Official speed |
129.57 wpm (80.02 seconds elapsed during race) |
Without ending ping |
130.11 wpm (332 ms delay sending score to TypeRacer’s server) |
Timerless |
130.45 wpm (209 ms elapsed before first character typed; 79.48 seconds elapsed during race) |
Timerless minus one |
130.30 wpm, ignoring the first character typed |
Race Start |
March 12, 2024 8:55:22pm UTC |
Race Finish |
March 12, 2024 8:56:42pm UTC |
Outcome |
Win (1 of 3) |
Opponents |
2. exalted777 (111.16 wpm)
3. osama_alkhodairy (83.21 wpm)
|
Accuracy |
97.7% |
Points |
349.85 |
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 at tool that helps us understand how a chacnnge in one quanittity is related to a chance gge in another. How does the speed of a falling object change a as s a function of time? How does the level of water in a barrel change as a function of the maouamount of liquid poured into it? We see chanfgege ocucuring inring in nearly everythig ng we observe in the wolrld and unviverse, and powerful modern instruments help us see more and more. In this esection 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 PO on the curve .W. We give precise developments of the ise important concepts in the next chapter, but for now we use an informal approach so you will see how the leay lead naturally to the main idea of this chapter, the limit. The idea of a limit plays a foundational role throughotu caut calculus. |
Timing |
Character |
C |
a |
l |
c |
u |
l |
u |
s |
|
i |
s |
|
a |
t |
-t |
|
t |
o |
o |
l |
|
t |
h |
a |
t |
Milliseconds |
209 |
58 |
62 |
84 |
235 |
295 |
130 |
48 |
54 |
49 |
74 |
59 |
67 |
73 |
349 |
93 |
62 |
79 |
107 |
115 |
58 |
40 |
90 |
25 |
54 |
Character |
|
h |
e |
l |
p |
s |
|
u |
s |
|
u |
n |
d |
e |
r |
s |
t |
a |
n |
d |
|
h |
o |
w |
|
Milliseconds |
56 |
275 |
103 |
67 |
38 |
85 |
39 |
72 |
80 |
56 |
69 |
59 |
51 |
84 |
56 |
99 |
69 |
7 |
107 |
63 |
60 |
34 |
61 |
15 |
68 |
Character |
a |
|
c |
h |
a |
c |
n |
-n |
-c |
n |
g |
e |
|
i |
n |
|
o |
n |
e |
|
q |
u |
a |
n |
i |
Milliseconds |
86 |
114 |
73 |
127 |
47 |
141 |
25 |
296 |
103 |
128 |
77 |
49 |
33 |
60 |
45 |
79 |
103 |
40 |
90 |
56 |
71 |
98 |
130 |
75 |
87 |
Character |
t |
-t |
-i |
t |
i |
t |
y |
|
i |
s |
|
r |
e |
l |
a |
t |
e |
d |
|
t |
o |
|
a |
|
c |
Milliseconds |
34 |
258 |
94 |
64 |
81 |
83 |
180 |
41 |
92 |
66 |
45 |
114 |
52 |
81 |
57 |
