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2
×
4
=
8
{\displaystyle {{2}\times {4}}=8}
×
{\displaystyle \times }
1
{\displaystyle 1}
2
{\displaystyle 2}
3
{\displaystyle 3}
4
{\displaystyle 4}
5
{\displaystyle 5}
6
{\displaystyle 6}
7
{\displaystyle 7}
8
{\displaystyle 8}
9
{\displaystyle 9}
1
{\displaystyle 1}
1
{\displaystyle 1}
2
{\displaystyle 2}
3
{\displaystyle 3}
4
{\displaystyle 4}
5
{\displaystyle 5}
6
{\displaystyle 6}
7
{\displaystyle 7}
8
{\displaystyle 8}
9
{\displaystyle 9}
2
{\displaystyle 2}
2
{\displaystyle 2}
4
{\displaystyle 4}
6
{\displaystyle 6}
8
{\displaystyle 8}
10
{\displaystyle 10}
12
{\displaystyle 12}
14
{\displaystyle 14}
16
{\displaystyle 16}
18
{\displaystyle 18}
3
{\displaystyle 3}
3
{\displaystyle 3}
6
{\displaystyle 6}
9
{\displaystyle 9}
12
{\displaystyle 12}
15
{\displaystyle 15}
18
{\displaystyle 18}
21
{\displaystyle 21}
24
{\displaystyle 24}
27
{\displaystyle 27}
4
{\displaystyle 4}
4
{\displaystyle 4}
8
{\displaystyle 8}
12
{\displaystyle 12}
16
{\displaystyle 16}
20
{\displaystyle 20}
24
{\displaystyle 24}
28
{\displaystyle 28}
32
{\displaystyle 32}
36
{\displaystyle 36}
5
{\displaystyle 5}
5
{\displaystyle 5}
10
{\displaystyle 10}
15
{\displaystyle 15}
20
{\displaystyle 20}
25
{\displaystyle 25}
30
{\displaystyle 30}
35
{\displaystyle 35}
40
{\displaystyle 40}
45
{\displaystyle 45}
6
{\displaystyle 6}
6
{\displaystyle 6}
12
{\displaystyle 12}
18
{\displaystyle 18}
24
{\displaystyle 24}
30
{\displaystyle 30}
36
{\displaystyle 36}
42
{\displaystyle 42}
48
{\displaystyle 48}
54
{\displaystyle 54}
7
{\displaystyle 7}
7
{\displaystyle 7}
14
{\displaystyle 14}
21
{\displaystyle 21}
28
{\displaystyle 28}
35
{\displaystyle 35}
42
{\displaystyle 42}
49
{\displaystyle 49}
56
{\displaystyle 56}
63
{\displaystyle 63}
8
{\displaystyle 8}
8
{\displaystyle 8}
16
{\displaystyle 16}
24
{\displaystyle 24}
32
{\displaystyle 32}
40
{\displaystyle 40}
48
{\displaystyle 48}
56
{\displaystyle 56}
64
{\displaystyle 64}
72
{\displaystyle 72}
9
{\displaystyle 9}
9
{\displaystyle 9}
18
{\displaystyle 18}
27
{\displaystyle 27}
36
{\displaystyle 36}
45
{\displaystyle 45}
54
{\displaystyle 54}
63
{\displaystyle 63}
72
{\displaystyle 72}
81
{\displaystyle 81}
+
{\displaystyle +}
1
{\displaystyle 1}
2
{\displaystyle 2}
3
{\displaystyle 3}
4
{\displaystyle 4}
5
{\displaystyle 5}
6
{\displaystyle 6}
7
{\displaystyle 7}
8
{\displaystyle 8}
9
{\displaystyle 9}
1
{\displaystyle 1}
2
{\displaystyle 2}
3
{\displaystyle 3}
4
{\displaystyle 4}
5
{\displaystyle 5}
6
{\displaystyle 6}
7
{\displaystyle 7}
8
{\displaystyle 8}
9
{\displaystyle 9}
10
{\displaystyle 10}
2
{\displaystyle 2}
3
{\displaystyle 3}
4
{\displaystyle 4}
5
{\displaystyle 5}
6
