38 lines
662 B
Plaintext
38 lines
662 B
Plaintext
|
|
Na początku określamy zmienną jako x:
|
|
x=var('x')
|
|
1.
|
|
a)
|
|
solve(x^6-9*x^5+10*x^4+18*x^3+49*x^2+135*x+84==0,x)
|
|
b)
|
|
show(solve(x^3-5*x^2+8*x-40 == 0,x))
|
|
c)
|
|
show(find_root(cos(x)==x,0,pi))
|
|
|
|
2.
|
|
a)
|
|
integral(x*sin(x),x)
|
|
b)
|
|
integral(e^(1/x^2),x,-2,4)
|
|
c)
|
|
show(diff((sqrt(x^2*sin(x)+2)),x))
|
|
d)
|
|
show(diff((x*e^(cos(x)))^3,x))
|
|
e)
|
|
x,y=var('x,y')
|
|
f=x^2+sin(x*y)-y
|
|
f.diff(y)
|
|
|
|
3.
|
|
x=var('x')
|
|
u=var('u')
|
|
u=function('u')(x)
|
|
RR=(diff(u,x,2)-x*diff(u,x)+u)==0
|
|
show(desolve(RR, u, contrib_ode=True,show_method=True))
|
|
|
|
4.
|
|
A=matrix([[1, -4, 7],[14,6,8],[-4,-1,2]])
|
|
B=matrix([[2,3,9],[-1,17,6],[0,5,-7]])
|
|
show(A*B)
|
|
show(A.determinant())
|
|
show(B^(-1)) |