63 |
61 |
102 |
0 |
129 |
35 |
73 |
66 |
103 |
63 |
Character |
h |
a |
n |
c |
e |
|
- |
-e |
g |
-g |
-c |
g |
e |
|
i |
n |
|
a |
n |
o |
t |
h |
e |
r |
. |
Milliseconds |
62 |
53 |
90 |
40 |
50 |
33 |
182 |
99 |
221 |
81 |
106 |
47 |
43 |
29 |
49 |
49 |
78 |
72 |
43 |
59 |
58 |
77 |
49 |
51 |
70 |
Character |
|
H |
o |
w |
|
d |
o |
e |
s |
|
t |
h |
e |
|
s |
p |
e |
e |
d |
|
o |
f |
|
a |
|
Milliseconds |
61 |
98 |
61 |
66 |
44 |
63 |
65 |
50 |
122 |
43 |
80 |
53 |
50 |
61 |
70 |
72 |
84 |
129 |
74 |
14 |
94 |
62 |
43 |
308 |
76 |
Character |
f |
a |
l |
l |
i |
n |
g |
|
o |
b |
j |
e |
c |
t |
|
c |
h |
a |
n |
g |
e |
|
a |
|
a |
Milliseconds |
58 |
57 |
56 |
122 |
117 |
56 |
41 |
48 |
45 |
91 |
172 |
41 |
46 |
139 |
51 |
114 |
67 |
62 |
75 |
40 |
40 |
69 |
73 |
103 |
108 |
Character |
-a |
s |
|
- |
-s |
- |
s |
|
a |
|
f |
u |
n |
c |
t |
i |
o |
n |
|
o |
f |
|
t |
i |
m |
Milliseconds |
130 |
83 |
57 |
94 |
104 |
103 |
95 |
65 |
67 |
108 |
26 |
67 |
108 |
50 |
134 |
9 |
88 |
69 |
63 |
67 |
82 |
82 |
58 |
40 |
45 |
Character |
e |
? |
|
H |
o |
w |
|
d |
o |
e |
s |
|
t |
h |
e |
|
l |
e |
v |
e |
l |
|
o |
f |
|
Milliseconds |
41 |
122 |
159 |
125 |
60 |
78 |
45 |
60 |
47 |
69 |
118 |
55 |
70 |
46 |
64 |
56 |
93 |
66 |
48 |
81 |
55 |
69 |
80 |
28 |
99 |
Character |
w |
a |
t |
e |
r |
|
i |
n |
|
a |
|
b |
a |
r |
r |
e |
l |
|
c |
h |
a |
n |
g |
e |
|
Milliseconds |
65 |
60 |
81 |
80 |
78 |
17 |
99 |
28 |
77 |
26 |
131 |
52 |
46 |
71 |
174 |
54 |
91 |
79 |
31 |
76 |
64 |
75 |
50 |
49 |
326 |
Character |
a |
s |
|
a |
|
f |
u |
n |
c |
t |
i |
o |
n |
|
o |
f |
|
t |
h |
e |
|
m |
a |
o |
u |
Milliseconds |
79 |
117 |
80 |
74 |
95 |
18 |
76 |
115 |
42 |
140 |
13 |
85 |
66 |
64 |
77 |
95 |
79 |
69 |
53 |
90 |
51 |
65 |
4 |
97 |
77 |
Character |
-u |
-o |
-a |
-m |
a |
m |
o |
u |
n |
t |
|
o |
f |
|
l |
i |
q |
u |
i |
d |
|
p |
o |
u |
r |
Milliseconds |
185 |
91 |
94 |
116 |
108 |
53 |
100 |
80 |
116 |
36 |
75 |
55 |
91 |
43 |
64 |
54 |
311 |
72 |
111 |
49 |
57 |
242 |
232 |
83 |
103 |
Character |
e |
d |
|
i |
n |
t |
o |
|
i |
t |
? |
|
W |
e |
|
s |
e |
e |
|
c |
h |
a |
n |
f |
g |
Milliseconds |
77 |
95 |
8 |
68 |
50 |
93 |
39 |
124 |
72 |
61 |
108 |
232 |
156 |
157 |
58 |
99 |
131 |
122 |
63 |
90 |
70 |
34 |
111 |
74 |
17 |
Character |
e |
-e |
-g |
-f |
g |
e |
|
o |
c |
u |
-u |
c |
u |
r |
i |
n |
g |
|
i |
n |