{\displaystyle 6}
7
{\displaystyle 7}
8
{\displaystyle 8}
9
{\displaystyle 9}
10
{\displaystyle 10}
11
{\displaystyle 11}
3
{\displaystyle 3}
4
{\displaystyle 4}
5
{\displaystyle 5}
6
{\displaystyle 6}
7
{\displaystyle 7}
8
{\displaystyle 8}
9
{\displaystyle 9}
10
{\displaystyle 10}
11
{\displaystyle 11}
12
{\displaystyle 12}
4
{\displaystyle 4}
5
{\displaystyle 5}
6
{\displaystyle 6}
7
{\displaystyle 7}
8
{\displaystyle 8}
9
{\displaystyle 9}
10
{\displaystyle 10}
11
{\displaystyle 11}
12
{\displaystyle 12}
13
{\displaystyle 13}
5
{\displaystyle 5}
6
{\displaystyle 6}
7
{\displaystyle 7}
8
{\displaystyle 8}
9
{\displaystyle 9}
10
{\displaystyle 10}
11
{\displaystyle 11}
12
{\displaystyle 12}
13
{\displaystyle 13}
14
{\displaystyle 14}
6
{\displaystyle 6}
7
{\displaystyle 7}
8
{\displaystyle 8}
9
{\displaystyle 9}
10
{\displaystyle 10}
11
{\displaystyle 11}
12
{\displaystyle 12}
13
{\displaystyle 13}
14
{\displaystyle 14}
15
{\displaystyle 15}
7
{\displaystyle 7}
8
{\displaystyle 8}
9
{\displaystyle 9}
10
{\displaystyle 10}
11
{\displaystyle 11}
12
{\displaystyle 12}
13
{\displaystyle 13}
14
{\displaystyle 14}
15
{\displaystyle 15}
16
{\displaystyle 16}
8
{\displaystyle 8}
9
{\displaystyle 9}
10
{\displaystyle 10}
11
{\displaystyle 11}
12
{\displaystyle 12}
13
{\displaystyle 13}
14
{\displaystyle 14}
15
{\displaystyle 15}
16
{\displaystyle 16}
17
{\displaystyle 17}
9
{\displaystyle 9}
10
{\displaystyle 10}
11
{\displaystyle 11}
12
{\displaystyle 12}
13
{\displaystyle 13}
14
{\displaystyle 14}
15
{\displaystyle 15}
16
{\displaystyle 16}
17
{\displaystyle 17}
18
{\displaystyle 18}
−
{\displaystyle -}
1
{\displaystyle 1}
2
{\displaystyle 2}
3
{\displaystyle 3}
4
{\displaystyle 4}
5
{\displaystyle 5}
6
{\displaystyle 6}
7
{\displaystyle 7}
8
{\displaystyle 8}
9
{\displaystyle 9}
1
{\displaystyle 1}
0
{\displaystyle 0}
−
1
{\displaystyle -1}
−
2
{\displaystyle -2}
−
3
{\displaystyle -3}
−
4
{\displaystyle -4}
−
5
{\displaystyle -5}
−
6
{\displaystyle -6}
−
7
{\displaystyle -7}
−
8
{\displaystyle -8}
2
{\displaystyle 2}
1
{\displaystyle 1}
0
{\displaystyle 0}
−
1
{\displaystyle -1}
−
2
{\displaystyle -2}
−
3
{\displaystyle -3}
−
4
{\displaystyle -4}
−
5
{\displaystyle -5}
−
6
{\displaystyle -6}
−
7
{\displaystyle -7}
3
{\displaystyle 3}
2
{\displaystyle 2}
1
{\displaystyle 1}
0
{\displaystyle 0}
−
1
{\displaystyle -1}
−
2
{\displaystyle -2}
−
3
{\displaystyle -3}
−
4
{\displaystyle -4}
−
5
{\displaystyle -5}
−
6
{\displaystyle -6}
4
{\displaystyle 4}
3
{\displaystyle 3}
2
{\displaystyle 2}
1
{\displaystyle 1}
0
{\displaystyle 0}
−
1
{\displaystyle -1}
−
2
{\displaystyle -2}
−
3
{\displaystyle -3}
−
4
{\displaystyle -4}
−
5
{\displaystyle -5}
5
{\displaystyle 5}
4
{\displaystyle 4}
