高等数学实验1-函数与极限---参考答案

-第1页共5页1高等数学实验1函数与极限参考答案一．用MATLAB计算：1．4333sinlog210.23452435sin(3*pi/5)+log(21)/log(3)-0.23^4+452^(1/3)-sqrt(43)ans=4.83652．2ln6451.2374cos484*cos(4*pi/7)+3*2.1^8/(sqrt(645))-log(2)ans=43.0950二.用MATLAB计算：设向量(1,2,3,4,5)x，求1．sin2yxxclearx=[1,2,3,4,5];y=sin(x)+2*xy=2.84154.90936.14117.24329.04112．23sinzxxxz=3*x.*sin(x)-x.^2z=1.52441.4558-7.7299-25.0816-39.38393．2cos2sin1ln(21)xxxuexu=((cos(2.*x)).^2+(sin(x)+1).^(1/2))./(exp(x)-log(2.*x+1))u=0.94480.31300.10970.00980.0062-第2页共5页2三．用MATLAB绘图：1．设数据表如下：x12.133.95.36.16.989.1y1.013.988.9916.0125.4137.0148.8963.8981.21在坐标系中描出点(x,y);clearx=[1,2.1,3,3.9,5.3,6.1,6.9,8,9.1];y=[1.01,3.98,8.99,16.01,25.41,37.01,48.89,63.89,81.21];plot(x,y)holdonplot(x,y,'s')2.作出函数2yx与3yxx[-3，3]的图象；clearholdofffplot('x^2',[-3,3])fplot('x^2',[-3,3],'r')holdonfplot('x^3',[-3,3],'g')3．在同一坐标系作出下列函数的图形，并用不同颜色表示。（1）sinyxx（2）cosyxxclearholdofffplot('x+sin(x)',[-5,5],'s')holdonfplot('x+cos(x)',[-5,5],'r')holdoffezplot('(y-(x+sin(x)))*x*y',[-5,5])holdonfplot('x+cos(x)',[-5,5],'r')4．作下列函数图形：-第3页共5页3（1）1sin1,1yxx（2）1sin1,1yxxxclearholdofffplot('sin(1/x)',[-1,1],'g')holdonfplot('x*sin(1/x)',[-1,1],'r')holdoffezplot('(y-sin(1/x))*x*y',[-1,1])holdonfplot('x*sin(1/x)',[-1,1],'r')xy(y-sin(1/x))xy=0-1-0.8-0.6-0.4-0.200.20.40.60.81-1-0.8-0.6-0.4-0.200.20.40.60.81xy(y-(x+sin(x)))xy=0-5-4-3-2-1012345-5-4-3-2-1012345-第4页共5页4四．用MATLAB计算下列极限：用MATLAB计算极限的命令语句如下：clearsymsxymn（生成符号变量nmyx）limit(f(x),x,a)（求lim()xafx）limit(f(x),x,inf)（求lim()xfx）limit(f(x),x,a,'right')（求lim()xafx）limit(f(x),x,a,'left')（求lim()xafx）（1）xexx1lim20；（2）xekxx1lim0；（3）11232limxxxx；（4）xxxtan001lim；（5）knxxxm1lim；（6）kynymy1lim0；（7）nxmxxtansinlim0；（8）nxxmxxsintanlim0。解（1）clear（7）symsxclearlimit((exp(2*x)-1)/x,x,0)symsxmnans=limit(sin(m*x)/tan(n*x),x,0)2ans=m/n（2）clear（8）symsxksymsxmnlimit((exp(k*x)-1)/x,x,0)limit((tan(m*x)+x)/sin(n*x),x,0)ans=ans=k(m+1)/n（3）clearsymsxlimit(((2*x+3)/(2*x-1))^(x+1),x,inf)ans=exp(2)（4）clearsymsxlimit((1/x)^tan(x),x,0,'right')ans=1（5）clear-第5页共5页5symsxmnklimit((1+m/x)^(n*x+k),x,inf)ans=exp(m*n)（6）clearsymsymnklimit((1+m*y)^(n/y+k),y,0)ans=exp(m*n)