matlab习题第八章_原创文档.pdf

第八章

实验指导

1、

symsxy;

A=x^4-y^4;

factor(A)

ans=

(x-y)*(x+y)*(x^2+y^2)

a=5135;

factor(a)

ans=

51379

2、(1)

symsx

f=(x-2)/(x^2-4);

limit(f,x,2)

ans=

1/4

（2）

symsx

f=(sqrt(pi)-sqrt(acos(x)))/sqrt(x+1);

limit(f,x,-1,right)

ans=

-Inf

3、

（1）

symsxy

f=sin(1/x);

diff(f)

ans=

-cos(1/x)/x^2

diff(f,x,2)

ans=

(2*cos(1/x))/x^3-sin(1/x)/x^4

f=(1-cos(2x))/x;

(2)

f=(1-cos(2*x))/x

f=

-(cos(2*x)-1)/x

diff(f)

ans=

(2*sin(2*x))/x+(cos(2*x)-1)/x^2

diff(f,x,2)

ans=

(4*cos(2*x))/x-(4*sin(2*x))/x^2-(2*(cos(2*x)-1))/x^3

4、

(1)、

x=sym(x);

f=sqrt(exp(x)+1);

int(f)

ans=

atan((exp(x)+1)^(1/2)*i)*2*i+2*(exp(x)+1)^(1/2)

(2)

x=sym(x);

y=sym(y);

f=x/(x+y);

int(f,y)

ans=

x*log(x+y)

(3)

symsx;

syms(x);

f=exp(x)*(exp(x)+1)^2;

int(f,0,log10(2))

ans=

(exp(5422874305198591/18014398509481984)*(3*exp(5422874305198

591/18014398509481984)+exp(5422874305198591/9007199254740992)

+3))/3-7/3

(4)

sym(x);

f=x*log10(x);

int(f,1,exp(1))

ans=

(18733482797859000068490812234738*log(3060513257434037/112589

9906842624)-

8099090798701270632748702911993)/(50706024009129176059868128

21504*log(10))

5、(1)

symsn;

s=symsum((-1)^(n+1)*1/n,1,inf)

s=

log(2)

(2)

symsn

s=symsum(x^(2*n-1)/(2*n-1),1,inf)

s=

piecewise([real(n)0,zeta(1-2*n)/(2*n-1)])

6、(1)

symsx;

f=(exp(x)+exp(-1*x))/2;

taylor(f,x,5,0)

ans=

x^4/24+x^2/2+1

(2)

symsx;

f=sqrt(x^3-2*x+1);

taylor(f,x,6,0)

ans=

-x^5/8-x^4/8-x^2/2-x+1

7、(1)

symsxa;

x=solve(x^3+a*x+1,x)

x=

((a^3/27+1/4)^(1/2)-1/2)^(1/3)-a/(3*((a^3/27+1/4)^(1/2)-1/2)^(1/3))

(3^(1/2)*(a/(3*((a^3/27+1/4)^(1/2)-1/2)^(1/3))+((a^3/27+1/4)^(1/2)-

1/2)^(1/3))*i)/2+a/(6*((a^3/27+1/4)^(1/2)-1/2)^(1/3))-((a^3/27+

1/4)^(1/2)-1/2)^(1/3)/2

a/(6*((a^3/27+1/4)^(1/2)-1/2)^(1/3))-(3