4.7求下列函数在指定点z0处的泰勒展式:-|||-(1) 1/(x^2) _(0)=1 ;-|||-(2)sin z, _(0)=1 ;-|||-(3) dfrac (1)(4-3z), _(0)=1+i ;-|||-(4)tanz, _(0)=dfrac (pi )(4)

4.7 求下列函数在指定点z0处的泰勒展式:-|||-(1) dfrac (1)({z)^2} ,_(0)=1 ;-|||-(2)sinz, _(0)=1 ;-

_(0)=2;-|||-(3) dfrac (1)({2)^2} , _(0)=-1;-|||-(4) dfrac (1)(4-3z), _(0)=1+i;-|

1.求下列函数的留数:-|||-(1) (z)=dfrac ({e)^z-1}({z)^5} 在 z=0 处;-|||-(2) (z)=(e)^dfrac (1

3.求下列函数在给定点的Taylor级数,并指出收敛半径.-|||-(1) dfrac (z-1)(z+1) , _(0)=1 :-|||-(2)sinz^2,

z=0是函数(z)=dfrac (z)(sin {z)^2cdot ((e)^z-1)}的几级极点A 1 B 2 C 3 D 4z=0是函数的

[ dfrac (sin z)({z)^2},0] =-|||-A 1-|||-B .-1-|||-C dfrac (1)(2)

过点(1,1,1)、 (-2,-2,2) 和(1,-1,1) 的平面方程是 ()-|||-A x+4z+3=0-|||-B x+3z-4=0-|||-C x+4

4.设 (z)=dfrac (1)(z)-zsin dfrac (1)({z)^2}, 则 [ f(z),0] =-|||-(A)1; (B)2; (C)0;

设f（x,y,z）=^2+2(y)^2+3(z)^2+xy+3x-2y-6z,求grad f(0, 0, 0) 及grad f(1, 1, 1)设f（x,y,z

7.求通过点 P(1,0,-2) 而与平面 3x-y+2z-1=0 平行,且与直线-|||-dfrac (x-1)(4)=dfrac (y-3)(-2)=dfr