数学建模答案(完整版)

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1建立一个命令M文件:求数60.70.80,权数分别为1.1，1.3,1.2的加权平均数。在指令窗口输入指令edit，打开空白的M文件编辑器；里面输入s=60*1.1+70*1.3+80*1.2;
ave=s/3然后保存即可
2编写函数M文件SQRT.M;函数f(x（保留有效x在x=567.889与0.0368处的近似值
数四位）
在指令窗口输入指令edit，打开空白的M文件编辑器；里面输入symsx1x2s1s2zhi1zhi2
x1=567.889;x2=0.368;s1=sqrt(x1;s2=sqrt(x2;zhi1=vpa(s1,4zhi2=vpa(s2,4
然后保存并命名为SQRT.M即可
a2b2
3用matlab计算f(x的值,其中a=2.3,b=4.89.
ab
>>symsab
>>a=2.3;b=4.89;
>>sqrt(a^2+b^2/abs(a-b
ans=
2.0864
4用matlab计算函数f(x
sinxcosx在x=处的值.2
31x
>>symsx
>>x=pi/3;
>>sqrt(sin(x+cos(x/abs(1-x^2
ans=
12.0962
5用matlab计算函数f(xarctanxln(x1在x=1.23处的值.>>symsx>>x=1.23;
>>atan(x+sqrt(log(x+1
ans=
1.7837



a2b2sinxcosx
f(x6用matlab计算函数f(x在x=-2.1处的值.2
ab31x
>>symsx
>>x=-2.1;
>>2-3^x*log(abs(xans=
1.9261
7用蓝色.点连线.叉号绘制函数y=2>>symsxy
>>x=0:0.2:2;y=2*sqrt(x;>>plot(x,y,'b.-'
x在[0,2]上步长为0.1的图像.

8用紫色.叉号.实连线绘制函数ylnx10在[20,15]上步长为0.2的图像.>>symsxy
>>x=-20:0.2:-15;y=log(abs(x+10;>>plot(x,y,'mx-'
ylnx10[20,15]x



9用红色.加号连线虚线绘制函数ysin(>>symsxy;
>>x=-10:0.2:10;y=sin(x/2-pi/2;>>plot(x,y,'r+--'
x
在[-10,10]上步长为0.2的图像.22







10用紫红色.圆圈.点连线绘制函数ysin(2x像.ysin(2x

3
在[0,4]上步长为0.2的图

x
ysin([0,4]322
>>symsxy
>>x=0:0.2:4*pi;y=sin(2*x+pi/3;>>plot(x,y,'mo-.'


11在同一坐标中,用分别青色.叉号.实连线与红色.星色.虚连线绘制y=cos3x与
y3cosx的图像.
>>symsxy1y2
>>x=0:pi/50:2*pi;y1=cos(3*sqrt(x;y2=3*cos(sqrt(x;>>plot(x,y1,'cx-',x,y2,'r*--'




12在同一坐标系中绘制函数yx2,yx3,yx4这三条曲线的图标,并要求用两种方法加各种标注.yx2,yx3,yx4
>>symsxy1y2y3;
>>x=-2:0.1:2;y1=x.^2;y2=x.^3;y3=x.^4;plot(x,y1,x,y2,x,y3;





xt2
13作曲线ysint的3维图像
zt
>>symsxytz>>t=0:1/50:2*pi;>>x=t.^2;y=sin(t;z=t;
>>stem3(x,y,z
x(1cosucosv
14作环面y(1cosusinv在(0,2(0,2上的3维图像
zsinu
>>symsxyuvz
>>u=0:pi/50:2*pi;v=0:pi/50:2*pi;
>>x=(1+cos(u.*cos(v;y=(1+cos(u.*sin(v;z=sin(u;>>plot3(x,y,z




15求极限lim
x0
sin2xsin2x
lim
x01cosx1cosx

>>symsxy
>>y=sin(2^0.5*x/sqrt(1-cos(x;>>limit(y,x,0,'right'ans=2
121x16求极限lim(x03
>>symsyx
>>y=(1/3^(1/(2*x;>>limit(y,x,0,'right'ans=017求极限
x
lim
xcosx1x
3

