数学实验1-3章习题答案

2一元微积分实验2.1曲线绘图练习题2.1会出下列常见曲线的图形（其中a=1,b=2,c=3）.1.立方抛物线3xysymsxy;ezplot('y=x^(1/3)',[-5,5])title('y=x^(1/3)')-5-4-3-2-1012345-5-4-3-2-1012345xyy=x(1/3)2.高斯曲线2xeysymsxy;ezplot('y=exp(-x^2)',[-5,5])title('y=exp(-x^2)')-5-4-3-2-1012345-5-4-3-2-1012345xyy=exp(-x2)3.笛卡尔曲线22213,13tatytatx)3(33axyyxsymsxy;ezplot('x^3+y^3=3*x*y',[-2,2])title('x^3+y^3-3*x*y=0')-2-1.5-1-0.500.511.52-2-1.5-1-0.500.511.52xyx3+y3-3*x*y=04.蔓叶线).(1,1322322xaxytatytatxsymsxy;ezplot('y^2*(1-x)=x^3',[-10,10])title('y^2=x^3/(1-x)')-10-8-6-4-20246810-10-8-6-4-20246810xyy2=x3/(1-x)5.摆线).cos1(),sin(tbyttaxsymst;x=t-sin(t);y=2-2*cos(t);ezplot(x,y)012345600.511.522.533.54xyx=t-sin(t),y=2-2cos(t)6.星形线)(sin,cos32323233ayxtaytaxsymst;x=cos(t)^3;y=sin(t)^3;ezplot(x,y)-1-0.500.51-0.8-0.6-0.4-0.200.20.40.60.8xyx=cos(t)3,y=sin(t)37.螺旋线ctztbytax,sin,cost=0:0.1:30;x=cos(t);y=2*sin(t);z=3*t;plot3(x,y,z);-1-0.500.51-2-10120204060801008.阿基米得螺旋线.artheta=0:0.1:6;r=theta;plot(r,theta)012345601234562.2极限与导数1.求出下列极限：（1）nnnn3lim3symsn;limit((n^3+3^n)^(1/n),n,inf)ans=3（2）)122(limnnnnsymsn;limit((n+2)^(1/2)-2*(n+1)^(1/2)+n^(1/2),n,3)ans=5^(1/2)-4+3^(1/2)vpa(ans,20)ans=-.318812149313330101e-1（3）xxx2cotlim0symsx;limit(x*cot(2*x),x,0)ans=1/2（4）xxxm)(coslimclearsymsxm;limit(cos(m/x)^x,x,inf)ans=1（5）)111(lim1xxexsymsx;limit('1/x-1/(exp^x-1)',x,1)ans=(exp-2)/(exp-1)(6))(lim2xxxxclearsymsx;limit((x^2+x)^(1/2)-x,x,inf)ans=1/22.有个客户看重某套面积为1802m，每平方米7500的房子.他计划首付30%，其余70%用20年按揭贷款（贷款年利率5.04%）.按揭贷款中还有10万元为公积金贷款（贷款年利率4.05%），请问他的房屋总价、收付款额和月付款额分别为多少？functionc=fukuan(m),c=(7500*180*(1+0.0504)^20+100000*(1+0.0405)^20)*m总付款：m=1;y=fukuan(m)c=3.8306e+006y=3.8306e+006首付：m=0.3;c=fukuan(m)c=1.1492e+006c=1.1492e+006月付款额：clearm=0.7/(20*12);c=fukuan(m)c=1.1172e+004c=1.1172e+0043.作出下列函数及其导函数的图形，观察极值点、最值点的位置并求出所有驻点以及对应的二阶导数值，求出函数的单调区间.(1)];2,2[),2sin()(22xxxxf函数的图形：fplot('x^2*sin(x^2-x-2)',[-2,2])gridontitle('f(x)=x^2*sin(x^2-x-2),[-2,2]')-2-1.5-1-0.500.511.52-4-3-2-10123f(x)=x2*sin(x2-x-2),[-2,2]导函数的图形：clearsymsxyy=x^2*sin(x^2-x-2);yx=diff(y,x)yx=2*x*sin(x^2-x-2)+x^2*cos(x^2-x-2)*(2*x-1)fplot('yx',[-2,2])-2-1.5-1-0.500.511.52-2-1.5-1-0.500.511.52极值1：f=inline('-x^2*sin(x^2-x-2)','x');[x,f]=fminsearch(f,-1.5)x=-1.5326f=-2.2364极值2：f=inline('x^2*sin(x^2-x-2)','x');[x,f]=fminsearch(f,-0.6)x=-0.7315f=-0.3582极值3：f=inline('x^2*sin(x^2-x-2)','x');[x,f]=fminsearch(f,0)x=1.5951f=-2.2080最值1：x=-2:0.1:-1.8;y=x.