3
{\displaystyle 3}
2
{\displaystyle 2}
1
{\displaystyle 1}
0
{\displaystyle 0}
−
1
{\displaystyle -1}
−
2
{\displaystyle -2}
−
3
{\displaystyle -3}
−
4
{\displaystyle -4}
6
{\displaystyle 6}
5
{\displaystyle 5}
4
{\displaystyle 4}
3
{\displaystyle 3}
2
{\displaystyle 2}
1
{\displaystyle 1}
0
{\displaystyle 0}
−
1
{\displaystyle -1}
−
2
{\displaystyle -2}
−
3
{\displaystyle -3}
7
{\displaystyle 7}
6
{\displaystyle 6}
5
{\displaystyle 5}
4
{\displaystyle 4}
3
{\displaystyle 3}
2
{\displaystyle 2}
1
{\displaystyle 1}
0
{\displaystyle 0}
−
1
{\displaystyle -1}
−
2
{\displaystyle -2}
8
{\displaystyle 8}
7
{\displaystyle 7}
6
{\displaystyle 6}
5
{\displaystyle 5}
4
{\displaystyle 4}
3
{\displaystyle 3}
2
{\displaystyle 2}
1
{\displaystyle 1}
0
{\displaystyle 0}
−
1
{\displaystyle -1}
9
{\displaystyle 9}
8
{\displaystyle 8}
7
{\displaystyle 7}
6
{\displaystyle 6}
5
{\displaystyle 5}
4
{\displaystyle 4}
3
{\displaystyle 3}
2
{\displaystyle 2}
1
{\displaystyle 1}
0
{\displaystyle 0}
/
{\displaystyle /}
1
{\displaystyle 1}
2
{\displaystyle 2}
3
{\displaystyle 3}
4
{\displaystyle 4}
5
{\displaystyle 5}
6
{\displaystyle 6}
7
{\displaystyle 7}
8
{\displaystyle 8}
9
{\displaystyle 9}
1
{\displaystyle 1}
1
{\displaystyle 1}
0.5
{\displaystyle 0.5}
0.33333333333333
{\displaystyle 0.33333333333333}
0.25
{\displaystyle 0.25}
0.2
{\displaystyle 0.2}
0.16666666666667
{\displaystyle 0.16666666666667}
0.14285714285714
{\displaystyle 0.14285714285714}
0.125
{\displaystyle 0.125}
0.11111111111111
{\displaystyle 0.11111111111111}
2
{\displaystyle 2}
2
{\displaystyle 2}
1
{\displaystyle 1}
0.66666666666667
{\displaystyle 0.66666666666667}
0.5
{\displaystyle 0.5}
0.4
{\displaystyle 0.4}
0.33333333333333
{\displaystyle 0.33333333333333}
0.28571428571429
{\displaystyle 0.28571428571429}
0.25
{\displaystyle 0.25}
0.22222222222222
{\displaystyle 0.22222222222222}
3
{\displaystyle 3}
3
{\displaystyle 3}
1.5
{\displaystyle 1.5}
1
{\displaystyle 1}
0.75
{\displaystyle 0.75}
0.6
{\displaystyle 0.6}
0.5
{\displaystyle 0.5}
0.42857142857143
{\displaystyle 0.42857142857143}
0.375
{\displaystyle 0.375}
0.33333333333333
{\displaystyle 0.33333333333333}
4
{\displaystyle 4}
4
{\displaystyle 4}
2
{\displaystyle 2}
1.3333333333333
{\displaystyle 1.3333333333333}
1
{\displaystyle 1}
0.8
{\displaystyle 0.8}
0.66666666666667
{\displaystyle 0.66666666666667}
0.57142857142857
{\displaystyle 0.57142857142857}
0.5
{\displaystyle 0.5}
0.44444444444444
{\displaystyle 0.44444444444444}
5
{\displaystyle 5}
5
{\displaystyle 5}
2.5
{\displaystyle 2.5}
1.6666666666667
{\displaystyle 1.6666666666667}
1.25
{\displaystyle 1.25}
1
{\displaystyle 1}
0.83333333333333
{\displaystyle 0.83333333333333}
0.71428571428571
