1 семестр / Математический Анализ / Кучеренко_06
.docx
>> syms x
>> fplot('(2*x-1)/(x-1)',[-20 20])
>> fplot('(2*x-1)/(x-1)',[-20 20],'b*')
>> hold on, grid on
>> xlabel('x'),ylabel('y')
>> line([-20 20],[0 0],'linewidth',1)
>> line([0 0],[30 -30],'linewidth',1)
>> title('y=(2x-1)/(x-1)')
>>
fplot('(2*x-1)/abs(x-1)',[-15 15])
>> fplot('(2*x-1)/abs(x-1)',[-15 15],'b*')
>> hold on, grid on
>> line([0 0],[60 -10],'linewidth',1,'color','black')
>> line([-15 15],[0 0],'linewidth',1,'color','black')
>> xlabel('x'),ylabel('y')
>> title('y=(2x-1)/|x-1|')
>>
fplot('abs((2*x-1)/(x-1))',[-15 15],'b*')
>> line([0 0],[60 0],'linewidth',1,'color','black')
>> line([-15 15],[0 0],'linewidth',1,'color','black')
>> xlabel('x'),ylabel('y')
>> hold on, grid on
>> title('y=|(2x-1)/(x-1)|')
>> fplot('abs(3*x-6)/(x-2)',([-15 15 -5 5]),'b*')
>> hold on, grid on
>> xlabel('x'),ylabel('y')
>> line([-15 15],[0 0],'linewidth',1,'color','black')
>> line([0 0],[-5 5],'linewidth',1,'color','black')
>> title('|3x-6|(x-2)')
>> title('|3x-6|/(x-2)')
>>
Упражнение 2
>> fplot('(1+x)^1/x',[-10 10])
>> fplot('(1+x)^1/x',[-10 10 -2 2])
>> fplot('(1+x)^1/x',[-10 10 -2 2],'b*')
>> fplot('(1+x)^1/x',[-10 10 -15 15],'b*')
>> grid on
>> xlabel('x'),ylabel('y')
>> line([-10 10],[0 0],'linewidth',1,'color','black')
>> line([0 0],[15 -15],'linewidth',1,'color','black')
>> line([-10 10],[1 1],'linewidth',1,'color','red')
>>
>> fplot('sin((x^2)/sqrt(1-x^3))/(x*log(1-x^3))',[-20 20 -20 20],'bo')
Warning: Imaginary parts of complex X and/or Y arguments ignored
> In fplot at 153
>> hold on,grid on
>> line([0 0],[20 -20],'linewidth',1,'color','red')
>> line([0 0],[20 -20],'linewidth',1,'color','black')
>> line([-20 20],[0 0],'linewidth',1,'color','red')
>> xlabel('x'),ylabel('y')
>>
>> fplot('log(x)*sin(x)',[-20 20 -20 20],'bo')
Warning: Imaginary parts of complex X and/or Y arguments ignored
> In fplot at 153
>> xlabel('x'),ylabel('y')
>> line([-20 20],[0 0],'linewidth',1,'color','black')
>> line([0 0],[20 -20],'linewidth',1,'color','black')
>> hold on,grid on
>>
>> hold on,grid on
>> n=1:100;
>> plot(n,(2.^n)./factorial(n),'b*')
>> line([0 100],[0 0],'color','r')
>> xlabel('n'),ylabel('y')
>> title('y=2^n/n!')
Упражнение 3.
Вычислите точные значения пределов из упражнения 2 а) - г). Соответствуют ли они полученным приближениям?
1)
>> syms x
limit((1+x)^(1/x),x,Inf)
ans =
1
2)
>> limit(sin(x^2/sqrt(1-x^3))/x*log(1-x^3),x,0)
ans =
0
3) >> limit(log(x)*sin(x),x,inf)
ans =
NaN
4)??
>> syms n
>> limit(2.^n/factorial(n),n,inf)
??? Error using ==> factorial at 17
N must be a matrix of non-negative integers.