^2.*sin(x.^2-x-2);[mk]=min(y)m=-3.0272k=1x(k)ans=-2最值2：x=-1.8:0.1:2;y=x.^2.*sin(x.^2-x-2);[mk]=max(y)m=2.2140k=4x(k)ans=-1.5000驻点1及相应的二阶导数值：f=inline('-x^2*sin(x^2-x-2)','x');[x,f]=fminsearch(f,-1.5)x=-1.5326f=-2.2364symsxyy=x^2*sin(x^2-x-2);yxx=diff(y,x,2);x=-1.5326;eval(yxx)ans=-44.1089驻点2及相应的二阶导数值：clearf=inline('x^2*sin(x^2-x-2)','x');[x,f]=fminsearch(f,-0.6)x=-0.7315f=-0.3582symsxyy=x^2*sin(x^2-x-2);yxx=diff(y,x,2);x=-0.7315;eval(yxx)ans=6.9830驻点3及相应的二阶导数值：clearf=inline('x^2*sin(x^2-x-2)','x');[x,f]=fminsearch(f,1.5)x=1.5951f=-2.2080symsxyy=x^2*sin(x^2-x-2);yxx=diff(y,x,2);x=1.5951;eval(yxx)ans=18.3287函数的单调区间为：(1)单调递增区间:-2x-1.5326-0.7315x0以及1.5951x2;(2)单调递减区间：-1.5326x-0.7315以及0x1.5951.(2)];3,3[,10203)(35xxxf函数的图形为：clearfplot('3*x^5-20*x^3+10',[-3,3])gridontitle('f(x)=3*x^5-20*x^3+10,x,[-3,3]')-3-2-10123-200-150-100-50050100150200f(x)=3*x5-20*x3+10,x,[-3,3]导函数的图形：clearfplot('3*x^5-20*x^3+10',[-3,3])gridontitle('f(x)=3*x^5-20*x^3+10,x,[-3,3]')symsxyy=3*x^5-20*x^3+10;yx=diff(y,x)yx=15*x^4-60*x^2fplot('yx',[-3,3])-3-2-10123-3-2-10123极值点1：ff=inline('-(3*x^5-20*x^3+10)','x');[x,f]=fminsearch(ff,-2)x=-2f=-74极值点2：ff=inline('3*x^5-20*x^3+10','x');[x,f]=fminsearch(ff,2)x=2f=-54最值1：clearx=-3:0.1:-1;y=3.*x.^5-20.*x.^3+10;[mk]=min(y)m=-179k=1x(k)ans=-3最值2：x=1:0.1:3;y=3.*x.^5-20.*x.^3+10;[mk]=max(y)m=199k=21x(k)ans=3驻点1及相应的二阶导数值：clearsymsxyy=3*x^5-20*x^3+10;yxx=diff(y,x,2);x=-2;eval(yxx)ans=-240驻点2及相应的二阶导数值：clearsymsxyy=3*x^5-20*x^3+10;yxx=diff(y,x,2);x=2;eval(yxx)ans=240函数的单调区间为：单调递减区间为：-2x0以及0x2;单调递增区间为：-3x-2以及2x3.(3)f(x)=].3,3[,223xxx)函数的图形为：fplot('abs(x^3-x^2-x-2)',[-3,3])gridontitle('f(x)=abs(x^3-x^2-x-2),x,-3,3')-3-2-1012305101520253035f(x)=abs(x3-x2-x-2),x,-3,3导函数的图形为：symsxyy=abs(x^3-x^2-x-2);yx=diff(y,x)yx=abs(1,x^3-x^2-x-2)*(3*x^2-2*x-1)fplot('yx',[-3,3])gridon-3-2-10123-3-2-10123极值点：ff=inline('abs(x^3-x^2-x-2)','x');[x,f]=fminsearch(ff,1)x=2.0000f=1.5543e-014最大值的相反数为：x=-3:0.1:-2;y=x.^3-x.^2-x-2;[mk]=min(y)m=-35k=1x(k)ans=-3（注：最大值为35）最小值是：[x,f]=fminsearch('abs(x^3-x^2-x-2)',2)x=2f=0驻点及相应的二阶导数值：clearsymsxyy=x^3-x^2-x-2;yxx=diff(y,x,2);x=2;eval(yxx)ans=10symsxyy=-(x^3-x^2-x-2);yxx=diff(y,x,2);x=2;eval(yxx)ans=-10函数的单调区间为：单调递增区间为：-3x2单调递减区间为2x3.2.3方程（组）求根1.求下列方程在限制条件下的根：（1）;22,24xxx.(1)clearfplot('x^4-2^x',[-2,2])gridon-2-1.5-1-0.500.511.52-20246810121416f=inline('x^4-2^x','x');y1=fzero(f,-1)y1=-0.8613y2=fze