{\displaystyle 0.71428571428571}
0.625
{\displaystyle 0.625}
0.55555555555556
{\displaystyle 0.55555555555556}
6
{\displaystyle 6}
6
{\displaystyle 6}
3
{\displaystyle 3}
2
{\displaystyle 2}
1.5
{\displaystyle 1.5}
1.2
{\displaystyle 1.2}
1
{\displaystyle 1}
0.85714285714286
{\displaystyle 0.85714285714286}
0.75
{\displaystyle 0.75}
0.66666666666667
{\displaystyle 0.66666666666667}
7
{\displaystyle 7}
7
{\displaystyle 7}
3.5
{\displaystyle 3.5}
2.3333333333333
{\displaystyle 2.3333333333333}
1.75
{\displaystyle 1.75}
1.4
{\displaystyle 1.4}
1.1666666666667
{\displaystyle 1.1666666666667}
1
{\displaystyle 1}
0.875
{\displaystyle 0.875}
0.77777777777778
{\displaystyle 0.77777777777778}
8
{\displaystyle 8}
8
{\displaystyle 8}
4
{\displaystyle 4}
2.6666666666667
{\displaystyle 2.6666666666667}
2
{\displaystyle 2}
1.6
{\displaystyle 1.6}
1.3333333333333
{\displaystyle 1.3333333333333}
1.1428571428571
{\displaystyle 1.1428571428571}
1
{\displaystyle 1}
0.88888888888889
{\displaystyle 0.88888888888889}
9
{\displaystyle 9}
9
{\displaystyle 9}
4.5
{\displaystyle 4.5}
3
{\displaystyle 3}
2.25
{\displaystyle 2.25}
1.8
{\displaystyle 1.8}
1.5
{\displaystyle 1.5}
1.2857142857143
{\displaystyle 1.2857142857143}
1.125
{\displaystyle 1.125}
1
{\displaystyle 1}
m
o
d
{\displaystyle mod}
1
{\displaystyle 1}
2
{\displaystyle 2}
3
{\displaystyle 3}
4
{\displaystyle 4}
5
{\displaystyle 5}
6
{\displaystyle 6}
7
{\displaystyle 7}
8
{\displaystyle 8}
9
{\displaystyle 9}
1
{\displaystyle 1}
0
{\displaystyle 0}
1
{\displaystyle 1}
1
{\displaystyle 1}
1
{\displaystyle 1}
1
{\displaystyle 1}
1
{\displaystyle 1}
1
{\displaystyle 1}
1
{\displaystyle 1}
1
{\displaystyle 1}
2
{\displaystyle 2}
0
{\displaystyle 0}
0
{\displaystyle 0}
2
{\displaystyle 2}
2
{\displaystyle 2}
2
{\displaystyle 2}
2
{\displaystyle 2}
2
{\displaystyle 2}
2
{\displaystyle 2}
2
{\displaystyle 2}
3
{\displaystyle 3}
0
{\displaystyle 0}
1
{\displaystyle 1}
0
{\displaystyle 0}
3
{\displaystyle 3}
3
{\displaystyle 3}
3
{\displaystyle 3}
3
{\displaystyle 3}
3
{\displaystyle 3}
3
{\displaystyle 3}
4
{\displaystyle 4}
0
{\displaystyle 0}
0
{\displaystyle 0}
1
{\displaystyle 1}
0
{\displaystyle 0}
4
{\displaystyle 4}
4
{\displaystyle 4}
4
{\displaystyle 4}
4
{\displaystyle 4}
4
{\displaystyle 4}
5
{\displaystyle 5}
0
{\displaystyle 0}
1
{\displaystyle 1}
2
{\displaystyle 2}
1
{\displaystyle 1}
0
{\displaystyle 0}
5
{\displaystyle 5}
5
{\displaystyle 5}
5
{\displaystyle 5}
5
{\displaystyle 5}
6
{\displaystyle 6}
0
{\displaystyle 0}
0
{\displaystyle 0}
0
{\displaystyle 0}
2
{\displaystyle 2}
1
{\displaystyle 1}
0
{\displaystyle 0}
6
{\displaystyle 6}
6
{\displaystyle 6}
6
{\displaystyle 6}
7
{\displaystyle 7}
0
{\displaystyle 0}
