1.求下列曲线的弧长:-|||-(1) =(x)^3/2, (2)、 sqrt (x)+sqrt (y)=1;-|||-(3) =a(cos )^3t, =a(sin )^3t(agt 0) leqslant tleqslant 2pi ;-|||-(4) =a(cos t+tsin t), =a(sin t-tcos t)(agt 0) leqslant tleqslant 2pi ;-|||-(5) =a(sin )^3dfrac (theta )(3)(agt 0,0leqslant theta leqslant 3pi ;-|||-(6) =alpha theta (agt 0) leqslant theta leqslant 2pi .leqslant xleqslant 4;1.求下列曲线的弧长:-|||-(1) =(x)^3/2, (2)、 sqrt (x)+sqrt (y)=1;-|||-(3) =a(cos )^3t, =a(sin )^3t(agt 0) leqslant tleqslant 2pi ;-|||-(4) =a(cos t+tsin t), =a(sin t-tcos t)(agt 0) leqslant tleqslant 2pi ;-|||-(5) =a(sin )^3dfrac (theta )(3)(agt 0,0leqslant theta leqslant 3pi ;-|||-(6) =alpha theta (agt 0) leqslant theta leqslant 2pi .leqslant xleqslant 4;

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

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

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.

2.应用格林公式计算下列曲线所围的平面面积:-|||-(1)星形线: =a(cos )^3t, =a(sin )^3t;-|||-(2)双纽线: (({x)^2

1.求下列函数的自然定义域:-|||-(1) =sqrt (3x+2);-|||-(3) =dfrac (1)(x)-sqrt (1-{x)^2};-|||-(

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

(B) ^(x^4-2x)-1.-|||-(C) (int )_(0)^(x^2)sin (t)^2dt. (D) sqrt (1+2x)-sqrt [3](1

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.

求下列极限：lim _(xarrow 0)dfrac (sin x-tan x)((sqrt [3]{1+{x)^2}-1)(sqrt (1+sin x)-1)

求过点 ( 1 , 1 , 3 ) 且与直线 ) x=3t y=-2t+1 z=t-1 .垂直相交的直线方程求过点(1,1,3)且与直线垂直相交的直线方程