-n |
-i |
- |
-g |
-n |
Milliseconds |
15 |
223 |
112 |
368 |
156 |
47 |
33 |
88 |
85 |
111 |
202 |
96 |
83 |
68 |
63 |
44 |
62 |
45 |
48 |
45 |
176 |
85 |
98 |
113 |
111 |
Character |
-i |
r |
i |
n |
g |
|
i |
n |
|
n |
e |
a |
r |
l |
y |
|
e |
v |
e |
r |
y |
t |
h |
i |
g |
Milliseconds |
122 |
75 |
74 |
64 |
55 |
45 |
76 |
49 |
71 |
127 |
65 |
27 |
56 |
48 |
133 |
67 |
104 |
77 |
73 |
52 |
153 |
97 |
86 |
40 |
99 |
Character |
|
- |
-g |
n |
g |
|
w |
e |
|
o |
b |
s |
e |
r |
v |
e |
|
i |
n |
|
t |
h |
e |
|
w |
Milliseconds |
65 |
162 |
100 |
194 |
55 |
66 |
57 |
49 |
51 |
53 |
71 |
83 |
117 |
69 |
28 |
89 |
40 |
85 |
26 |
78 |
36 |
84 |
52 |
68 |
56 |
Character |
o |
l |
-l |
r |
l |
d |
|
a |
n |
d |
|
u |
n |
v |
-v |
i |
v |
e |
r |
s |
e |
, |
|
a |
n |
Milliseconds |
52 |
190 |
177 |
98 |
76 |
68 |
52 |
87 |
225 |
111 |
32 |
77 |
44 |
99 |
353 |
92 |
64 |
104 |
63 |
105 |
117 |
77 |
54 |
253 |
56 |
Character |
d |
|
p |
o |
w |
e |
r |
f |
u |
l |
|
m |
o |
d |
e |
r |
n |
|
i |
n |
s |
t |
r |
u |
m |
Milliseconds |
82 |
41 |
65 |
34 |
52 |
595 |
63 |
110 |
47 |
137 |
66 |
113 |
36 |
53 |
107 |
53 |
48 |
94 |
54 |
57 |
31 |
63 |
118 |
32 |
117 |
Character |
e |
n |
t |
s |
|
h |
e |
l |
p |
|
u |
s |
|
s |
e |
e |
|
m |
o |
r |
e |
|
a |
n |
d |
Milliseconds |
83 |
45 |
63 |
150 |
51 |
50 |
100 |
72 |
58 |
215 |
119 |
130 |
82 |
111 |
152 |
133 |
70 |
42 |
54 |
59 |
55 |
43 |
132 |
77 |
79 |
Character |
|
m |
o |
r |
e |
. |
|
I |
n |
|
t |
h |
i |
s |
|
e |
-e |
s |
e |
c |
t |
i |
o |
n |
|
Milliseconds |
47 |
74 |
59 |
61 |
52 |
75 |
65 |
78 |
132 |
60 |
55 |
40 |
50 |
60 |
56 |
240 |
251 |
73 |
108 |
107 |
164 |
45 |
79 |
81 |
55 |
Character |
w |
e |
|
i |
n |
t |
r |
o |
d |
u |
c |
e |
|
t |
h |
e |
|
i |
d |
e |
a |
s |
|
o |
f |
Milliseconds |
68 |
91 |
153 |
141 |
39 |
54 |
120 |
61 |
95 |
90 |
88 |
57 |
57 |
94 |
63 |
71 |
64 |
75 |
59 |
65 |
66 |
106 |
48 |
92 |
45 |
Character |
|
a |
v |
e |
r |
a |
g |
e |
|
a |
n |
d |
|
i |
n |
s |
t |
a |
n |
t |
a |
n |
e |
o |
u |
Milliseconds |
60 |
49 |
109 |
58 |
91 |
59 |
75 |
36 |
49 |
122 |
89 |
62 |
50 |
84 |
29 |
67 |
52 |
63 |
71 |
66 |
262 |
123 |
104 |
151 |
68 |
Character |
s |
|
r |
a |
t |
e |
s |
|
o |
f |
|
c |
h |
a |
n |
g |
e |
, |
|
a |
n |
d |
|
s |
h |
Milliseconds |
113 |
95 |
104 |
47 |
112 |
70 |
157 |
71 |
319 |
133 |
126 |
135 |
83 |
89 |
83 |
