求曲线 [tex=2.143x1.214]qa5WVUu3fWRoGfEYEJkBIg==[/tex], [tex=2.071x1.429]iLiArOi6Py4Z6Re2WSQrLQ==[/tex] 在点 [tex=2.286x1.357]IznYKk7kywvI5iLU+xoABA==[/tex] 处的曲率.

2022-06-17

求曲线 [tex=2.143x1.214]qa5WVUu3fWRoGfEYEJkBIg==[/tex], [tex=2.071x1.429]iLiArOi6Py4Z6Re2WSQrLQ==[/tex] 在点 [tex=2.286x1.357]IznYKk7kywvI5iLU+xoABA==[/tex] 处的曲率.

答案：

解: 当 [tex=2.429x1.0]CN/1pboBqLxTG+spiDy+LQ==[/tex], [tex=2.357x1.214]gGdLfojHBJ8/4hH5wXVhtA==[/tex] 时, [tex=2.214x1.0]BpxcreL3CDJho/Eib9KD2A==[/tex]. 记 [tex=1.643x0.786]KdISP2Sw6k1BOwq+K6d2Mw==[/tex][tex=3.357x1.5]PnT7vx+MlOmRRNA5npnLAjPUPLK8diImWjL2Q/X4U0g=[/tex], [tex=4.643x1.5]v/qBYiX8K0PDjl27Se2dGQ==[/tex], 则[br][/br][tex=4.143x1.286]ifY8Z2pdBY3xmLR1Mq74OZ/kd5sBggXHpEjIwC4sEsM=[/tex], [tex=4.571x1.286]ByuA4d/OaIDDnoVl/VX1Lbz2wHBefspV1OPkcjQAZi0=[/tex], [tex=3.929x1.286]ifY8Z2pdBY3xmLR1Mq74ORMtSVVdyYxddWuOmLkRTMk=[/tex], [tex=4.0x1.286]ByuA4d/OaIDDnoVl/VX1LYzLRVkDP277i6yd18zLPtA=[/tex], [tex=4.0x1.286]ifY8Z2pdBY3xmLR1Mq74OX5cQuetrX2YXKnTTegwTJe7SORhdSkTaSEIE6l5cx1f[/tex], [tex=4.143x1.286]ifY8Z2pdBY3xmLR1Mq74OaMV4mSM5terpfxoaU0hgRYpwuAlcZaeiKPjjWKleIwV[/tex], [tex=4.429x1.286]wQP+4Uzd2HiJl25WHHJ/cthscFXktPTcgt4vRB3UT0hy+2eZOscGVXVGl4EgtVm3[/tex], [tex=4.214x1.286]wQP+4Uzd2HiJl25WHHJ/clwwxhk9/c/A0sdMTQTfIw4=[/tex].代入公式, 所求曲率[tex=1.643x1.0]t/Fz7GKXMX/XG+gW4AKQzg==[/tex][tex=11.643x3.0]1U4jlFNHeE64jBu5qakD2UCZ9JSAJcnyfVUa/uWEe0Wcd3YpV7ZE94I7gvMsI3wp+6AW7YYCBRf7NkEdnSTGk3ZgY4kFJGl42FjIu1L43M7WNXF2pPJ2WgTzBPf29u2918I/3tdzZ2BBusvG5ZN42JZmKWgTke0Sba3W5COipNfbaroOpqkodWVw7H7RfYGDx1KMzzCza42Dlo9dd9L9BltyUq4rj94rlsrkBgzli0r1yD5yT9wnYL3OF+KIRpHq[/tex][tex=7.286x2.643]NuvO9oDUqLsMuDh2hsCp7zYsLM9H6c20QB0AHHIcSQJesbJJKNE/niEzmyRv9Lf1wr7N6pZUrez+EXlG3dDhV08uadL5KmccQv0/6QotF8o=[/tex][tex=2.929x2.214]zY3qq0ejtSXuaxcggvtJPkJH2hVBnSoO+C3L+rCMArw=[/tex].

举一反三

内容

0
若曲线 [tex=8.0x1.429]Wg8WRwU92NL+dTvukLgTSFsvIsvn+Pw3lJrWT+3PQ0Q=[/tex] 在点 [tex=2.429x1.0]bOlCq/PHWhsSVMaVf7Obdg==[/tex] 处有极值 [tex=2.643x1.214]Ai7e7jFrXJHE2W8Bz/+wKQ==[/tex] 点 [tex=2.286x1.357]IznYKk7kywvI5iLU+xoABA==[/tex] 为拐点,求 [tex=2.786x1.214]Ip3OlDS0nB3RQIfRs9SDRw==[/tex] 的值.
1
求曲线[tex=4.143x1.429]pIWh6A1cn7l8Pp992ZRnEw==[/tex]的曲率以及在点[tex=2.286x1.357]Q31zUTZmPwwHO8bSBLtlYA==[/tex]的曲率半径.
2
求双曲线[tex=2.357x1.214]VAB6WWwKHw7IV0XYy8uSTQ==[/tex]在点[tex=2.286x1.357]iR9MYYeeL46YJUX50/3ZSw==[/tex]处的曲率.
3
求下列各曲线在指定点处的曲率:[br][/br] [tex=2.357x1.214]Hy3o6DKhIInweqFmQyuaYg==[/tex], 在点[tex=2.286x1.357]33T341VNhz20Mh+YHkpRLQ==[/tex]
4
求曲线 [tex=3.143x1.571]9HM4h4HT19jvj1EgixlW/ZCNk5trIS/0KixspVSrGUI=[/tex] 上点 [tex=2.286x1.357]IznYKk7kywvI5iLU+xoABA==[/tex] 处的切线方程和法线方程.