南邮数学实验问题详解
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第一次练习题
1、求032=-x e x 的所有根。
>>x=-5:0.01:5;y=exp(x)-3*x.^2;plot(x,y);grid on
>> fsolve('exp(x)-3*x.^2',-1)
Equation solved.
fsolve completed because the vector of function values is near zero
as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.
ans =
-0.4590
>> fsolve('exp(x)-3*x.^2',1)
Equation solved.
fsolve completed because the vector of function values is near zero as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.
ans =
0.9100
>> fsolve('exp(x)-3*x.^2',4)
Equation solved.
fsolve completed because the vector of function values is near zero as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.
ans =
3.7331
2、求下列方程的根。
1)0155=++x x 2） 至少三个根）(021
sin =-x x
3） 所有根0cos sin 2=-x x x
1) >> p=[1,0,0,0,5,1];r=roots(p)
r =
1.1045 + 1.0598i
1.1045 - 1.0598i
-1.0045 + 1.0609i
-1.0045 - 1.0609i
-0.1999
2) >> x=-10:0.01:10;y=x.*sin(x)-1/2;plot(x,y);grid on
>> fsolve('x.*sin(x)-1/2',-6)
Equation solved.
fsolve completed because the vector of function values is near zero as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.
ans =
-6.3619
>> fsolve('x.*sin(x)-1/2',-4)
Equation solved.
fsolve completed because the vector of function values is near zero as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.
ans =
-2.9726
>> fsolve('x.*sin(x)-1/2',2)
Equation solved.
fsolve completed because the vector of function values is near zero as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.
ans =
0.7408
3) >> x=-3:0.01:3;y=sin(x).*cos(x)-x.^2;plot(x,y);grid on
>> fsolve('sin(x).*cos(x)-x.^2',-1)
Equation solved.
fsolve completed because the vector of function values is near zero as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.
ans =
-6.8434e-010
>> fsolve('sin(x).*cos(x)-x.^2',1)
Equation solved.
fsolve completed because the vector of function values is near zero as measured by the default value of the function tolerance, and
the problem appears regular as measured by the gradient.