49 |
48 |
61 |
50 |
56 |
74 |
55 |
34 |
141 |
65 |
Character |
o |
w |
|
t |
h |
a |
t |
|
t |
h |
e |
y |
|
a |
r |
e |
|
c |
l |
o |
s |
e |
l |
y |
|
Milliseconds |
55 |
58 |
37 |
84 |
69 |
29 |
76 |
35 |
80 |
53 |
62 |
83 |
163 |
46 |
52 |
54 |
64 |
109 |
67 |
130 |
26 |
135 |
80 |
102 |
68 |
Character |
r |
e |
l |
a |
t |
e |
d |
|
t |
o |
|
t |
h |
e |
|
s |
l |
o |
p |
e |
|
o |
f |
|
a |
Milliseconds |
89 |
56 |
55 |
56 |
82 |
63 |
96 |
5 |
201 |
39 |
348 |
116 |
83 |
50 |
64 |
104 |
70 |
148 |
74 |
40 |
49 |
97 |
54 |
74 |
19 |
Character |
|
c |
u |
r |
v |
e |
|
a |
t |
|
a |
|
p |
o |
i |
n |
t |
|
P |
O |
|
- |
-O |
|
o |
Milliseconds |
104 |
111 |
73 |
94 |
150 |
28 |
59 |
113 |
73 |
60 |
72 |
76 |
48 |
37 |
127 |
66 |
10 |
74 |
120 |
0 |
56 |
269 |
108 |
154 |
87 |
Character |
n |
|
t |
h |
e |
|
c |
u |
r |
v |
e |
|
. |
W |
-W |
-. |
- |
. |
|
W |
e |
|
g |
i |
v |
Milliseconds |
46 |
68 |
53 |
71 |
56 |
50 |
214 |
78 |
73 |
131 |
39 |
93 |
57 |
71 |
195 |
100 |
116 |
119 |
88 |
49 |
133 |
68 |
70 |
99 |
119 |
Character |
e |
|
p |
r |
e |
c |
i |
s |
e |
|
d |
e |
v |
e |
l |
o |
p |
m |
e |
n |
t |
s |
|
o |
f |
Milliseconds |
151 |
61 |
191 |
78 |
64 |
128 |
105 |
26 |
126 |
49 |
81 |
73 |
79 |
68 |
28 |
123 |
65 |
147 |
81 |
84 |
40 |
133 |
70 |
87 |
69 |
Character |
|
t |
h |
e |
|
i |
-i |
- |
s |
e |
|
i |
m |
p |
o |
r |
t |
a |
n |
t |
|
c |
o |
n |
c |
Milliseconds |
67 |
87 |
44 |
53 |
47 |
107 |
282 |
104 |
183 |
120 |
68 |
92 |
127 |
88 |
51 |
13 |
116 |
59 |
92 |
60 |
52 |
172 |
51 |
53 |
48 |
Character |
e |
p |
t |
s |
|
i |
n |
|
t |
h |
e |
|
n |
e |
x |
t |
|
c |
h |
a |
p |
t |
e |
r |
, |
Milliseconds |
55 |
64 |
66 |
122 |
35 |
71 |
18 |
72 |
60 |
87 |
58 |
56 |
90 |
57 |
140 |
146 |
45 |
99 |
68 |
57 |
91 |
35 |
83 |
78 |
48 |
Character |
|
b |
u |
t |
|
f |
o |
r |
|
n |
o |
w |
|
w |
e |
|
u |
s |
e |
|
a |
n |
|
i |
n |
Milliseconds |
56 |
114 |
68 |
48 |
52 |
86 |
35 |
99 |
46 |
42 |
60 |
54 |
52 |
106 |
142 |
41 |
92 |
66 |
130 |
30 |
79 |
98 |
84 |
74 |
39 |
Character |
f |
o |
r |
m |
a |
l |
|
a |
p |
p |
r |
o |
a |
c |
h |
|
s |
o |
|
y |
o |
u |
|
w |
i |
Milliseconds |
50 |
91 |
70 |
79 |
72 |
346 |
96 |
51 |
62 |
106 |
46 |
102 |
306 |
73 |
87 |
61 |
77 |
62 |
86 |
67 |
48 |
37 |
70 |
56 |
61 |
Character |
l |
l |
|
s |
e |
e |
|
h |
o |
w |
|
t |
h |
e |
|
l |
e |
a |
-a |
-e |
-l |
