曲线\(y = \sin x\) 在点\(({\pi \over 2},1)\)处的曲率为 ( )
A: \({1 \over 2}\)
B: \(1\)
C: \(2\)
D: \(3\)
A: \({1 \over 2}\)
B: \(1\)
C: \(2\)
D: \(3\)
举一反三
- 曲线\(y = \cos x\)在点\(({\pi \over 2},0)\)处的曲率为 ( ) A: \({1 \over 2}\) B: \(0\) C: \(1\) D: \(2\)
- 函数\(y = \sin {1 \over x}\)的导数为( ). A: \({1 \over { { x^2}}}\sin {1 \over x}\) B: \( - {1 \over { { x^2}}}\sin {1 \over x}\) C: \( - {1 \over { { x^2}}}\cos {1 \over x}\) D: \({1 \over { { x^2}}}\cos {1 \over x}\)
- 抛物线\(y = {x^2} - 4x + 3\)在其顶点的曲率与曲率半径为( ). A: \(2,{1 \over 2}\) B: \({1 \over 2},2\) C: \(3,{1 \over 3}\) D: \({1 \over 3},3\)
- 球面 \(x^2 + {y^2} + {z^2} = {a^2}\)含在圆柱面\({x^2} + {y^2} = ax\) 内部的那部分面积为 ( ) A: \(4{a^2}({\pi \over 2} - 1)\) B: \(4{a^2}({\pi \over 3} - 1)\) C: \(4{a^2}({\pi \over 2} + 1)\) D: \(4{a^2}({\pi \over 3} + 1)\)
- $\int {{{x\cos x} \over {{{\sin }^3}x}}} dx = \left( {} \right)$ A: $ - {x \over {2{{\sin }^2}x}} - {1 \over 2}\tan x + C$ B: $ - {x \over {2{{\sin }^2}x}} - {1 \over 2}\cot x + C$ C: $ - {x \over {2{{\cos }^2}x}} - {1 \over 2}\cot x + C$ D: $ - {x \over {2{{\cos }^2}x}} - {1 \over 2}\tan x + C$