matlab数学实验作业.doc

文档介绍：数
学
实
验
报
告
数学1202班
王小雪
20120921118
课堂练****br/>3、求函数的极限
>> sym x
>> limit((cos(x)-exp(-x^2/2))/x^4,x,0)
ans =
-1/12
>> sym x
>> limit((x-2)/(x^4-4),x,2)
ans =
0
>> syms x t
>> limit((1+2*t/x)^(3*x),x,inf)
ans =
exp(6*t)
>> sym x
>> limit((1/x),x,0,'right')
ans =
Inf
>> sym x
>> limit((2^x-log(2^x)-1)/(1-cos(x)),x,0)
ans =
log(2)^2
>> syms x a
>> y=limit((1+a/x)^x,x,inf)
y =
exp(a)
>> y1=limit(exp(-x),x,inf)
y1 =
0
>> v=[y,y1]
v =
[ exp(a), 0]
4、求函数的导数
>> syms x
>> diff(sin(x)*log(x^2+1),x)
ans =
log(x^2 + 1)*cos(x) + (2*x*sin(x))/(x^2 + 1)
>> diff(sin(x)*log(x^2+1),x,3)
ans =
(6*cos(x))/(x^2 + 1) - log(x^2 + 1)*cos(x) - (6*x*sin(x))/(x^2 + 1) - (12*x*sin(x))/(x^2 + 1)^2 - (12*x^2*cos(x))/(x^2 + 1)^2 + (16*x^3*sin(x))/(x^2 + 1)^3
>> syms x
>> diff(x^2*exp(2*x),x,20)
ans =
99614720*exp(2*x) + 20971520*x*exp(2*x) + 1048576*x^2*exp(2*x)
syms a t x
x=diff(a*(t-sin(t)),t);
>> y= diff(a*(1-cos(t)),t);
>> y/x
ans =
-sin(t)/(cos(t) - 1)
>> syms x y
>> diff((x^2+y^2)^(1/2),x)
ans =
x/(x^2 + y^2)^(1/2)
>> diff((x^2+y^2)^(1/2),x,2)
ans =
1/(x^2 + y^2)^(1/2) - x^2/(x^2 + y^2)^(3/2)
>> syms x y
a=diff((x^2+y^2)^(1/2),x);
b=diff(a,y)
b =
-(x*y)/(x^2 + y^2)^(3/2)
>> syms x y z
diff(x^2+y^2+z^2-4*z,x);
>> syms x y z
>> zx=diff(x^2+y^2+z^2-4*z,x);
>> zy=diff(x^2+y^2+z^2-4*z,y);
>> zxx=diff(zx,x);
>> zxy=diff(zx,y);
>> zyy=diff(zy,y);
>> a=(2*zx*zy*zxy-(zy)^2*zxx-(zx)^2*zyy)/(zy)^3
a =
-(8*x^2 + 8*y^2)/(8*y^3)
5、求函数积分
>> sym x
>> int(x^3*exp(-x^2),x)
ans =
-(exp(-x^2)*(x^2 + 1))/2
>> int(1/(x*(x^2+1)^(1/2)),x)
ans =
-asinh((1/x^2)^(1/2))
Sym x
>> int(((sin(x))^4)*((cos(x))^2),x,0,pi/2)
ans =
pi/32
>> int(abs(x-1),0,2)
ans =
1
>> syms x t
>> int(1/log(t),t,0,x)
Warning: Explicit integral could not be found.
ans =
piecewise([x < 1, Li(x)], [1 <= x, int(1/log(t), t == 0..x)])
>> syms x y
>> a=int(x*sin(x),x,y,y^(1/2));
>> int(a,y,0,1)
ans =
5*sin(1) - 4*cos(1) - 2
>> syms x