1
{\displaystyle 1}
1
{\displaystyle 1}
3
{\displaystyle 3}
2
{\displaystyle 2}
1
{\displaystyle 1}
0
{\displaystyle 0}
7
{\displaystyle 7}
7
{\displaystyle 7}
8
{\displaystyle 8}
0
{\displaystyle 0}
0
{\displaystyle 0}
2
{\displaystyle 2}
0
{\displaystyle 0}
3
{\displaystyle 3}
2
{\displaystyle 2}
1
{\displaystyle 1}
0
{\displaystyle 0}
8
{\displaystyle 8}
9
{\displaystyle 9}
0
{\displaystyle 0}
1
{\displaystyle 1}
0
{\displaystyle 0}
1
{\displaystyle 1}
4
{\displaystyle 4}
3
{\displaystyle 3}
2
{\displaystyle 2}
1
{\displaystyle 1}
0
{\displaystyle 0}
x
y
{\displaystyle x^{y}}
1
{\displaystyle 1}
2
{\displaystyle 2}
3
{\displaystyle 3}
4
{\displaystyle 4}
5
{\displaystyle 5}
6
{\displaystyle 6}
7
{\displaystyle 7}
8
{\displaystyle 8}
9
{\displaystyle 9}
1
{\displaystyle 1}
1
{\displaystyle 1}
1
{\displaystyle 1}
1
{\displaystyle 1}
1
{\displaystyle 1}
1
{\displaystyle 1}
1
{\displaystyle 1}
1
{\displaystyle 1}
1
{\displaystyle 1}
1
{\displaystyle 1}
2
{\displaystyle 2}
2
{\displaystyle 2}
4
{\displaystyle 4}
8
{\displaystyle 8}
16
{\displaystyle 16}
32
{\displaystyle 32}
64
{\displaystyle 64}
128
{\displaystyle 128}
256
{\displaystyle 256}
512
{\displaystyle 512}
3
{\displaystyle 3}
3
{\displaystyle 3}
9
{\displaystyle 9}
27
{\displaystyle 27}
81
{\displaystyle 81}
243
{\displaystyle 243}
729
{\displaystyle 729}
2187
{\displaystyle 2187}
6561
{\displaystyle 6561}
19683
{\displaystyle 19683}
4
{\displaystyle 4}
4
{\displaystyle 4}
16
{\displaystyle 16}
64
{\displaystyle 64}
256
{\displaystyle 256}
1024
{\displaystyle 1024}
4096
{\displaystyle 4096}
16384
{\displaystyle 16384}
65536
{\displaystyle 65536}
262144
{\displaystyle 262144}
5
{\displaystyle 5}
5
{\displaystyle 5}
25
{\displaystyle 25}
125
{\displaystyle 125}
625
{\displaystyle 625}
3125
{\displaystyle 3125}
15625
{\displaystyle 15625}
78125
{\displaystyle 78125}
390625
{\displaystyle 390625}
1953125
{\displaystyle 1953125}
6
{\displaystyle 6}
6
{\displaystyle 6}
36
{\displaystyle 36}
216
{\displaystyle 216}
1296
{\displaystyle 1296}
7776
{\displaystyle 7776}
46656
{\displaystyle 46656}
279936
{\displaystyle 279936}
1679616
{\displaystyle 1679616}
10077696
{\displaystyle 10077696}
7
{\displaystyle 7}
7
{\displaystyle 7}
49
{\displaystyle 49}
343
{\displaystyle 343}
2401
{\displaystyle 2401}
16807
{\displaystyle 16807}
117649
{\displaystyle 117649}
823543
{\displaystyle 823543}
5764801
{\displaystyle 5764801}
40353607
{\displaystyle 40353607}
8
{\displaystyle 8}
8
{\displaystyle 8}
64
{\displaystyle 64}
512
{\displaystyle 512}
4096
{\displaystyle 4096}
32768
{\displaystyle 32768}
262144
{\displaystyle 262144}
2097152
{\displaystyle 2097152}
16777216
{\displaystyle 16777216}
134217728
{\displaystyle 134217728}
