设 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 在 [tex=2.929x1.357]QpSc4Vs3d1MTNQAH70ziEw==[/tex] 上连续, [tex=15.214x2.714]hwwEFF1lM66NsXg2BtY7qLySRzxsmq+0lIPLrJkpGry3RmXGg5V0AW1t8KThK6Bo+uPhhFrrphSNtj23ahdtoD7dz5UiP7Z4lVAmYgmX+BY=[/tex] 求 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]

2022-06-16

设 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 在 [tex=2.929x1.357]QpSc4Vs3d1MTNQAH70ziEw==[/tex] 上连续, [tex=15.214x2.714]hwwEFF1lM66NsXg2BtY7qLySRzxsmq+0lIPLrJkpGry3RmXGg5V0AW1t8KThK6Bo+uPhhFrrphSNtj23ahdtoD7dz5UiP7Z4lVAmYgmX+BY=[/tex] 求 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]

答案：

设 [tex=8.714x2.714]WdYFOXfG5nnGW/WgiEfXS6ECvTRKdytB5Q3owQAbkSKrN7dpsE9DnIXFbZnhMxIN[/tex]  则有 [tex=12.929x2.429]ofcNknDiM5BcLJUxZ7YAq2EOYVoM7MenOh9Vvn4qfuCdK1jjDyZHmhwCGUUQNd5btZWj+3rNdcMdRegx288ilQ==[/tex],两端积分 [tex=21.857x2.714]WdYFOXfG5nnGW/WgiEfXS6ECvTRKdytB5Q3owQAbkSIKguvSXzOR8bMlp6Aeh6z3slRP7b4po1Ey3Vqa/Ozq+6dSiDw6NZUrz/mpbgIX9hoQzNmSE9XoL7TwUA8+PEaA9MT/JZmNI/wo5hOdqCj82q38+n8YQXs+y8FR5ULar6U=[/tex]利用被积函数的奇偶性得：[tex=9.429x2.643]xNgPgOmBEi8Bvks/pku2D0U6ir7wsd20w+3KjItskBv1np7tgvB4n02lDAVGSwsv9hrmjXSz7A0CVANroCyGYg==[/tex][tex=11.429x1.643]dJGCnF6UyCTQeGp0d0BssXjN9JJ5TkYgQAXwlTm4Rr74GD/+ioGzFvvXWE6tquBLznMHIM/w3EOsPH0Exua416N8vJRYmEfVG6PIyNCws4EasUyFBCSzsObYUtP1/NVTRgaVem+fcVy4JSaaCoJdqw==[/tex][tex=8.0x2.643]ln4g/96jA+It6zagxKz37xcYrIqNLriDNWTh/5OASN/nA4jryAuyHS8hAkO9lsrWrwy2voENs/QDO0ezSFyjig==[/tex][tex=20.0x2.714]sLs3dWCaxtjTPbq1xPxwxg8ci10T/JfAIKK/SLA6wASd+03Qpu0BPfwqfI+onsXmmgxSQFaLzeLN2Dd6Bj2fdxElx7pKJG3ykiqgFpUFJ58ktlltm2thrrq8KCHqjQk0zBmD4Ycs3fPkIo2qVwXPJnEx25gw7fIzlt5Fai4OoSQ=[/tex]

举一反三

内容

0
设 [tex=11.643x1.357]oTHWUnECoN4UNiGFVZoHA6aTyRMpVVzUfRE1/OUCXUda+cK8PWDBj4DGgVDCvWMH[/tex] 求适合下列条件的点[tex=0.571x0.786]ZKO2xs0EgSemzoH7MSmYTA==[/tex](1) [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 的最大、最小值点.(2) [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 增加最快、最慢的点.(3) [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 图像的切线斜率增加最快的点.
1
设函数[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]连续，[tex=7.214x2.643]2ZJQOGzPP+WXkSjEhj0ot/8XbWpx0nNxKCDDSnV56LI=[/tex]，试证：(1) 若[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]是奇函数，则[tex=2.0x1.357]6D04mYW2ivsCmiBu0E4w8w==[/tex]是偶函数;(2) 若[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]是偶函数，则[tex=2.0x1.357]6D04mYW2ivsCmiBu0E4w8w==[/tex]是奇函数.
2
设[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]是周期为[tex=1.071x1.0]tieuzjBYrMcmxP3HXZSPGQ==[/tex]的函数，它在[tex=2.929x1.357]QpSc4Vs3d1MTNQAH70ziEw==[/tex]上的表达式为[tex=11.571x3.357]ACpG7W/lXiEwdW69ASBj8yR7ZB6xaVwV4+6J1bev3ILj3tA7vDVPo+BrnXZPAmu+emfWfKcv63KHT7/Qxg1KijeKB2NCcnT7DP7krA+8LEo6CbtyQfb+n7/d0Von8dTRK8UD0vyIYGyNQdvoFTEbYA==[/tex]将[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]展开成Fourier级数.
3
设 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex] 连续, 且积分 [tex=8.5x2.786]BL7n5ddwJNHAhb4R+nxZA5ywU1gR80QQQ33J/mBX1n0oq5p5lu1KM79R224W0TLc[/tex] 与 [tex=0.571x0.786]ZKO2xs0EgSemzoH7MSmYTA==[/tex] 无关. 求 [tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex].
4
将下列以[tex=1.071x1.0]tieuzjBYrMcmxP3HXZSPGQ==[/tex]为周期的函数[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]展开为傅里叶级数，如果[tex=1.857x1.357]bZ4KhrFbnCaidqbMGQZfww==[/tex]在[tex=2.929x1.357]QpSc4Vs3d1MTNQAH70ziEw==[/tex]上的表达式：[tex=11.286x1.5]uoK9dXTY5b+zhHj119y5pCgzedituUCxRZojcLgLEJHLEJv3ATnVkUij7MXL+UY/[/tex].