Matlab-高等数学-极限与连续

% 函数表达式f(x)在x0处的极限
L=limit(f,x,x0);
L=limit(f,x,x0,'left');
L=limit(f,x,x0,'right');

function continuity(x0,fun_left,fun_x0,fun_right)
    fx0=subs(fun_x0,'x',x0);
    fx0_left=subs(fun_left,'x',x0,'left');
    fx0_right=subs(fun_right,'x',x0,'right');
    if isequal(fx0_left,fx0) && isequal(fx0_right,fx0)
        str='函数在该点连续';
    else
        str='函数在该点间断';
    end
    disp(str);
end

function breakpoint(x0,fun_left,fun_x0,fun_right)
    fx0=subs(fun_x0,'x',x0);
    fx0_left=subs(fun_left,'x',x0,'left');
    fx0_right=subs(fun_right,'x',x0,'right');
    if isinf(double(fx0_left)) || isinf(double(fx0_right)) || isnan(fx0_left) || isnan(fx0_right)
       str='第二类间断点';
    elseif ~isequal(fx0_left,fx0_right)
        str='跳跃间断点';
    elseif ~isequal(fx0,fx0_left,fx0_right) || isempty(x0)
        str='可去间断点';
    end
    disp(str);
end

fplot(@(x)atan(x),'LineWidth',1.5);

ax=gca;
ax.XAxisLocation='origin';
ax.YAxisLocation='origin';
ax.Box='off';

title('$y=arctan(x)$','Interpreter','latex','FontSize',20)

xlim([-pi,pi]);
ylim([-pi,pi]);
yticks([-pi/2,0,pi/2]);
yticklabels({'-\pi/2','0','\pi/2'});