用Laplace变换求解微分方程''-3y'+2y=6(e)^-t (0)=0, '(0)=0.

(omega )=F[ f(t)] ，求(omega )=F[ f(t)] .

5.12 求下列各积分之值:-|||-(1) (int )_(0)^2pi dfrac (dtheta )(a+cos theta )(agt 1);-|||-(2) (int )_(0)^2pi dfrac (dtheta )(5+3cos theta )-|||-(3)(int )_(-x)^ndfrac ({x)^2}({({x)^2+(a)^2)}^2}dx(agt 0);(4)(int )_(-infty )^+infty dfrac (cos x)({x)^2+4x+5}dx;

2.验证极限lim _(xarrow 0)dfrac ({x)^2sin dfrac (1)(x)}(sin x)存在,但不能用洛必达法则得出.

[例5.14]求微分方程 y''-5y'+6y=0 的通解.

14.设 (alpha )_(1)=(1,-1,2,4) (alpha )_(2)=(0,3,1,2), (alpha )_(3)=(3,0,7,14), (alpha )_(4)=(1,-1,2,0) (alpha )_(5)=(2,1,5,6)-|||-(1)证明α1,α2线性无关;-|||-(2)把α1,α2扩充成一极大线性无关组。

10.求下列函数图形的拐点及凹或凸的区间:-|||-(2) =x(e)^-x ;-|||-(1) =(x)^3-5(x)^2+3x+5 ;-|||-(4) =ln ((x)^2+1) ;-|||-(3) =((x+1))^4+(e)^x ;-|||-(6) =(x)^4(12ln x-7).-|||-(5) =(e)^arctan x ;

8.设X与Y的联合密度函数为-|||-(1) f(x,y)= {y)^2,0leqslant xleqslant 2,0leqslant yleqslant 1 0,1leqslant xleqslant 0 .-|||-试求(X,Y)关于X及Y的边缘密度函数、条件分布密度并判-|||-别X与Y的相互独立性.

求下列不定积分:-|||-(22) int dfrac (cos 2x)({cos )^2x(sin )^2x}dx ;

求下列向量组的秩及一个极大无关组,并将不属于极大无关组的向量由极大无关-|||-组线性表示:-|||-(1) 1 -3 -1 1)-|||-α1= 3 α2= 2 α3= -3 α4= 4 α5= 5-|||-1 2 -9 -8 -1

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