>>symsxy
>>y=(x*cos(x/sqrt(1+x^3;>>limit(y,x,+infans=0
18求极限
x
lim(
x12x
x1
>>symsxy
>>y=((x+1/(x-1^(2*x;>>limit(y,x,+infans=
exp(4
19求极限lim
1cos2x

x0xsinx



>>symsxy
>>y=(1-cos(2*x/(x*sin(x;>>limit(y,x,0ans=2
20求极限lim
x0
1x1x

x
>>symsxy
>>y=(sqrt(1+x-sqrt(1-x/x;>>limit(y,x,0ans=1
x22x1
21求极限lim2
xxx2
>>symsxy
>>y=(x^2+2*x+1/(x^2-x+2;>>limit(y,x,+infans=1
22求函数y=(2x1arctanx的导数>>symsxy
>>y=(2*x-1^5+atan(x;>>diff(yans=
10*(2*x-1^4+1/(x^2+123求函数y=y
5
xtanx
的导数2
1x
>>symsyx
>>y=(x*tan(x/(1+x^2;>>diff(yans=



tan(x/(x^2+1+(x*(tan(x^2+1/(x^2+1-(2*x^2*tan(x/(x^2+1^2
24求函数ye3xtanx的导数
>>symsyx
>>y=exp^(-3*x*tan(x>>y=exp(-3*x*tan(xy=
exp(-3*x*tan(x
>>diff(yans=
exp(-3*x*(tan(x^2+1-3*exp(-3*x*tan(x25求函数y=2lnxsin
2
x
2
在x=1的导数
>>symsxy
>>y=(1-x/(1+x;>>diff(y,x,2ans=
2/(x+1^2-(2*(x-1/(x+1^3
>>symsxy
>>y=2*log(x+sin(pi*x/2^2;>>dxdy=diff(y
dxdy=
2/x+pi*cos((pi*x/2*sin((pi*x/2zhi=subs(dxdy,1
zhi=
2
26求函数y=lim>>symsxy

1cos2x1x
的二阶导数
x0xsinx1x


>>y=(1-x/(1+x;>>diff(y,x,2ans=
2/(x+1^2-(2*(x-1/(x+1^3
(x13(32x2
27求函数y=5
(1x4
5
(x13(32x2
的导数;
(1x4
>>symsxy
>>y=((x-1^3*(3+2*x^2/(1+x^4^0.2;>>diff(yans=
(((8*x+12*(x-1^3/(x+1^4+(3*(2*x+3^2*(x-1^2/(x+1^4-(4*(2*x+3^2*(x-1^3/(x+1^5/(5*(((2*x+3^2*(x-1^3/(x+1^4^(4/5
28在区间(,内求函数f(x3x44x31的最值.>>f='-3*x^4+4*x^3-1';>>[x,y]=fminbnd(f,-inf,infx=
NaNy=
NaN
>>f='3*x^4-4*x^3+1';
>>[x,y]=fminbnd(f,-inf,infx=
NaNy=
NaN
29在区间(-1,5内求函数发

f(x(x13x5的最值.


>>f='(x-1*x^0.6';
>>[x,y]=fminbnd(f,-1,5x=
0.3750y=
-0.3470>>
>>f='-(x-1*x^0.6';
>>[x,y]=fminbnd(f,-1,5x=
4.9999y=
-10.5059
30求不定积分(ln3x2sinxdx>>symsxy
>>y=log(3*x-2*sin(x;>>int(yans=
2*cos(x-x+x*log(3+x*log(x
x2
31求不定积分esinxdx
(ln3x2sinxdx

>>symsxy
>>y=exp(x*sin(x^2;>>int(yans=
-(exp(x*(cos(2*x+2*sin(2*x-5/10



32.求不定积分

xarctanx1x
dx
>>symsxy
>>y=x*atan(x/(1+x^0.5;>>int(y
Warning:Explicitintegralcouldnotbefound.ans=
int((x*atan(x/(x+1^(1/2,x
33.计算不定积分(2xcosxe

x2
dx
>>symsxy
>>y=1/exp(x^2*(2*x-cos(x;>>int(y
Warning:Explicitintegralcouldnotbefound.ans=
int(exp(-x^2*(2*x-cos(x,x34.计算定积分
e
0
1
x
(3x2dx
>>symsxy
>>y=exp(-x*(3*x+2;>>int(y,0,1ans=
5-8*exp(-1


1
0
ex(3x2dx
1x1x
35.计算定积分lim
x0x
>>symsyx
>>y=(x^2+1*acos(x;>>int(y,0,1ans=


1
0
(x21arccosxdx


11/9
36.计算定积分
cosxln(x1dx
0
1

>>symsxy
>>y=(cos(x*log(x+1;>>int(y,0,1
Warning:Explicitintegralcouldnotbefound.ans=
int(log(x+1*cos(x,x==0..137计算广义积分

1
x2x2
2

dx;
>>symsyx
>>y=(1/(x^2+2*x+2;>>int(y,-inf,infans=pi
38.计算广义积分>>symsxy
>>y=x^2*exp(-x;>>int(y,0,+infans=2
xe
0

2x
dx；


数学建模答案(完整版)

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