把下列函数展开为Fourier级数，它们在一个周期内的定义分别为：[tex=9.786x1.357]IWx2n1TFkWgtG4EqIE4SxgaLwmiMKPSZBN7jaRAyv/s=[/tex]

2022-05-30

把下列函数展开为Fourier级数，它们在一个周期内的定义分别为：[tex=9.786x1.357]IWx2n1TFkWgtG4EqIE4SxgaLwmiMKPSZBN7jaRAyv/s=[/tex]

答案：

[tex=1.857x1.357]BGkv0wKMIn2R4tUsMDFEFA==[/tex]在[tex=2.643x1.357]Lye101DFWXdreM9prWxbvg==[/tex]内连续，因此[tex=21.357x3.071]EpNOgNd4/gX8883vrKXktTxPClzNlYv3NWZ6hmXD0xlHGcYGrS0UXJIYOggoHOxsKkXcclIel5d/+gbSQD8gl6qZKWY2Z1Bwo/y2Hx25x8KStd/XIeMtCBljNS/QtKuu236WC3gSCFlxW5JLpOY0UwvhwkcJJay3QpzJ2wxbZTEV2+9HXRyo7j3eLXRO7nHHTXL4JdfOvloQUVfN7MuR6A==[/tex][tex=22.786x12.071]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[/tex][tex=25.286x6.214]a0s3MH7cLIdmiBRR0YN067dVnkV92ljngsLJ3LhrhVO7HkyftnTwOBbO4OIpTpMBFXNDwvuOpEzsLDiyMVXvuIaZ0/rmt4aDqf/0clKVcAYJng+I/+C7U3Uz13UmoHxXhlX3LiE5BK8dHoGZzzojcMIvHsSNK9HUORgXAtKAVe8HwTbnQbhTJVJ6ILDQqvIVRXlTLc4aQV5PIag9K4M8O2JlMs2rIt6CK6UR5FLA3AZhu5A3jlEca4Zbm9ybVvexYE/Xwaam3SjoFIStaiflx7S79IeHKtYy8Jv21ro5VvI05XkOFVVbT+vin98rSsqSb3wDFlYgF/3uQJLFR0RQVDBu+UH1DfWBOVxwhE83+vGdplUT8u9uvdDh7+V70kCH1gZHGttc5dIQgL2X65bQ3k14KG90ZW12fPDFBuglV9rN7q1dnPRuTXVSbqBGfGxNUHokCCmGWIXVE/4i23uGeg==[/tex]所以[tex=24.571x3.571]4QZmYKuA4PeV5LcYCiKx7ubLmwyjgpVFaUMB0y50PGWDci7p/dS6nRrng5/HV6uT/pxQshfO0biyFjFD0sXhiqGLlc942AK1qUWdNUziMMFVD2LrrEQZA4yNVTVC5OplMzk4bLhucbRtH3eXWrauw9t+eiQnLKrIahMgzLZndLdtdOXEC2Va7iT00/0R5okqCJBAP3bNMNVwBtrabKp55r2rD7slrGeLGtLmUYbxwkc=[/tex]，[tex=2.786x1.357]OUehs9ajQZXAhjSSfiVZmw==[/tex]

举一反三

内容

0
将下列以[tex=1.071x1.0]tieuzjBYrMcmxP3HXZSPGQ==[/tex]为周期的函数展开成Fourier级数，它们在一个周期内分别定义为：[tex=11.786x2.786]ACpG7W/lXiEwdW69ASBj84fMrBxwMU644a9+h+bYe65tIZo2eJxJaqC9JBvkpuEO1NL13myoq9BqBqc52QhSTrk96lvYyeFH36AK4TtPS4YCYQbHS5B24PMXKKY3V8PVv9IyL6Ixlf46f3tNvZ8NUQ==[/tex]
1
将下列以[tex=1.071x1.0]tieuzjBYrMcmxP3HXZSPGQ==[/tex]为周期的函数展开成Fourier级数，它们在一个周期内分别定义为：[tex=5.357x1.5]gM2i5baU3YBqHJYr82tOFQ==[/tex]，[tex=5.214x1.071]u1/YDWxpoVh9F/V9zqvqeTMVri3sqIBBjZw5SsSB2Pc=[/tex].
2
将下列以[tex=1.071x1.0]tieuzjBYrMcmxP3HXZSPGQ==[/tex]为周期的函数展开成Fourier级数，它们在一个周期内分别定义为：[tex=12.0x2.929]ACpG7W/lXiEwdW69ASBj84qoYJO3m1mabcnCHpRr13ejFFiOX+yRIRgAlZJFy9XysWk2XlKu7snDvseH4u1cWFpr52so6UlqHqq5NMpVBv2EghTJOFVg6wFnruyDaiMwY5HW2FQdggFwquP2gRXYGA==[/tex]（[tex=0.571x0.786]7G1MINzwputr5mgALyjQfA==[/tex]，[tex=0.429x1.0]dX3JVuFw9r8t2KlWf+/Z+A==[/tex]为常数, 且[tex=4.143x1.071]s/pfy3+Y58zyYZgBJhqbrQ==[/tex]）.
3
将下列函数展开为指定的Fourier级数.[tex=5.143x2.143]65STRfmeJpsBGxWEnjmP0kX8xuXtOB6OBcoykUtzIiU=[/tex]，[tex=3.929x1.357]fHypTF8qEraADhqFVLuxbQ==[/tex]展开成正弦级数.
4
下列关于Fourier级数的命题，错误的是 ____ . A: 如果\(f(x)\)是一个偶函数，则\(f(x)\)的Fourier级数满足\(b_n = 0\)； B: 如果\(f(x)\)是一个奇函数，则\(f(x)\)的Fourier级数满足\(a_n = 0\)； C: 周期为\(2\pi\)的三角多项式的Fourier级数就是它本身； D: 定义在\((-\infty,+\infty)\)上的非周期函数\(f(x)\),不存在Fourier级数展开形式；