y??x?y

?y??e?ycos(x) ?y(0)?1?(x?2xyyy?)??x?2xyy?

2222 xy??x?0

2 yy?6y?cos3x????解：

?y???2y??12y?x?sin3x?y(0)?1 ??y (0)?2?11.在0点分别用3，6，9阶Taylor级数展开函数f(x)=2?cos(并在一张图上绘制出原函数及各展开图像。 >> clear >> syms x;

>> y=sin(x)/(2+cos(x)); >> taylor(y,x,3,0)

x=linspace(0,2*pi,60); y=sin(x)/(2+cos(x)); t=x/3;

c=x/3 - x.^5/540;

b=- x.^7/4536 - x.^5/540 + x/3; subplot(2,2,1); plot(x,y); subplot(2,2,2);

sin(x)x)，

plot(x,t); subplot(2,2,3); plot(x,c); subplot(2,2,4); plot(x,b);

10.50-0.5-10246850-5-10-15-2002468

2.521.510.5002468500-50-100-15002468