高等數(shù)學(xué)實驗-指導(dǎo)

PAGE第4-頁共5頁淮陰工學(xué)院數(shù)學(xué)軟件課堂作業(yè)項目11高等數(shù)學(xué)實驗指導(dǎo)姓名學(xué)號成績內(nèi)容(下面題目中,m為你的學(xué)號后兩位)函數(shù)與極限案例學(xué)習(xí)符號變量說明:symsxythalimit(f,x,a)limit(f,a)默認變量x或唯一符號變量limit(f)默認變量x,且a=0limit(f,x,a,’right’)右極限limit(f,x,a,’left’)左極限例題：symsxhalimit(sin(x)/x)1limit(sin(x)/x,inf)0limit((x-2)/(x^2-4),2)1/4limit(1/x,x,0,’right’)inflimit(1/x,x,0,’left’)-inflimit((sin(x+h)-sin(x))/h,h,0)cos(x)limit((1+a/x)*sin(x),x,a)2*sin(a)二、求一元函數(shù)極小值[x,feal,exitflag,output]=fminbnd(fun,x1,x2,options)[x,feal,exitflag,output]=fminsearch(fun,x0,options)%若exitflag給出數(shù)大于0，則成功找到極值點，x，fval分別是極值點和對應(yīng)的目標函數(shù)極值運用函數(shù)的例子：在-10《x《10區(qū)間，求函數(shù)最小值x1=-10;x2=10;yx=@(x)(sin(x)^2)*exp(-0.1*x)-0.5*sin(x)*(x+0.1);[xn0,fval,exitflag,output]=fminbnd(yx,x1,x2)微分及其應(yīng)用學(xué)習(xí)案例Matlab的高等數(shù)學(xué)運算之求導(dǎo)數(shù)diff函數(shù)：diff解釋：假如y=f(x)1、diff(y)表示y對x求1次導(dǎo)數(shù)2、diff(y,n)表示y對x求n次導(dǎo)數(shù)3、diff(y,x,n)表示y對x求n次導(dǎo)數(shù)備注：A：對于y=f(a,b,c……)這類多元函數(shù)，其中y要對a求n1次導(dǎo),對b求n2次導(dǎo),對c求n3次導(dǎo)……則可依次分別對某個變量求導(dǎo)，最終得到結(jié)果?？蠢?B：對于x=f(t),y=f(t),求dy/dx這類參數(shù)方程的求導(dǎo),可以參看例子4C：對于f(x,y)=0,求dy/dx這類隱函數(shù)的求導(dǎo),可以參看例子5例子1：>>symsx;>>y=1/sin(x);%函數(shù)原型>>diff(y)ans=-cos(x)/sin(x)^2>>例子2：>>symsx;>>y=tan(x)/((sin(x))^2+log(x));%log即ln>>diff(y,2)ans=(tan(x)*(2*sin(x)^2-2*cos(x)^2+1/x^2))/(sin(x)^2+log(x))^2-(2*(2*cos(x)*sin(x)+1/x)*(tan(x)^2+1))/(sin(x)^2+log(x))^2+(2*tan(x)*(tan(x)^2+1))/(sin(x)^2+log(x))+(2*tan(x)*(2*cos(x)*sin(x)+1/x)^2)/(sin(x)^2+log(x))^3>>例子3：>>symsxyz;>>f=x^2*log(y)/sin(z);%函數(shù)原型，且log即ln>>fx=diff(f,x,1);%對x求1次導(dǎo)數(shù)>>fy=diff(fx,y,2);%對y求2次導(dǎo)數(shù)>>fz=diff(fy,z,3)%對z求3次導(dǎo)數(shù)fz=(12*x*cos(z)^3)/(y^2*sin(z)^4)+(10*x*cos(z))/(y^2*sin(z)^2)例子4：>>symsxyt;>>x=sin(t)*log(t)+5*t^2;%函數(shù)原型>>y=tan(t)/(t^2+45*sin(t));%函數(shù)原型>>dx=diff(x,t,1);>>dy=diff(y,t,1);>>dy/dxans=((tan(t)^2+1)/(45*sin(t)+t^2)-(tan(t)*(2*t+45*cos(t)))/(45*sin(t)+t^2)^2)/(10*t+cos(t)*log(t)+sin(t)/t)>>例子5：>>symsxyf;>>f=sin(x)*cos(y)+x^2*y^3-5*x+exp(x)+exp(y);%函