9
{\displaystyle 9}
9
{\displaystyle 9}
81
{\displaystyle 81}
729
{\displaystyle 729}
6561
{\displaystyle 6561}
59049
{\displaystyle 59049}
531441
{\displaystyle 531441}
4782969
{\displaystyle 4782969}
43046721
{\displaystyle 43046721}
387420489
{\displaystyle 387420489}
Dual number
1+0.5ε
ε
0
=
1
{\displaystyle {{\varepsilon }^{0}}=1}
ε
1
=
ε
{\displaystyle {{\varepsilon }^{1}}=\varepsilon }
ε
2
=
0
{\displaystyle {{\varepsilon }^{2}}=0}
ε
3
=
0
{\displaystyle {{\varepsilon }^{3}}=0}
1
+
ε
=
1
+
0.5
ε
{\displaystyle {\sqrt {{1}+{\varepsilon }}}=1+0.5\varepsilon }
0.1
+
ε
=
0.31622776601684
+
1.5811388300842
ε
{\displaystyle {\sqrt {{0.1}+{\varepsilon }}}=0.31622776601684+1.5811388300842\varepsilon }
0.01
+
ε
=
0.1
+
5
ε
{\displaystyle {\sqrt {{0.01}+{\varepsilon }}}=0.1+5\varepsilon }
0.001
+
ε
=
0.031622776601684
+
15.811388300842
ε
{\displaystyle {\sqrt {{0.001}+{\varepsilon }}}=0.031622776601684+15.811388300842\varepsilon }
1
×
10
−
7
+
ε
=
0.00031622776601684
+
1581.1388300842
ε
{\displaystyle {\sqrt {{{1}\times {{10}^{-{7}}}}+{\varepsilon }}}=0.00031622776601684+1581.1388300842\varepsilon }
1
×
10
−
10
+
ε
=
1
×
10
−
05
+
50000
ε
{\displaystyle {\sqrt {{{1}\times {{10}^{-{10}}}}+{\varepsilon }}}=1\times 10^{-05}+50000\varepsilon }
(
1
+
ε
)
−
1
=
1
−
ε
{\displaystyle \left({{1}+{\varepsilon }}\right)^{-1}=1-\varepsilon }
(
0.1
+
ε
)
−
1
=
10
−
100
ε
{\displaystyle \left({{0.1}+{\varepsilon }}\right)^{-1}=10-100\varepsilon }
(
0.01
+
ε
)
−
1
=
100
−
10000
ε
{\displaystyle \left({{0.01}+{\varepsilon }}\right)^{-1}=100-10000\varepsilon }
(
0.001
+
ε
)
−
1
=
1000
−
1000000
ε
{\displaystyle \left({{0.001}+{\varepsilon }}\right)^{-1}=1000-1000000\varepsilon }
(
1
×
10
−
7
+
ε
)
−
1
=
10000000
−
1
×
10
+
14
ε
{\displaystyle \left({{{1}\times {{10}^{-{7}}}}+{\varepsilon }}\right)^{-1}=10000000-1\times 10^{+14}\varepsilon }
(
1
×
10
−
10
+
ε
)
−
1
=
10000000000
−
1
×
10
+
20
ε
{\displaystyle \left({{{1}\times {{10}^{-{10}}}}+{\varepsilon }}\right)^{-1}=10000000000-1\times 10^{+20}\varepsilon }
1
+
ε
=
1
+
0.5
ε
{\displaystyle {\sqrt {{1}+{\varepsilon }}}=1+0.5\varepsilon }
1
+
ε
1
+
ε
=
1
+
ε
{\displaystyle {{\sqrt {{1}+{\varepsilon }}}\,{\sqrt {{1}+{\varepsilon }}}}=1+\varepsilon }
e
2
+
3
ε
=
7.3890560989307
+
22.167168296792
ε
{\displaystyle e^{{2}+{{3}\,{\varepsilon }}}=7.3890560989307+22.167168296792\varepsilon }
ln
e
2
+
3
ε
=
2
+
3
ε
{\displaystyle \ln e^{{2}+{{3}\,{\varepsilon }}}=2+3\varepsilon }
(
2
+
3
ε
)
5
+
7
ε
=
32
+
395.26496844543
ε
{\displaystyle {{\left({{2}+{{3}\,{\varepsilon }}}\right)}^{{5}+{{7}\,{\varepsilon }}}}=32+395.26496844543\varepsilon }
log
2
+
3
ε
(
(
2
+
3
ε
)
5
+
7
ε
)
=
5
+
7
ε
