如图示,设在弦[tex=1.571x1.214]5jCRvPeX9JCOjkpX/QJlawifeNMps2l84IiSgpjY+sg=[/tex]上方有一条光滑的曲线弧[tex=9.929x1.643]SS/D+3a4MweQ0YODPtJ+9VzunVeQwuh6ERjpYaGiwKtjy3Z65GT1+kBjzBwwuh3yPPoHGj1nEPkZ+aXS+u/bXw==[/tex].若对于弧[tex=1.571x1.357]PMGb7h9IjxfEHb9PBGfRng==[/tex]上任意点[tex=2.929x1.357]25jAdQ4EVKhlk22U111yAg==[/tex], 弧[tex=1.429x1.357]4qugySyuftH1Uf7Q83wkbA==[/tex]与弦[tex=1.429x1.214]C26ycS8I13Ebk2Vr0pXdr+UaAjA+Q2ufM5vUsljuMDs=[/tex]围成图形的面积等于点[tex=2.929x1.357]25jAdQ4EVKhlk22U111yAg==[/tex]横坐标的立方,求曲线弧[tex=1.571x1.357]4qbj/7HUN9CF+z3PNvWriihrjogvmWNxKzUOpPVxTQU=[/tex]的方程[tex=3.143x1.357]ee8UVMi6ncRcyeiuuPl14g==[/tex].[img=213x185]179c74d07eb5b2e.png[/img]
举一反三
- 设有连接点[tex=2.857x1.357]YWtkApgNymqGUfnZfMRAzQ==[/tex]和点[tex=2.857x1.357]k1fyl87ihgHd1j9V9uPr9A==[/tex]的一段向上凸的曲线弧[tex=1.571x1.357]iyz0b29FzOWj+O8UfHQWWA==[/tex],对于曲线弧[tex=1.571x1.357]rW86OGq3hMsl9h7e/G8r9w==[/tex]上任意一 点[tex=2.929x1.357]XSSvH23cbIYXnWROlVlfSQ==[/tex],曲线弧[tex=1.571x1.357]tD2/O1XfhtRoupoWo8qnHYa4NvYh/wGtk3C3dQ5ObAo=[/tex]与直线段下[tex=1.643x1.286]XlLEr7N9Oo7TQ6z2s+nn8WIlcroIJEExdXdlqzKqO44=[/tex]所围图形的面积为[tex=1.0x1.214]lLaJjo1WAgOsvIRtwh+bGQ==[/tex],求曲线弧[tex=1.571x1.357]iyz0b29FzOWj+O8UfHQWWA==[/tex]的方程。
- 设在[tex=1.857x1.286]c+Z4Z8NGrrwjZdvrK/yxYw==[/tex]面内有一分布着质量的曲线弧L,在点[tex=2.214x1.286]Cv8pj5T6IBFBezH8urMOfw==[/tex]处它的线密度为[tex=2.857x1.286]HAgr4vvbbRh39nHbtGr1Yw==[/tex]。用对弧长的曲线积分分别表达:(1)这曲线弧对x轴,对y轴的转动惯量[tex=2.214x1.286]0hlnfAqdsj8gXUVV2/uwZg==[/tex](2)这曲线弧的质心坐标[tex=1.571x1.071]rxaJ+U7633dB5xw/8lPdQtGi1SYqW7bm4LWqUs+5u10=[/tex]
- 若:(1)函数 f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]有导数,而函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数;(2)函数f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]没有导数,而函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]有导数;(3)函数f(x)在点[tex=3.714x1.357]7VByCIzkNySq3s2l9I6f5zccNJDeV+6SQrVr3iwjgB0=[/tex]没有导数及函数g(x)在点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]没有导数,则函数[tex=5.643x1.357]GmtX7Vop79exGU/rpqXUYw==[/tex]在已知点[tex=2.286x1.0]DSJKaWfJALImFxxTg/8qhA==[/tex]的可微性怎样?
- 判断下列命题是否为真:(1)[tex=3.643x1.357]/5abqJjwKZ1qr+6hsVFF5EBvfq3ggOFNlHMClz0h9nk=[/tex](2)[tex=2.929x1.357]rGJpyjIjJpbcoBTWxP0Jiw==[/tex](3)[tex=4.5x1.357]2wycHMoqU83MyEp17iBils58bR7YLuCTI2G9NVAdlfY=[/tex](4)[tex=5.214x1.357]CTz2gu+IIm1GgNmYMGaduCRtA41wnW4WqwRWwEhq6aA=[/tex](5)[tex=4.857x1.357]1DcE2BMMOaZhTuxR/mjgsboXxfg5ET59Dp4I/jjEDuw=[/tex](6)[tex=4.643x1.357]BSryrsQYOvTP2hTWRu6t4nAuJwlSs4L9jaq70EpB+Us=[/tex](7)若[tex=6.0x1.357]y0IZLUnBO88nR8WBZYvd7QXv5S1OMINV5cQNzPyiyAc=[/tex],则[tex=3.429x1.357]1brfPwTkVVIX4GfoMIUskA==[/tex](8)若[tex=7.643x1.357]MhLfJXZnhbXiB0x3oNtFzThV4Y1mJxe1VYr7PkJE/T6hmTD3WWp+UxbNwvUQ6DHk[/tex],则[tex=4.143x1.357]LZUA94ISo1po5HWsOVeBCjo0rMvj7uw3bGw5HiZenrI=[/tex]
- 求函数[tex=3.286x1.429]kdT+eIE7CHPynuN6CaN40g==[/tex](抛物线)隐函数的导数[tex=1.071x1.429]BUw1BPFU3fsJlAl/vt9M9w==[/tex]当x=2与y=4及当x=2与y=0时,[tex=0.786x1.357]Hq6bf3CacUy07X+VImUMaA==[/tex]等于什么?