matlab习题第八章
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
第八章
实验指导
1、
>> syms x y;
>> A=x^4-y^4;
>> factor(A)
ans =
(x - y)*(x + y)*(x^2 + y^2)
>> a=5135;
>> factor(a)
ans =
5 13 79 2、(1)
>> syms x
>> f=(x-2)/(x^2-4);
>> limit(f,x,2)
ans =
1/4
（2）
>> syms x
f=(sqrt(pi)-sqrt(acos(x)))/sqrt(x+1); limit(f,x,-1,'right')
ans =
-Inf
3、
（1）
>> syms x y
>> 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)
>> 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)
>> s=symsum((-1)^(n+1)*1/n,1,inf)
s =
log(2)
(2)
>> syms n
>> 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)
>> syms x;
>> f=(exp(x)+exp(-1*x))/2;
>> taylor(f,x,5,0)
ans =
x^4/24 + x^2/2 + 1
(2)
>> syms x;
>> 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)
>> syms x a;
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^(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^3/27 + 1/4)^(1/2) - 1/2)^(1/3)/2
(2)
>> syms x
>> x=solve('sin(x)+2*cos(x)-sqrt(x)=0','x')