川农数学实验第一次实验

第一次实验 姓名 学号 班级 四个求极限的题

13 )lim((1?3)x?-1x?1x?1

syms x;

f=1/(x+1)-3/(x^3+1); limit(f,x,-1) ans = -1 1x(2)lim(1?)x x?? syms x

limit((1+1/x)^x,x,inf) ans = exp(1)

|x|(3)lim? x?0x

syms x

limit(abs(x)/x,x,0,’right’)

ans = 1

222sin x?1/(y?x)((1? 4)lime2x?1/yx y??

syms x y a;

f=exp(-1/(y^2+x^2))*sin(x)^2/ ... x^2*(1+1/y^2)^(x+a^2*y^2); L=limit(limit(f,x,1/sqrt(y)),y,inf) L =

exp(a^2)

1x?a2y2)2y

四个函数求导

(1)y?ex(sinx?cosx)

syms x

y=exp(x)*(sin(x)+cos(x)); diff(y) ans =

exp(x)*(sin(x)+cos(x))+exp(x)*(cos(x)-sin(x))

x3?1(2)f(x)?ln2x?1syms x

f=log((x^3+1)/(x^2+1)); diff(f) ans =

(3*x^2/(x^2+1)-2*(x^3+1)/(x^2+1)^2*x)/(x^3+1)*(x^2+1)

(3)设x2?y2?R2,求y?

syms x y;

f=solve('x^2+y^2-R^2=0',y); diff(f,x)

ans =-1/(-x^2+R^2)^(1/2)*x1/(-x^2+R^2)^(1/2)*x

1(4)已知函数f(x)?,求f?(1),f?(2)x

syms x;

f=1/x; f1=diff(f,x); ff=inline(f1) ff =

Inline function: ff(x) = -1./x.^2 x=1; ff(1) ans =-1 x=-2; ff(-2) ans =-0.2500

四个定积分

(1)

?101?x2dxsyms x;

f=sqrt(1-x^2); int(f,x,0,1) ans = 1/4*pi

(2)?|x?1|dx02syms x;

int(abs(x-1),0,2) ans= 1 9 (3)x(1?x)dx4

syms x; f=sqrt(x)+x; I=int(f,x,4,9) I =

271/6

e?2t ?2x2?1dx (4)I(t)?cost(2x2?3x?1)2

syms x t;

f=(-2*x^2+1)/(2*x^2-3*x+1)^2 I=simple(int(f,x,cos(t),exp(-2*t))) I =

-(2*exp(-2*t)*cos(t)-1)*(exp(-2*t)-cos(t))/(exp(-2*t)-1)/(2*exp(-2*t)-1)/(cos(t)-1)/(2*cos(t)-1)

??四个不定积分

2(1)(x?3x?2)dx?

syms x; y=x^2-3*x+2; int(y) ans =

1/3*x^3-3/2*x^2+2*x

(2)?cos(3x?4)dxsyms x;

int(cos(3*x+4)) ans =

sin(3*x + 4)/3

(3)

syms x;

f=exp(x)*(5^x+(exp(-x)/tan(x))); int(f,x) ans =

log(tan(x)) -log(tan(x)^2 + 1)/2 + (5^x*exp(x))/(log(5) + 1)

(4)

syms x; f=1/(x^3); int(f,x) ans = -1/(2*x^2)

dx