{\displaystyle \log _{{2}+{{3}\,{\varepsilon }}}\left({{\left({{2}+{{3}\,{\varepsilon }}}\right)}^{{5}+{{7}\,{\varepsilon }}}}\right)=5+7\varepsilon }
(
5
+
7
ε
)
−
1
=
0.2
−
0.28
ε
{\displaystyle \left({{5}+{{7}\,{\varepsilon }}}\right)^{-1}=0.2-0.28\varepsilon }
(
5
+
7
ε
)
(
5
+
7
ε
)
−
1
=
1
{\displaystyle {{\left({{5}+{{7}\,{\varepsilon }}}\right)}\,{\left({{5}+{{7}\,{\varepsilon }}}\right)^{-1}}}=1}
sin
(
1.5
+
2
ε
)
=
0.99749498660405
+
0.14147440333541
ε
{\displaystyle \sin \left({{1.5}+{{2}\,{\varepsilon }}}\right)=0.99749498660405+0.14147440333541\varepsilon }
arcsin
sin
(
1.5
+
2
ε
)
=
1.5
+
2
ε
{\displaystyle \arcsin \sin \left({{1.5}+{{2}\,{\varepsilon }}}\right)=1.5+2\varepsilon }
arccos
(
0.5
+
π
ε
)
=
1.0471975511966
−
3.6275987284684
ε
{\displaystyle \arccos \left({{0.5}+{{\pi }\,{\varepsilon }}}\right)=1.0471975511966-3.6275987284684\varepsilon }
cos
arccos
(
0.5
+
π
ε
)
=
0.5
+
3.1415926535898
ε
{\displaystyle \cos \arccos \left({{0.5}+{{\pi }\,{\varepsilon }}}\right)=0.5+3.1415926535898\varepsilon }
×
{\displaystyle \times }
1
{\displaystyle 1}
ε
{\displaystyle \varepsilon }
1
{\displaystyle 1}
1
{\displaystyle 1}
ε
{\displaystyle \varepsilon }
ε
{\displaystyle \varepsilon }
ε
{\displaystyle \varepsilon }
0
{\displaystyle 0}
×
{\displaystyle \times }
1
{\displaystyle 1}
i
{\displaystyle i}
ε
{\displaystyle \varepsilon }
i
ε
{\displaystyle i\varepsilon }
1
{\displaystyle 1}
1
{\displaystyle 1}
i
{\displaystyle i}
ε
{\displaystyle \varepsilon }
i
ε
{\displaystyle i\varepsilon }
i
{\displaystyle i}
i
{\displaystyle i}
−
1
{\displaystyle -1}
i
ε
{\displaystyle i\varepsilon }
−
ε
{\displaystyle -\varepsilon }
ε
{\displaystyle \varepsilon }
ε
{\displaystyle \varepsilon }
−
i
ε
{\displaystyle -i\varepsilon }
0
{\displaystyle 0}
0
{\displaystyle 0}
i
ε
{\displaystyle i\varepsilon }
i
ε
{\displaystyle i\varepsilon }
ε
{\displaystyle \varepsilon }
0
{\displaystyle 0}
0
{\displaystyle 0}
×
{\displaystyle \times }
1
{\displaystyle 1}
i
{\displaystyle i}
ε
j
{\displaystyle \varepsilon j}
ε
k
{\displaystyle \varepsilon k}
1
{\displaystyle 1}
1
{\displaystyle 1}
i
{\displaystyle i}
ε
j
{\displaystyle \varepsilon j}
ε
k
{\displaystyle \varepsilon k}
i
{\displaystyle i}
i
{\displaystyle i}
−
1
{\displaystyle -1}
ε
k
{\displaystyle \varepsilon k}
−
ε
j
{\displaystyle -\varepsilon j}
ε
j
{\displaystyle \varepsilon j}
ε
j
{\displaystyle \varepsilon j}
−
ε
k
{\displaystyle -\varepsilon k}
0
{\displaystyle 0}
0
{\displaystyle 0}
ε
k
{\displaystyle \varepsilon k}
ε
k
{\displaystyle \varepsilon k}
ε
j
{\displaystyle \varepsilon j}
0
{\displaystyle 0}
0
{\displaystyle 0}
上述
文档
嵌入
自
Module:沙盒/a2569875/NumberTest/doc
。
(
编辑
|
历史
)
编者可以在本模块的沙盒
(
创建
|
镜像
)
和测试样例
(
创建
)
页面进行实验。
本模块的子页面
。
local
p
=
{}
return
p
开关有限宽度模式
