2.求下列各曲线在指定点处的曲率:-|||-(4) =a(cos )^3t, =a(sin )^3t(agt 0), 在 =dfrac (pi )(4) 的点.

[题目]-|||-4.求曲线 =a(cos )^3t =a(sin )^3t 在 =(t)_(0) 相应的点处的曲率.

1.求下列曲线的弧长:-|||-(1) =(x)^3/2, (2)、 sqrt (x)+sqrt (y)=1;-|||-(3) =a(cos )^3t, =a(

求振动_(1)=4cos 3t和_(1)=4cos 3t (SI)的合振动方程.求振动和(SI)的合振动方程.

求曲线 =t-sin t, =1-cos t =4sin dfrac (t)(2) 在点 (dfrac (pi )(2)-1,1,2sqrt (2)) 处的切线

求曲线 =f(t)=(t-sin t)i+(1-cos t)i+(4sin dfrac (t)(2))k 在与 _(0)=dfrac (pi )(2) 相应的点

2.求下列函数在指定点的导数:-|||-(1)设 =f(x)=sin x-cos x, 求 (dfrac (pi )(4)), (dfrac (pi )(2))

6.求由下列各曲线所围成的图形的面积：(1)ρ=2acosθ; (2)x=acos^3t,y=asin^3t; (3)ρ=2a(2+cosθ).6.求由下列

25.计算星形线 =a(cos )^3t, =a(sin )^3t 图 -26 的全长.

3 求曲线r=f(t)=(t-sin t)i+(1-cos t)j+(4sin(t)/(2))k在与t_(0)=(pi)/(2)相应的点处的切线及法平面方程.3

6.求由下列参量方程所确定的函数的二阶导数 dfrac ({d)^2y}(d{x)^2}:-|||-(1) ) x=a(cos )^3t, y=a(sin