
58 |
100 |
44 |
78 |
66 |
50 |
81 |
83 |
22 |
69 |
207 |
Character |
n |
d |
a |
t |
i |
o |
n |
a |
l |
|
r |
o |
l |
e |
|
t |
h |
r |
o |
u |
g |
h |
o |
u |
t |
Milliseconds |
218 |
89 |
79 |
82 |
58 |
34 |
72 |
85 |
73 |
64 |
70 |
53 |
128 |
40 |
52 |
54 |
65 |
101 |
12 |
54 |
77 |
89 |
202 |
39 |
79 |
Character |
|
c |
h |
-h |
a |
l |
c |
u |
l |
u |
s |
. |
Milliseconds |
55 |
182 |
80 |
208 |
69 |
78 |
79 |
120 |
118 |
125 |
68 |
65 |
|
WPM Timing |
Seconds |
WPM |
1.59 |
98.1 |
3.18 |
128.29 |
4.77 |
128.29 |
6.36 |
128.29 |
7.95 |
114.7 |
9.54 |
123.26 |
11.13 |
132.6 |
12.72 |
135.83 |
14.31 |
134.16 |
15.9 |
130.55 |
17.49 |
123.48 |
19.08 |
117.6 |
20.67 |
121.9 |
22.26 |
124.51 |
23.85 |
124.77 |
25.44 |
124.04 |
27.03 |
124.29 |
28.62 |
124.51 |
30.21 |
123.12 |
31.8 |
121.12 |
33.39 |
120.74 |
34.98 |
123.14 |
36.57 |
124.68 |
38.16 |
126.09 |
39.75 |
127.99 |
41.34 |
128.29 |
42.93 |
128.57 |
44.53 |
129.1 |
46.12 |
125.42 |
47.71 |
124.51 |
49.3 |
126.34 |
50.89 |
127.11 |
52.48 |
126 |
54.07 |
125.4 |
55.66 |
126.78 |
57.25 |
125.35 |
58.84 |
125.43 |
60.43 |
126.1 |
62.02 |
127.51 |
63.61 |
128.48 |
65.2 |
129.02 |
66.79 |
128.47 |
68.38 |
129.34 |
69.97 |
130.69 |
71.56 |
130.63 |
73.15 |
130.75 |
74.74 |
130.21 |
76.33 |
130.33 |
77.92 |
131.06 |
79.51 |
130.4 |
|