- |
y |
|
l |
Milliseconds |
123 |
94 |
60 |
75 |
159 |
136 |
64 |
32 |
58 |
51 |
72 |
55 |
55 |
67 |
189 |
107 |
72 |
38 |
127 |
86 |
107 |
112 |
106 |
53 |
90 |
Character |
e |
a |
d |
|
n |
a |
t |
u |
r |
a |
l |
l |
y |
|
t |
o |
|
t |
h |
e |
|
m |
a |
i |
n |
Milliseconds |
72 |
37 |
68 |
35 |
187 |
83 |
49 |
72 |
74 |
38 |
55 |
96 |
45 |
47 |
102 |
78 |
59 |
59 |
76 |
60 |
59 |
52 |
86 |
41 |
56 |
Character |
|
i |
d |
e |
a |
|
o |
f |
|
t |
h |
i |
s |
|
c |
h |
a |
p |
t |
e |
r |
, |
|
t |
h |
Milliseconds |
55 |
105 |
98 |
72 |
64 |
52 |
109 |
63 |
59 |
76 |
27 |
46 |
94 |
23 |
70 |
78 |
63 |
75 |
61 |
82 |
78 |
14 |
97 |
73 |
66 |
Character |
e |
|
l |
i |
m |
i |
t |
. |
|
T |
h |
e |
|
i |
d |
e |
a |
|
o |
f |
|
a |
|
l |
i |
Milliseconds |
81 |
57 |
11 |
57 |
145 |
48 |
82 |
80 |
63 |
61 |
51 |
78 |
38 |
101 |
72 |
50 |
38 |
78 |
124 |
68 |
73 |
53 |
86 |
88 |
36 |
Character |
m |
i |
t |
|
p |
l |
a |
y |
s |
|
a |
|
f |
o |
u |
n |
d |
a |
t |
i |
o |
n |
a |
l |
|
Milliseconds |
176 |
59 |
90 |
54 |
48 |
51 |
55 |
51 |
147 |
56 |
140 |
88 |
125 |
107 |
60 |
108 |
28 |
73 |
84 |
10 |
77 |
65 |
60 |
302 |
135 |
Character |
r |
o |
l |
e |
|
t |
h |
r |
o |
u |
g |
h |
o |
t |
u |
|
c |
a |
-a |
-c |
- |
-u |
-t |
u |
t |
Milliseconds |
53 |
45 |
112 |
40 |
52 |
71 |
65 |
126 |
53 |
72 |
82 |
78 |
55 |
82 |
14 |
60 |
84 |
48 |
143 |
88 |
98 |
114 |
106 |
124 |
76 |
Character |
|
c |
a |
l |
c |
u |
l |
u |
s |
. |
Milliseconds |
20 |
130 |
27 |
67 |
93 |
82 |
125 |
151 |
49 |
78 |
|
WPM Timing |
Seconds |
WPM |
1.6 |
97.48 |
3.2 |
108.72 |
4.8 |
132.47 |
6.4 |
123.72 |
8 |
121.47 |
9.6 |
116.22 |
11.2 |
126.4 |
12.8 |
128.41 |
14.4 |
129.14 |
16 |
128.22 |
17.6 |
131.56 |
19.2 |
134.97 |
20.8 |
135.55 |
22.41 |
131.76 |
24.01 |
131.47 |
25.61 |
130.75 |
27.21 |
127.47 |
28.81 |
123.72 |
30.41 |
123.13 |
32.01 |
122.6 |
33.61 |
123.54 |
35.21 |
122.02 |
36.81 |
121.28 |
38.41 |
123.1 |
40.01 |
123.27 |
41.61 |
123.43 |
43.21 |
123.58 |
44.81 |
125.33 |
46.41 |
125.66 |
48.01 |
124.97 |
49.61 |
126.74 |
51.21 |
127.47 |
52.81 |
127.7 |
54.41 |
127.91 |
56.01 |
127.04 |
57.61 |
126.01 |
59.21 |
126.46 |
60.81 |
125.69 |
62.41 |
126.89 |
64.01 |
127.85 |
65.62 |
128.38 |
67.22 |
128.36 |
68.82 |
128.34 |
70.42 |
127.81 |
72.02 |
128.97 |
73.62 |
130.08 |
75.22 |
130.98 |
76.82 |
130.91 |
78.42 |
130.38 |
80.02 |
129.57 |
|